From 8733df4608875cb5b16bf753b5a4806f6caa824f Mon Sep 17 00:00:00 2001 From: Joshua Lampert Date: Tue, 10 Sep 2024 20:44:58 +0200 Subject: [PATCH 01/36] add BBMEquation1D --- NEWS.md | 5 + README.md | 1 + examples/bbm_1d/bbm_1d_basic.jl | 40 ++++ examples/bbm_1d/bbm_1d_fourier.jl | 42 ++++ examples/bbm_1d/bbm_1d_manufactured.jl | 40 ++++ examples/bbm_1d/bbm_1d_relaxation.jl | 43 ++++ src/DispersiveShallowWater.jl | 5 +- src/callbacks_step/analysis.jl | 1 + src/equations/bbm_1d.jl | 195 ++++++++++++++++++ src/equations/bbm_bbm_1d.jl | 8 +- src/equations/equations.jl | 60 ++++-- .../hyperbolic_serre_green_naghdi_1d.jl | 4 +- src/equations/serre_green_naghdi_1d.jl | 2 +- src/equations/svaerd_kalisch_1d.jl | 2 +- src/semidiscretization.jl | 4 +- test/runtests.jl | 1 + test/test_bbm_1d.jl | 125 +++++++++++ test/test_unit.jl | 29 +++ test/test_util.jl | 18 +- 19 files changed, 590 insertions(+), 35 deletions(-) create mode 100644 examples/bbm_1d/bbm_1d_basic.jl create mode 100644 examples/bbm_1d/bbm_1d_fourier.jl create mode 100644 examples/bbm_1d/bbm_1d_manufactured.jl create mode 100644 examples/bbm_1d/bbm_1d_relaxation.jl create mode 100644 src/equations/bbm_1d.jl create mode 100644 test/test_bbm_1d.jl diff --git a/NEWS.md b/NEWS.md index b816ac38..6a09fae1 100644 --- a/NEWS.md +++ b/NEWS.md @@ -6,6 +6,11 @@ used in the Julia ecosystem. Notable changes will be documented in this file for human readability. +## Changes in the v0.4 lifecycle + +#### Added +- Add `BBMEquation1D` ([#150]). + ## Changes when updating to v0.5 from v0.4.x #### Changed diff --git a/README.md b/README.md index c0327188..ec66a4b7 100644 --- a/README.md +++ b/README.md @@ -12,6 +12,7 @@ **DispersiveShallowWater.jl** is a [Julia](https://julialang.org/) package that implements structure-preserving numerical methods for dispersive shallow water models. To date, it provides provably conservative, entropy-conserving and well-balanced numerical schemes for some dispersive shallow water models: +* the [BBM equation](https://doi.org/10.4208/cicp.OA-2020-0119) * the [BBM-BBM equations with varying bottom topography](https://iopscience.iop.org/article/10.1088/1361-6544/ac3c29), * the [dispersive shallow water model proposed by Magnus Svärd and Henrik Kalisch](https://arxiv.org/abs/2302.09924), * the [Serre-Green-Naghdi equations](https://arxiv.org/abs/2408.02665). diff --git a/examples/bbm_1d/bbm_1d_basic.jl b/examples/bbm_1d/bbm_1d_basic.jl new file mode 100644 index 00000000..c60c2a5a --- /dev/null +++ b/examples/bbm_1d/bbm_1d_basic.jl @@ -0,0 +1,40 @@ +using OrdinaryDiffEq +using DispersiveShallowWater + +############################################################################### +# Semidiscretization of the BBM equation + +equations = BBMEquation1D() + +initial_condition = initial_condition_convergence_test +boundary_conditions = boundary_condition_periodic + +# create homogeneous mesh +coordinates_min = -90.0 +coordinates_max = 90.0 +N = 512 +mesh = Mesh1D(coordinates_min, coordinates_max, N) + +# create solver with periodic SBP operators of accuracy order 4 +accuracy_order = 4 +solver = Solver(mesh, accuracy_order) + +# semidiscretization holds all the necessary data structures for the spatial discretization +semi = Semidiscretization(mesh, equations, initial_condition, solver, + boundary_conditions = boundary_conditions) + +############################################################################### +# Create `ODEProblem` and run the simulation +tspan = (0.0, 1000.0) +ode = semidiscretize(semi, tspan) +summary_callback = SummaryCallback() +analysis_callback = AnalysisCallback(semi; interval = 10, + extra_analysis_errors = (:conservation_error,), + extra_analysis_integrals = (waterheight_total, + entropy_modified, + invariant_cubic)) +callbacks = CallbackSet(analysis_callback, summary_callback) + +saveat = range(tspan..., length = 100) +sol = solve(ode, Tsit5(), abstol = 1e-7, reltol = 1e-7, + save_everystep = false, callback = callbacks, saveat = saveat) diff --git a/examples/bbm_1d/bbm_1d_fourier.jl b/examples/bbm_1d/bbm_1d_fourier.jl new file mode 100644 index 00000000..d54c9dee --- /dev/null +++ b/examples/bbm_1d/bbm_1d_fourier.jl @@ -0,0 +1,42 @@ +using OrdinaryDiffEq +using DispersiveShallowWater +using SummationByPartsOperators: fourier_derivative_operator + +############################################################################### +# Semidiscretization of the BBM equation + +equations = BBMEquation1D() + +initial_condition = initial_condition_convergence_test +boundary_conditions = boundary_condition_periodic + +# create homogeneous mesh +coordinates_min = -90.0 +coordinates_max = 90.0 +N = 512 +mesh = Mesh1D(coordinates_min, coordinates_max, N) + +# create solver with Fourier SBP operators +D1 = fourier_derivative_operator(xmin(mesh), xmax(mesh), nnodes(mesh)) +D2 = D1^2 +solver = Solver(D1, D2) + +# semidiscretization holds all the necessary data structures for the spatial discretization +semi = Semidiscretization(mesh, equations, initial_condition, solver, + boundary_conditions = boundary_conditions) + +############################################################################### +# Create `ODEProblem` and run the simulation +tspan = (0.0, 1000.0) +ode = semidiscretize(semi, tspan) +summary_callback = SummaryCallback() +analysis_callback = AnalysisCallback(semi; interval = 10, + extra_analysis_errors = (:conservation_error,), + extra_analysis_integrals = (waterheight_total, + entropy_modified, + invariant_cubic)) +callbacks = CallbackSet(analysis_callback, summary_callback) + +saveat = range(tspan..., length = 100) +sol = solve(ode, Tsit5(), abstol = 1e-7, reltol = 1e-7, + save_everystep = false, callback = callbacks, saveat = saveat) diff --git a/examples/bbm_1d/bbm_1d_manufactured.jl b/examples/bbm_1d/bbm_1d_manufactured.jl new file mode 100644 index 00000000..285359ab --- /dev/null +++ b/examples/bbm_1d/bbm_1d_manufactured.jl @@ -0,0 +1,40 @@ +using OrdinaryDiffEq +using DispersiveShallowWater + +############################################################################### +# Semidiscretization of the BBM equation + +equations = BBMEquation1D() + +initial_condition = initial_condition_manufactured +source_terms = source_terms_manufactured +boundary_conditions = boundary_condition_periodic + +# create homogeneous mesh +coordinates_min = -1.0 +coordinates_max = 1.0 +N = 512 +mesh = Mesh1D(coordinates_min, coordinates_max, N) + +# create solver with periodic SBP operators of accuracy order 4 +accuracy_order = 4 +solver = Solver(mesh, accuracy_order) + +# semidiscretization holds all the necessary data structures for the spatial discretization +semi = Semidiscretization(mesh, equations, initial_condition, solver, + boundary_conditions = boundary_conditions, + source_terms = source_terms) + +############################################################################### +# Create `ODEProblem` and run the simulation +tspan = (0.0, 1.0) +ode = semidiscretize(semi, tspan) +summary_callback = SummaryCallback() +analysis_callback = AnalysisCallback(semi; interval = 10, + extra_analysis_errors = (:conservation_error,), + extra_analysis_integrals = (waterheight_total,)) +callbacks = CallbackSet(analysis_callback, summary_callback) + +saveat = range(tspan..., length = 100) +sol = solve(ode, Tsit5(), abstol = 1e-7, reltol = 1e-7, + save_everystep = false, callback = callbacks, saveat = saveat) diff --git a/examples/bbm_1d/bbm_1d_relaxation.jl b/examples/bbm_1d/bbm_1d_relaxation.jl new file mode 100644 index 00000000..a78d2a80 --- /dev/null +++ b/examples/bbm_1d/bbm_1d_relaxation.jl @@ -0,0 +1,43 @@ +using OrdinaryDiffEq +using DispersiveShallowWater + +############################################################################### +# Semidiscretization of the BBM equation + +equations = BBMEquation1D() + +initial_condition = initial_condition_convergence_test +boundary_conditions = boundary_condition_periodic + +# create homogeneous mesh +coordinates_min = -90.0 +coordinates_max = 90.0 +N = 512 +mesh = Mesh1D(coordinates_min, coordinates_max, N) + +# create solver with periodic SBP operators of accuracy order 4 +accuracy_order = 4 +solver = Solver(mesh, accuracy_order) + +# semidiscretization holds all the necessary data structures for the spatial discretization +semi = Semidiscretization(mesh, equations, initial_condition, solver, + boundary_conditions = boundary_conditions) + +############################################################################### +# Create `ODEProblem` and run the simulation +tspan = (0.0, 1000.0) +ode = semidiscretize(semi, tspan) +summary_callback = SummaryCallback() +analysis_callback = AnalysisCallback(semi; interval = 10, + extra_analysis_errors = (:conservation_error,), + extra_analysis_integrals = (waterheight_total, + entropy_modified, + invariant_cubic)) + +relaxation_callback = RelaxationCallback(invariant = entropy_modified) +# Always put relaxation_callback before analysis_callback to guarantee conservation of the invariant +callbacks = CallbackSet(relaxation_callback, analysis_callback, summary_callback) + +saveat = range(tspan..., length = 100) +sol = solve(ode, Tsit5(), abstol = 1e-7, reltol = 1e-7, + save_everystep = false, callback = callbacks, saveat = saveat) diff --git a/src/DispersiveShallowWater.jl b/src/DispersiveShallowWater.jl index 3e2ef6a4..6c8d0ba8 100644 --- a/src/DispersiveShallowWater.jl +++ b/src/DispersiveShallowWater.jl @@ -61,7 +61,7 @@ include("util.jl") export examples_dir, get_examples, default_example, convergence_test export AbstractShallowWaterEquations, - BBMBBMEquations1D, + BBMEquation1D, BBMBBMEquations1D, SvärdKalischEquations1D, SvaerdKalischEquations1D, SerreGreenNaghdiEquations1D, HyperbolicSerreGreenNaghdiEquations1D @@ -71,7 +71,8 @@ export prim2prim, prim2cons, cons2prim, prim2phys, gravity_constant, bathymetry, still_water_surface, energy_total, entropy, lake_at_rest_error, - energy_total_modified, entropy_modified + energy_total_modified, entropy_modified, + invariant_cubic export Mesh1D, xmin, xmax, nnodes diff --git a/src/callbacks_step/analysis.jl b/src/callbacks_step/analysis.jl index c0eee27a..e2ed0725 100644 --- a/src/callbacks_step/analysis.jl +++ b/src/callbacks_step/analysis.jl @@ -339,3 +339,4 @@ pretty_form_utf(::typeof(energy_total)) = "∫e_total" pretty_form_utf(::typeof(entropy_modified)) = "∫U_modified" pretty_form_utf(::typeof(energy_total_modified)) = "∫e_modified" pretty_form_utf(::typeof(lake_at_rest_error)) = "∫|η-η₀|" +pretty_form_utf(::typeof(invariant_cubic)) = "∫(η + 1)³" diff --git a/src/equations/bbm_1d.jl b/src/equations/bbm_1d.jl new file mode 100644 index 00000000..ba4e3dc5 --- /dev/null +++ b/src/equations/bbm_1d.jl @@ -0,0 +1,195 @@ +# TODO: Use this nondimensionalized version or use dimensional version including gravity and depth? +@doc raw""" + BBMEquation1D(; bathymetry_type = bathymetry_flat, eta0 = 0.0) + +BBM (Benjamin–Bona–Mahony) equation in one spatial dimension. The equations are given by +```math +\begin{aligned} + \eta_t + \eta\eta_x + \eta_x - \eta_{xxt} &= 0. +\end{aligned} +``` + +The unknown quantity of the BBM equation is the total water height ``\eta``. The water height +is given by ``h = \eta - \eta_0``, where ``\eta_0`` is the constant still-water surface. + +Currently, the equations only support a flat bathymetry ``b = 0``, see [`bathymetry_flat`](@ref). + +The BBM equation is first described in Benjamin, Bona, and Mahony (1972). +The semidiscretization implemented here is developed in Ranocha, Mitsotakis, and Ketcheson (2020). +It conserves +- the total water mass (integral of ``h``) as a linear invariant +- the total modified energy + +- Thomas B. Benjamin, Jerry L. Bona and John J. Mahony (1972) + Model equations for long waves in nonlinear dispersive systems + [DOI: 10.1098/rsta.1972.0032](https://doi.org/10.1098/rsta.1972.0032) +- Hendrik Ranocha, Dimitrios Mitsotakis and David I. Ketcheson (2020) + A Broad Class of Conservative Numerical Methods for Dispersive Wave Equations + [DOI: 10.4208/cicp.OA-2020-0119](https://doi.org/10.4208/cicp.OA-2020-0119) +""" +struct BBMEquation1D{Bathymetry <: AbstractBathymetry, RealT <: Real} <: AbstractBBMEquation{1, 1} + bathymetry_type::Bathymetry # type of bathymetry + eta0::RealT # constant still-water surface +end + +function BBMEquation1D(; bathymetry_type = bathymetry_flat, eta0 = 0.0) + BBMEquation1D(bathymetry_type, eta0) +end + +""" + initial_condition_convergence_test(x, t, equations::BBMEquation1D, mesh) + +A travelling-wave solution used for convergence tests in a periodic domain. + +See section 4.1.3 in (there is an error in paper: it should be sech^2 instead of cosh): +- Hendrik Ranocha, Dimitrios Mitsotakis and David I. Ketcheson (2020) + A Broad Class of Conservative Numerical Methods for Dispersive Wave Equations + [DOI: 10.4208/cicp.OA-2020-0119](https://doi.org/10.4208/cicp.OA-2020-0119) +""" +function initial_condition_convergence_test(x, t, equations::BBMEquation1D, mesh) + c = 1.2 + A = 3 * (c - 1) + K = 0.5 * sqrt(1 - 1/c) + x_t = mod(x - c * t - xmin(mesh), xmax(mesh) - xmin(mesh)) + xmin(mesh) + eta = A * sech(K * x_t)^2 + return SVector(eta) +end + +""" + initial_condition_manufactured(x, t, equations::BBMEquation1D, mesh) + +A smooth manufactured solution in combination with [`source_terms_manufactured`](@ref). +""" +function initial_condition_manufactured(x, t, + equations::BBMEquation1D, + mesh) + eta = exp(t / 2) * sinpi(2 * (x - t / 2)) + return SVector(eta) +end + +""" + source_terms_manufactured(q, x, t, equations::BBMEquation1D, mesh) + +A smooth manufactured solution in combination with [`initial_condition_manufactured`](@ref). +""" +function source_terms_manufactured(q, x, t, equations::BBMEquation1D) + a3 = cospi(t - 2 * x) + a4 = sinpi(t - 2 * x) + a5 = sinpi(2 * t - 4 * x) + a14 = exp(t / 2) + dq1 = -2*pi^2*(a4 + 2*pi*a3)*a14 - a14*a4/2 + pi*a14*a3 - pi*exp(t)*a5 + + return SVector(dq1) +end + +function create_cache(mesh, equations::BBMEquation1D, + solver, initial_condition, + ::BoundaryConditionPeriodic, + RealT, uEltype) + invImD2 = lu(I - sparse(solver.D2)) + eta2 = zeros(RealT, nnodes(mesh)) + eta2_x = zero(eta2) + eta_x = zero(eta2) + etaeta_x = zero(eta2) + eta_xx = zero(eta2) + cache = (; invImD2, eta2, eta2_x, eta_x, etaeta_x, eta_xx, solver.D1, solver.D2) + if solver.D1 isa PeriodicUpwindOperators + eta_x_upwind = zero(eta2) + cache = (; cache..., eta_x_upwind) + end + return cache +end + +# Discretization that conserves the mass for eta and the modified energy for periodic boundary conditions, see +# - Hendrik Ranocha, Dimitrios Mitsotakis and David I. Ketcheson (2020) +# A Broad Class of Conservative Numerical Methods for Dispersive Wave Equations +# [DOI: 10.4208/cicp.OA-2020-0119](https://doi.org/10.4208/cicp.OA-2020-0119) +function rhs!(dq, q, t, mesh, equations::BBMEquation1D, initial_condition, + ::BoundaryConditionPeriodic, source_terms, solver, cache) + (; invImD2, eta2, eta2_x, eta_x, etaeta_x) = cache + if solver.D1 isa PeriodicUpwindOperators + (; eta_x_upwind) = cache + end + + eta, = q.x + deta, = dq.x + # energy and mass conservative semidiscretization + @trixi_timeit timer() "hyperbolic" begin + @.. eta2 = eta^2 + if solver.D1 isa PeriodicDerivativeOperator || + solver.D1 isa UniformPeriodicCoupledOperator || + solver.D1 isa FourierDerivativeOperator + mul!(eta2_x, solver.D1, eta2) + mul!(eta_x, solver.D1, eta) + @.. etaeta_x = eta * eta_x + # split form + @.. deta = -(1 / 3 * (eta2_x + etaeta_x) + eta_x) + elseif solver.D1 isa PeriodicUpwindOperators + mul!(eta2_x, solver.D1.central, eta2) + mul!(eta_x_upwind, solver.D1.minus, eta) + mul!(eta_x, solver.D1.central, eta) + @.. etaeta_x = eta * eta_x + # split form + @.. deta = -(1 / 3 * (eta2_x + etaeta_x) + eta_x_upwind) + else + @error "unknown type of first-derivative operator: $(typeof(solver.D1))" + end + + end + + @trixi_timeit timer() "source terms" calc_sources!(dq, q, t, source_terms, equations, + solver) + + @trixi_timeit timer() "elliptic" begin + solve_system_matrix!(deta, invImD2, equations) + end + return nothing +end + +""" + energy_total_modified!(e, q, equations::BBMEquation1D, cache) + +Return the modified total energy `e` of the primitive variables `q_global` for the +[`BBMEquation1D`](@ref). The `energy_total_modified` +is a conserved quantity (for periodic boundary conditions). + +It is given by +```math +\\frac{1}{2} \\eta^2 + \\frac{1}{2} \\eta_{xx}. +``` + +`q_global` is a vector of the primitive variables at ALL nodes. +`cache` needs to hold the SBP operators used by the `solver`. + +See also [`energy_total_modified`](@ref). +""" +function energy_total_modified!(e, q_global, equations::BBMEquation1D, cache) + eta, = q_global.x + + (; D1, D2, eta_xx, tmp1) = cache + if D1 isa PeriodicUpwindOperators + mul!(tmp1, D1.minus, eta) + mul!(eta_xx, D1.plus, tmp1) + else + mul!(eta_xx, D2, eta) + end + + @.. e = 0.5 * (eta^2 + eta_xx) + return nothing +end + +""" + invariant_cubic(q, equations::BBMEquation1D) + +Return the cubic invariant of the primitive variables `q` for the +[`BBMEquation1D`](@ref). The cubic invariant is given by +```math +(\\eta + 1)^3. +``` +""" +function invariant_cubic(q, equations::BBMEquation1D) + eta = waterheight_total(q, equations) + return (eta + 1)^3 +end + +varnames(::typeof(invariant_cubic), equations) = ("(η + 1)³",) diff --git a/src/equations/bbm_bbm_1d.jl b/src/equations/bbm_bbm_1d.jl index 6465e1f2..b23db9d2 100644 --- a/src/equations/bbm_bbm_1d.jl +++ b/src/equations/bbm_bbm_1d.jl @@ -13,7 +13,7 @@ The unknown quantities of the BBM-BBM equations are the total water height ``\et The gravitational constant is denoted by `g` and the constant bottom topography (bathymetry) ``b = \eta_0 - D``. The water height above the bathymetry is therefore given by ``h = \eta - \eta_0 + D``. The BBM-BBM equations are only implemented for ``\eta_0 = 0``. -Two types of variable `bathymetry_type` are supported: +Two types of `bathymetry_type` are supported: - [`bathymetry_flat`](@ref): flat bathymetry (typically ``b = 0`` everywhere) - [`bathymetry_variable`](@ref): general variable bathymetry @@ -29,7 +29,7 @@ One reference for the BBM-BBM system can be found in Bona et al. (1998). The semidiscretization implemented here was developed for flat bathymetry in Ranocha et al. (2020) and generalized for a variable bathymetry in Lampert and Ranocha (2024). It conserves -- the total water (integral of ``h``) as a linear invariant +- the total water mass (integral of ``h``) as a linear invariant - the total velocity (integral of ``v``) as a linear invariant for flat bathymetry - the total energy @@ -398,10 +398,6 @@ function create_cache(mesh, equations::BBMBBMEquations1D, return (; invImD2d, invImD2n, etav, Dv, v2, tmp2) end -function solve_system_matrix!(dv, system_matrix, ::BBMBBMEquations1D) - ldiv!(system_matrix, dv) -end - # Discretization that conserves # - the total water (integral of ``h``) as a linear invariant # - the total momentum (integral of ``v``) as a linear invariant for flat bathymetry diff --git a/src/equations/equations.jl b/src/equations/equations.jl index 7d51fe1b..20772bf6 100644 --- a/src/equations/equations.jl +++ b/src/equations/equations.jl @@ -81,6 +81,7 @@ it is also as useful. @inline prim2prim(q, ::AbstractEquations) = q varnames(::typeof(prim2prim), ::AbstractShallowWaterEquations) = ("η", "v", "D") +varnames(::typeof(prim2prim), ::AbstractEquations{1, 1}) = ("η",) """ prim2cons(q, equations) @@ -100,7 +101,13 @@ The inverse conversion is performed by [`cons2prim`](@ref). return SVector(h, hv, b) end -varnames(::typeof(prim2cons), ::AbstractShallowWaterEquations) = ("h", "hv", "hv") +function prim2cons(q, ::AbstractEquations{1, 1}) + h = waterheight(q, equations) + return SVector(h) +end + +varnames(::typeof(prim2cons), ::AbstractShallowWaterEquations) = ("h", "hv", "b") +varnames(::typeof(prim2cons), ::AbstractEquations{1, 1}) = ("h",) """ cons2prim(u, equations) @@ -121,6 +128,13 @@ The inverse conversion is performed by [`prim2cons`](@ref). return SVector(eta, v, D) end +function cons2prim(u, ::AbstractEquations{1, 1}) + h, = u + b = 0.0 + eta = h + b + return SVector(eta) +end + """ waterheight_total(q, equations) @@ -131,14 +145,14 @@ Return the total waterheight of the primitive variables `q` for a given set of `q` is a vector of the primitive variables at a single node, i.e., a vector of the correct length `nvariables(equations)`. """ -@inline function waterheight_total(q, ::AbstractShallowWaterEquations) +@inline function waterheight_total(q, ::AbstractEquations) return q[1] end varnames(::typeof(waterheight_total), equations) = ("η",) """ - waterheight(q, equations::AbstractShallowWaterEquations) + waterheight(q, equations) Return the waterheight of the primitive variables `q` for a given set of `equations`, i.e., the waterheight ``h`` above the bathymetry ``b``. @@ -148,7 +162,7 @@ of the correct length `nvariables(equations)`. See also [`waterheight_total`](@ref), [`bathymetry`](@ref). """ -@inline function waterheight(q, equations::AbstractShallowWaterEquations) +@inline function waterheight(q, equations::AbstractEquations) return waterheight_total(q, equations) - bathymetry(q, equations) end @@ -194,12 +208,12 @@ See [`momentum`](@ref). varnames(::typeof(discharge), equations) = ("P",) """ - still_water_surface(q, equations::AbstractShallowWaterEquations) + still_water_surface(q, equations) Return the still water surface ``\\eta_0`` (lake at rest) for a given set of `equations`. """ -@inline function still_water_surface(q, equations::AbstractShallowWaterEquations) +@inline function still_water_surface(q, equations::AbstractEquations) return equations.eta0 end @@ -207,6 +221,8 @@ end return q[3] end +still_waterdepth(q, equations::AbstractEquations{1, 1}) = still_water_surface(q, equations) + """ bathymetry(q, equations) @@ -216,28 +232,28 @@ Return the bathymetry of the primitive variables `q` for a given set of `q` is a vector of the primitive variables at a single node, i.e., a vector of the correct length `nvariables(equations)`. """ -@inline function bathymetry(q, equations::AbstractShallowWaterEquations) - D = q[3] +@inline function bathymetry(q, equations::AbstractEquations) + D = still_waterdepth(q, equations) eta0 = still_water_surface(q, equations) return eta0 - D end """ - lake_at_rest_error(q, equations::AbstractShallowWaterEquations) + lake_at_rest_error(q, equations) Calculate the error for the "lake-at-rest" test case where the [`waterheight_total`](@ref) ``\\eta = h + b`` should be a constant value over time (given by the value ``\\eta_0`` passed to the `equations` when constructing them). """ -@inline function lake_at_rest_error(q, equations::AbstractShallowWaterEquations) +@inline function lake_at_rest_error(q, equations::AbstractEquations) eta = waterheight_total(q, equations) eta0 = still_water_surface(q, equations) return abs(eta0 - eta) end """ - gravity_constant(equations::AbstractShallowWaterEquations) + gravity_constant(equations) Return the gravity constant ``g`` for a given set of `equations`. See also [`AbstractShallowWaterEquations`](@ref). @@ -290,7 +306,7 @@ varnames(::typeof(entropy), equations) = ("U",) # The modified entropy/total energy takes the whole `q_global` for every point in space """ - energy_total_modified(q_global, equations::AbstractShallowWaterEquations, cache) + energy_total_modified(q_global, equations, cache) Return the modified total energy of the primitive variables `q_global` for the `equations`. This modified total energy is a conserved quantity and can @@ -307,17 +323,17 @@ terms are present. Internally, this function allocates a vector for the output and calls [`DispersiveShallowWater.energy_total_modified!`](@ref). """ -function energy_total_modified(q_global, equations::AbstractShallowWaterEquations, cache) +function energy_total_modified(q_global, equations::AbstractEquations, cache) e = similar(q_global.x[begin]) return energy_total_modified!(e, q_global, equations, cache) end """ - energy_total_modified!(e, q_global, equations::AbstractShallowWaterEquations, cache) + energy_total_modified!(e, q_global, equations, cache) In-place version of [`energy_total_modified`](@ref). """ -function energy_total_modified!(e, q_global, equations::AbstractShallowWaterEquations, +function energy_total_modified!(e, q_global, equations::AbstractEquations, cache) # `q_global` is an `ArrayPartition` of the primitive variables at all nodes @assert nvariables(equations) == length(q_global.x) @@ -332,7 +348,7 @@ end varnames(::typeof(energy_total_modified), equations) = ("e_modified",) """ - entropy_modified(q_global, equations::AbstractShallowWaterEquations, cache) + entropy_modified(q_global, equations, cache) Alias for [`energy_total_modified`](@ref). """ @@ -342,7 +358,7 @@ Alias for [`energy_total_modified`](@ref). end """ - entropy_modified!(e, q_global, equations::AbstractShallowWaterEquations, cache) + entropy_modified!(e, q_global, equations, cache) In-place version of [`entropy_modified`](@ref). """ @@ -488,6 +504,11 @@ See also [`bathymetry_flat`](@ref) and [`bathymetry_mild_slope`](@ref). """ const bathymetry_variable = BathymetryVariable() +# BBM equation +abstract type AbstractBBMEquation{NDIMS, NVARS} <: + AbstractEquations{NDIMS, NVARS} end +include("bbm_1d.jl") + # BBM-BBM equations abstract type AbstractBBMBBMEquations{NDIMS, NVARS} <: AbstractShallowWaterEquations{NDIMS, NVARS} end @@ -501,7 +522,6 @@ include("svaerd_kalisch_1d.jl") # Serre-Green-Naghdi equations abstract type AbstractSerreGreenNaghdiEquations{NDIMS, NVARS} <: AbstractShallowWaterEquations{NDIMS, NVARS} end -const AbstractSerreGreenNaghdiEquations1D = AbstractSerreGreenNaghdiEquations{1} include("serre_green_naghdi_1d.jl") include("hyperbolic_serre_green_naghdi_1d.jl") @@ -529,6 +549,10 @@ function solve_system_matrix!(dv, system_matrix, rhs, return nothing end +function solve_system_matrix!(dv, system_matrix, ::Union{BBMEquation1D, BBMBBMEquations1D}) + ldiv!(system_matrix, dv) +end + """ initial_condition_dingemans(x, t, equations::AbstractShallowWaterEquations, mesh) diff --git a/src/equations/hyperbolic_serre_green_naghdi_1d.jl b/src/equations/hyperbolic_serre_green_naghdi_1d.jl index d550f154..1dbd9eb6 100644 --- a/src/equations/hyperbolic_serre_green_naghdi_1d.jl +++ b/src/equations/hyperbolic_serre_green_naghdi_1d.jl @@ -46,7 +46,7 @@ to the original [`SerreGreenNaghdiEquations1D`](@ref). However, the wave speeds of the hyperbolic system increase with increasing ``\lambda``, so that explicit time integration methods become more expensive. -Two types of variable `bathymetry_type` are supported: +Two types of `bathymetry_type` are supported: - [`bathymetry_flat`](@ref): flat bathymetry (typically ``b = 0`` everywhere) - [`bathymetry_mild_slope`](@ref): variable bathymetry with mild-slope approximation @@ -146,7 +146,7 @@ function set_approximation_variables!(q, mesh, return nothing end -# TODO: There is name clash. For the SerreGreenNaghdiEquations1D, +# TODO: There is a name clash. For the SerreGreenNaghdiEquations1D, # the corresponding function is called initial_condition_convergence_test # However, we cannot use that name since it's not an analytical solution. # How shall we handle this? diff --git a/src/equations/serre_green_naghdi_1d.jl b/src/equations/serre_green_naghdi_1d.jl index 97a7b879..7c4d1984 100644 --- a/src/equations/serre_green_naghdi_1d.jl +++ b/src/equations/serre_green_naghdi_1d.jl @@ -18,7 +18,7 @@ The gravitational constant is denoted by `g` and the bottom topography is therefore given by ``h = \eta - \eta_0 + D``. The total water height is therefore given by ``\eta = h + b``. -Three types of variable `bathymetry_type` are supported: +Three types of `bathymetry_type` are supported: - [`bathymetry_flat`](@ref): flat bathymetry (typically ``b = 0`` everywhere) - [`bathymetry_mild_slope`](@ref): variable bathymetry with mild-slope approximation - [`bathymetry_variable`](@ref): general variable bathymetry diff --git a/src/equations/svaerd_kalisch_1d.jl b/src/equations/svaerd_kalisch_1d.jl index 30df899f..07a95d98 100644 --- a/src/equations/svaerd_kalisch_1d.jl +++ b/src/equations/svaerd_kalisch_1d.jl @@ -32,7 +32,7 @@ Currently, the equations only support a general variable bathymetry, see [`bathy The equations by Svärd and Kalisch are presented and analyzed in Svärd and Kalisch (2023). The semidiscretization implemented here conserves -- the total water (integral of ``h``) as a linear invariant +- the total water mass (integral of ``h``) as a linear invariant - the total momentum (integral of ``h v``) as a nonlinear invariant for flat bathymetry - the total modified energy diff --git a/src/semidiscretization.jl b/src/semidiscretization.jl index b26247fd..a450f3b3 100644 --- a/src/semidiscretization.jl +++ b/src/semidiscretization.jl @@ -196,7 +196,9 @@ function compute_coefficients!(q, func, t, semi::Semidiscretization) solver) end -function check_bathymetry(equations, q0) +check_bathymetry(equations, q0) = nothing + +function check_bathymetry(equations::AbstractShallowWaterEquations, q0) if equations.bathymetry_type isa BathymetryFlat _, _, D = q0.x value = first(D) diff --git a/test/runtests.jl b/test/runtests.jl index 84983eb5..1526bd47 100644 --- a/test/runtests.jl +++ b/test/runtests.jl @@ -4,6 +4,7 @@ using Test include("test_aqua.jl") include("test_unit.jl") include("test_visualization.jl") + include("test_bbm_1d.jl") include("test_bbm_bbm_1d.jl") include("test_svaerd_kalisch_1d.jl") include("test_serre_green_naghdi_1d.jl") diff --git a/test/test_bbm_1d.jl b/test/test_bbm_1d.jl new file mode 100644 index 00000000..1908251a --- /dev/null +++ b/test/test_bbm_1d.jl @@ -0,0 +1,125 @@ +module TestBBMBBM1D + +using Test +using DispersiveShallowWater + +include("test_util.jl") + +EXAMPLES_DIR = joinpath(examples_dir(), "bbm_1d") + +@testset "BBM1D" begin + @trixi_testset "bbm_1d_basic" begin + @test_trixi_include(joinpath(EXAMPLES_DIR, "bbm_1d_basic.jl"), + tspan=(0.0, 100.0), + l2=[0.0002514795321988484], + linf=[9.756568022900591e-5], + cons_error=[7.105427357601002e-15], + change_waterheight=-7.105427357601002e-15, + change_entropy_modified=6.355536918301041e-6, + change_invariant_cubic=-3.198066679033218e-6) + + @test_allocations(semi, sol, allocs=5_000) + + # test upwind operators + using SummationByPartsOperators: upwind_operators, periodic_derivative_operator + using SparseArrays: sparse + using OrdinaryDiffEq: solve + D1 = upwind_operators(periodic_derivative_operator; derivative_order = 1, + accuracy_order = accuracy_order, xmin = mesh.xmin, + xmax = mesh.xmax, + N = mesh.N) + D2 = sparse(D1.minus) * sparse(D1.plus) + solver = Solver(D1, D2) + semi = Semidiscretization(mesh, equations, initial_condition, solver, + boundary_conditions = boundary_conditions) + ode = semidiscretize(semi, (0.0, 100.0)) + sol = solve(ode, Tsit5(), abstol = 1e-7, reltol = 1e-7, + save_everystep = false, callback = callbacks, saveat = saveat) + atol = 1e-12 + rtol = 1e-12 + errs = errors(analysis_callback) + l2 = [0.00018397011159873] + l2_measured = errs.l2_error[:, end] + for (l2_expected, l2_actual) in zip(l2, l2_measured) + @test isapprox(l2_expected, l2_actual, atol = atol, rtol = rtol) + end + linf = [7.190886191621448e-5] + linf_measured = errs.linf_error[:, end] + for (linf_expected, linf_actual) in zip(linf, linf_measured) + @test isapprox(linf_expected, linf_actual, atol = atol, rtol = rtol) + end + + @test_allocations(semi, sol, allocs=5_000) + end + + @trixi_testset "bbm_1d_relaxation" begin + @test_trixi_include(joinpath(EXAMPLES_DIR, "bbm_1d_relaxation.jl"), + tspan=(0.0, 100.0), + l2=[0.00026259713456399205], + linf=[0.00010095858421543813], + cons_error=[6.217248937900877e-15], + change_waterheight=6.217248937900877e-15, + change_entropy_modified=1.5543122344752192e-15, + change_invariant_cubic=-5.139088546002313e-5) + + @test_allocations(semi, sol, allocs=5_000) + end + + @trixi_testset "bbm_1d_fourier" begin + @test_trixi_include(joinpath(EXAMPLES_DIR, "bbm_1d_fourier.jl"), + tspan=(0.0, 100.0), + l2=[6.01265210291245e-7], + linf=[2.3226949846799627e-7], + cons_error=[1.1546319456101628e-14], + change_waterheight=-1.1546319456101628e-14, + change_entropy_modified=-4.4573640600731324e-7, + change_invariant_cubic=-3.1871549026618595e-6) + + @test_allocations(semi, sol, allocs=5_000) + end + + @trixi_testset "bbm_1d_manufactured" begin + @test_trixi_include(joinpath(EXAMPLES_DIR, "bbm_1d_manufactured.jl"), + tspan=(0.0, 1.0), + l2=[7.887878295265557e-9], + linf=[9.041914550422803e-9], + cons_error=[5.148179246187295e-13], + change_waterheight=5.148179246187295e-13) + + @test_allocations(semi, sol, allocs=5_000) + + # test upwind operators + using SummationByPartsOperators: upwind_operators, periodic_derivative_operator + using SparseArrays: sparse + using OrdinaryDiffEq: solve + D1 = upwind_operators(periodic_derivative_operator; derivative_order = 1, + accuracy_order = accuracy_order, xmin = mesh.xmin, + xmax = mesh.xmax, + N = mesh.N) + D2 = sparse(D1.minus) * sparse(D1.plus) + solver = Solver(D1, D2) + semi = Semidiscretization(mesh, equations, initial_condition, solver, + boundary_conditions = boundary_conditions, + source_terms = source_terms) + ode = semidiscretize(semi, (0.0, 1.0)) + sol = solve(ode, Tsit5(), abstol = 1e-7, reltol = 1e-7, + save_everystep = false, callback = callbacks, saveat = saveat) + atol = 1e-12 + rtol = 1e-12 + errs = errors(analysis_callback) + l2 = [9.784591180473132e-8] + l2_measured = errs.l2_error[:, end] + for (l2_expected, l2_actual) in zip(l2, l2_measured) + @test isapprox(l2_expected, l2_actual, atol = atol, rtol = rtol) + end + linf = [9.915897769552373e-8] + linf_measured = errs.linf_error[:, end] + for (linf_expected, linf_actual) in zip(linf, linf_measured) + @test isapprox(linf_expected, linf_actual, atol = atol, rtol = rtol) + end + + @test_allocations(semi, sol, allocs=5_000) + end +end + +end # module diff --git a/test/test_unit.jl b/test/test_unit.jl index 6990343e..65838d50 100644 --- a/test/test_unit.jl +++ b/test/test_unit.jl @@ -106,6 +106,35 @@ using SparseArrays: sparse, SparseMatrixCSC @test_nowarn display(boundary_conditions) end + @testset "BBMEquation1D" begin + equations = @test_nowarn @inferred BBMEquation1D() + @test_nowarn print(equations) + @test_nowarn display(equations) + conversion_functions = [ + waterheight_total, + waterheight, + entropy, + energy_total, + prim2cons, + prim2prim, + prim2phys, + energy_total_modified, + entropy_modified, + invariant_cubic, + ] + for conversion in conversion_functions + @test DispersiveShallowWater.varnames(conversion, equations) isa Tuple + end + q = [42.0] + @test @inferred(prim2prim(q, equations)) == q + @test isapprox(@inferred(cons2prim(prim2cons(q, equations), equations)), q) + @test @inferred(waterheight_total(q, equations)) == 42.0 + @test @inferred(waterheight(q, equations)) == 42.0 + @test @inferred(still_water_surface(q, equations)) == 0.0 + @test @inferred(prim2phys(q, equations)) == @inferred(prim2prim(q, equations)) + @test @inferred(invariant_cubic(q, equations)) == 43.0^3 + end + @testset "BBMBBMEquations1D" begin equations = @test_nowarn @inferred BBMBBMEquations1D(gravity_constant = 9.81) @test_nowarn print(equations) diff --git a/test/test_util.jl b/test/test_util.jl index fa022066..df0f18f2 100644 --- a/test/test_util.jl +++ b/test/test_util.jl @@ -8,6 +8,7 @@ using Test: @test change_velocity=nothing, change_entropy=nothing, change_entropy_modified=nothing, + change_invariant_cubic=nothing, lake_at_rest=nothing, atol=1e-12, rtol=sqrt(eps()), atol_ints=1e-11, rtol_ints=sqrt(eps())) @@ -17,8 +18,8 @@ By default, only the absence of error output is checked. If `l2`, `linf` or `cons_error` are specified, in addition the resulting L2/Linf/conservation errors are compared approximately against these reference values, using `atol, rtol` as absolute/relative tolerance. -If `change_waterheight`, `change_velocity`, `change_momemtum`, `change_entropy`, `change_entropy_modified` -or `lake_at_rest` are specified, in addition the resulting changes of the different errors are +If `change_waterheight`, `change_velocity`, `change_momemtum`, `change_entropy`, `change_entropy_modified`, +`invariant_cubic`, or `lake_at_rest` are specified, in addition the resulting changes of the different errors are compared approximately against these reference values, using `atol_ints`, `rtol_ints` as absolute/relative tolerance. """ macro test_trixi_include(example, args...) @@ -30,6 +31,7 @@ macro test_trixi_include(example, args...) local change_momentum = get_kwarg(args, :change_momentum, nothing) local change_entropy = get_kwarg(args, :change_entropy, nothing) local change_entropy_modified = get_kwarg(args, :change_entropy_modified, nothing) + local change_invariant_cubic = get_kwarg(args, :change_invariant_cubic, nothing) local lake_at_rest = get_kwarg(args, :lake_at_rest, nothing) local atol = get_kwarg(args, :atol, 1e-12) local rtol = get_kwarg(args, :rtol, sqrt(eps())) @@ -41,7 +43,7 @@ macro test_trixi_include(example, args...) if (arg.head == :(=) && !(arg.args[1] in (:l2, :linf, :cons_error, :change_waterheight, :change_velocity, :change_momentum, :change_entropy, - :change_entropy_modified, :lake_at_rest, + :change_entropy_modified, :change_invariant_cubic, :lake_at_rest, :atol, :rtol, :atol_ints, :rtol_ints))) push!(kwargs, Pair(arg.args...)) end @@ -88,7 +90,7 @@ macro test_trixi_include(example, args...) if !isnothing($change_waterheight) || !isnothing($change_velocity) || !isnothing($change_momentum) || !isnothing($change_entropy) || !isnothing($change_entropy_modified) || - !isnothing($lake_at_rest) + !isnothing($change_invariant_cubic) || !isnothing($lake_at_rest) ints = integrals(analysis_callback) if !isnothing($change_waterheight) @@ -126,6 +128,14 @@ macro test_trixi_include(example, args...) rtol = $rtol_ints) end + if !isnothing($change_invariant_cubic) + invariant_cubic_change_measured = ints.invariant_cubic[end] - + ints.invariant_cubic[1] + @test isapprox($change_invariant_cubic, invariant_cubic_change_measured, + atol = $atol_ints, + rtol = $rtol_ints) + end + if !isnothing($lake_at_rest) lake_at_rest_measured = ints.lake_at_rest_error[end] @test isapprox($lake_at_rest, lake_at_rest_measured, atol = $atol_ints, From 1e3d7cdfa2933c5f8d626163915f40ea9eb4eeca Mon Sep 17 00:00:00 2001 From: Joshua Lampert Date: Tue, 10 Sep 2024 20:45:37 +0200 Subject: [PATCH 02/36] format --- src/equations/bbm_1d.jl | 13 +++++++------ test/test_util.jl | 5 +++-- 2 files changed, 10 insertions(+), 8 deletions(-) diff --git a/src/equations/bbm_1d.jl b/src/equations/bbm_1d.jl index ba4e3dc5..7567b930 100644 --- a/src/equations/bbm_1d.jl +++ b/src/equations/bbm_1d.jl @@ -27,7 +27,8 @@ It conserves A Broad Class of Conservative Numerical Methods for Dispersive Wave Equations [DOI: 10.4208/cicp.OA-2020-0119](https://doi.org/10.4208/cicp.OA-2020-0119) """ -struct BBMEquation1D{Bathymetry <: AbstractBathymetry, RealT <: Real} <: AbstractBBMEquation{1, 1} +struct BBMEquation1D{Bathymetry <: AbstractBathymetry, RealT <: Real} <: + AbstractBBMEquation{1, 1} bathymetry_type::Bathymetry # type of bathymetry eta0::RealT # constant still-water surface end @@ -49,7 +50,7 @@ See section 4.1.3 in (there is an error in paper: it should be sech^2 instead of function initial_condition_convergence_test(x, t, equations::BBMEquation1D, mesh) c = 1.2 A = 3 * (c - 1) - K = 0.5 * sqrt(1 - 1/c) + K = 0.5 * sqrt(1 - 1 / c) x_t = mod(x - c * t - xmin(mesh), xmax(mesh) - xmin(mesh)) + xmin(mesh) eta = A * sech(K * x_t)^2 return SVector(eta) @@ -77,7 +78,8 @@ function source_terms_manufactured(q, x, t, equations::BBMEquation1D) a4 = sinpi(t - 2 * x) a5 = sinpi(2 * t - 4 * x) a14 = exp(t / 2) - dq1 = -2*pi^2*(a4 + 2*pi*a3)*a14 - a14*a4/2 + pi*a14*a3 - pi*exp(t)*a5 + dq1 = -2 * pi^2 * (a4 + 2 * pi * a3) * a14 - a14 * a4 / 2 + pi * a14 * a3 - + pi * exp(t) * a5 return SVector(dq1) end @@ -90,7 +92,7 @@ function create_cache(mesh, equations::BBMEquation1D, eta2 = zeros(RealT, nnodes(mesh)) eta2_x = zero(eta2) eta_x = zero(eta2) - etaeta_x = zero(eta2) + etaeta_x = zero(eta2) eta_xx = zero(eta2) cache = (; invImD2, eta2, eta2_x, eta_x, etaeta_x, eta_xx, solver.D1, solver.D2) if solver.D1 isa PeriodicUpwindOperators @@ -118,7 +120,7 @@ function rhs!(dq, q, t, mesh, equations::BBMEquation1D, initial_condition, @.. eta2 = eta^2 if solver.D1 isa PeriodicDerivativeOperator || solver.D1 isa UniformPeriodicCoupledOperator || - solver.D1 isa FourierDerivativeOperator + solver.D1 isa FourierDerivativeOperator mul!(eta2_x, solver.D1, eta2) mul!(eta_x, solver.D1, eta) @.. etaeta_x = eta * eta_x @@ -134,7 +136,6 @@ function rhs!(dq, q, t, mesh, equations::BBMEquation1D, initial_condition, else @error "unknown type of first-derivative operator: $(typeof(solver.D1))" end - end @trixi_timeit timer() "source terms" calc_sources!(dq, q, t, source_terms, equations, diff --git a/test/test_util.jl b/test/test_util.jl index df0f18f2..5259bd69 100644 --- a/test/test_util.jl +++ b/test/test_util.jl @@ -43,7 +43,8 @@ macro test_trixi_include(example, args...) if (arg.head == :(=) && !(arg.args[1] in (:l2, :linf, :cons_error, :change_waterheight, :change_velocity, :change_momentum, :change_entropy, - :change_entropy_modified, :change_invariant_cubic, :lake_at_rest, + :change_entropy_modified, :change_invariant_cubic, + :lake_at_rest, :atol, :rtol, :atol_ints, :rtol_ints))) push!(kwargs, Pair(arg.args...)) end @@ -130,7 +131,7 @@ macro test_trixi_include(example, args...) if !isnothing($change_invariant_cubic) invariant_cubic_change_measured = ints.invariant_cubic[end] - - ints.invariant_cubic[1] + ints.invariant_cubic[1] @test isapprox($change_invariant_cubic, invariant_cubic_change_measured, atol = $atol_ints, rtol = $rtol_ints) From 31a4613a9f89d06d15ffac004b4a876f02d29a86 Mon Sep 17 00:00:00 2001 From: Joshua Lampert Date: Tue, 10 Sep 2024 21:03:58 +0200 Subject: [PATCH 03/36] fix --- src/equations/equations.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/equations/equations.jl b/src/equations/equations.jl index 20772bf6..5088ac82 100644 --- a/src/equations/equations.jl +++ b/src/equations/equations.jl @@ -101,7 +101,7 @@ The inverse conversion is performed by [`cons2prim`](@ref). return SVector(h, hv, b) end -function prim2cons(q, ::AbstractEquations{1, 1}) +function prim2cons(q, equations::AbstractEquations{1, 1}) h = waterheight(q, equations) return SVector(h) end From 5cbb277f17d15a267820b8b5fe60033ade7f1f2c Mon Sep 17 00:00:00 2001 From: Joshua Lampert Date: Tue, 10 Sep 2024 21:11:52 +0200 Subject: [PATCH 04/36] add BBM to docs --- README.md | 2 +- docs/src/index.md | 1 + 2 files changed, 2 insertions(+), 1 deletion(-) diff --git a/README.md b/README.md index ec66a4b7..b9641a44 100644 --- a/README.md +++ b/README.md @@ -12,7 +12,7 @@ **DispersiveShallowWater.jl** is a [Julia](https://julialang.org/) package that implements structure-preserving numerical methods for dispersive shallow water models. To date, it provides provably conservative, entropy-conserving and well-balanced numerical schemes for some dispersive shallow water models: -* the [BBM equation](https://doi.org/10.4208/cicp.OA-2020-0119) +* the [BBM equation](https://doi.org/10.4208/cicp.OA-2020-0119), * the [BBM-BBM equations with varying bottom topography](https://iopscience.iop.org/article/10.1088/1361-6544/ac3c29), * the [dispersive shallow water model proposed by Magnus Svärd and Henrik Kalisch](https://arxiv.org/abs/2302.09924), * the [Serre-Green-Naghdi equations](https://arxiv.org/abs/2408.02665). diff --git a/docs/src/index.md b/docs/src/index.md index c7a1c8ab..b3007327 100644 --- a/docs/src/index.md +++ b/docs/src/index.md @@ -12,6 +12,7 @@ [**DispersiveShallowWater.jl**](https://github.com/JoshuaLampert/DispersiveShallowWater.jl) is a [Julia](https://julialang.org/) package that implements structure-preserving numerical methods for dispersive shallow water models. To date, it provides provably conservative, entropy-conserving and well-balanced numerical schemes for some dispersive shallow water models: +* the [BBM equation](https://doi.org/10.4208/cicp.OA-2020-0119), * the [BBM-BBM equations with varying bottom topography](https://iopscience.iop.org/article/10.1088/1361-6544/ac3c29), * the [dispersive shallow water model proposed by Magnus Svärd and Henrik Kalisch](https://arxiv.org/abs/2302.09924), * the [Serre-Green-Naghdi equations](https://arxiv.org/abs/2408.02665). From c9ee358b40db3f3ee1f39b08fd2e967cd2d230d0 Mon Sep 17 00:00:00 2001 From: Joshua Lampert Date: Tue, 10 Sep 2024 21:15:36 +0200 Subject: [PATCH 05/36] adjust docs --- src/equations/bbm_1d.jl | 2 ++ src/equations/bbm_bbm_1d.jl | 2 +- 2 files changed, 3 insertions(+), 1 deletion(-) diff --git a/src/equations/bbm_1d.jl b/src/equations/bbm_1d.jl index 7567b930..52deaa54 100644 --- a/src/equations/bbm_1d.jl +++ b/src/equations/bbm_1d.jl @@ -20,6 +20,8 @@ It conserves - the total water mass (integral of ``h``) as a linear invariant - the total modified energy +for periodic boundary conditions. + - Thomas B. Benjamin, Jerry L. Bona and John J. Mahony (1972) Model equations for long waves in nonlinear dispersive systems [DOI: 10.1098/rsta.1972.0032](https://doi.org/10.1098/rsta.1972.0032) diff --git a/src/equations/bbm_bbm_1d.jl b/src/equations/bbm_bbm_1d.jl index b23db9d2..238b4a7d 100644 --- a/src/equations/bbm_bbm_1d.jl +++ b/src/equations/bbm_bbm_1d.jl @@ -36,7 +36,7 @@ Lampert and Ranocha (2024). It conserves for periodic boundary conditions (see Lampert, Ranocha). For reflecting boundary conditions, the semidiscretization conserves - the total water (integral of ``h``) as a linear invariant -- the total energy +- the total energy. Additionally, it is well-balanced for the lake-at-rest stationary solution, see Lampert and Ranocha (2024). From 4f8a46c405d11a565a913f064bcf47e7bd7eb7b6 Mon Sep 17 00:00:00 2001 From: Joshua Lampert Date: Tue, 10 Sep 2024 21:17:58 +0200 Subject: [PATCH 06/36] fix names of testsets --- test/test_bbm_1d.jl | 2 +- test/test_bbm_bbm_1d.jl | 2 +- test/test_svaerd_kalisch_1d.jl | 2 +- 3 files changed, 3 insertions(+), 3 deletions(-) diff --git a/test/test_bbm_1d.jl b/test/test_bbm_1d.jl index 1908251a..b136c530 100644 --- a/test/test_bbm_1d.jl +++ b/test/test_bbm_1d.jl @@ -7,7 +7,7 @@ include("test_util.jl") EXAMPLES_DIR = joinpath(examples_dir(), "bbm_1d") -@testset "BBM1D" begin +@testset "BBMEquation1D" begin @trixi_testset "bbm_1d_basic" begin @test_trixi_include(joinpath(EXAMPLES_DIR, "bbm_1d_basic.jl"), tspan=(0.0, 100.0), diff --git a/test/test_bbm_bbm_1d.jl b/test/test_bbm_bbm_1d.jl index 1f96e0c3..747927fd 100644 --- a/test/test_bbm_bbm_1d.jl +++ b/test/test_bbm_bbm_1d.jl @@ -7,7 +7,7 @@ include("test_util.jl") EXAMPLES_DIR = joinpath(examples_dir(), "bbm_bbm_1d") -@testset "BBMBBM1D" begin +@testset "BBMBBMEquations1D" begin @trixi_testset "bbm_bbm_1d_basic" begin @test_trixi_include(joinpath(EXAMPLES_DIR, "bbm_bbm_1d_basic.jl"), tspan=(0.0, 1.0), diff --git a/test/test_svaerd_kalisch_1d.jl b/test/test_svaerd_kalisch_1d.jl index f4c6c83f..85550773 100644 --- a/test/test_svaerd_kalisch_1d.jl +++ b/test/test_svaerd_kalisch_1d.jl @@ -7,7 +7,7 @@ include("test_util.jl") EXAMPLES_DIR = joinpath(examples_dir(), "svaerd_kalisch_1d") -@testset "SvaerdKalisch1D" begin +@testset "SvaerdKalischEquations1D" begin @trixi_testset "svaerd_kalisch_1d_manufactured" begin @test_trixi_include(joinpath(EXAMPLES_DIR, "svaerd_kalisch_1d_manufactured.jl"), From de01822cf5dc9c7430417d798071eba806230cf6 Mon Sep 17 00:00:00 2001 From: Joshua Lampert <51029046+JoshuaLampert@users.noreply.github.com> Date: Wed, 11 Sep 2024 14:01:07 +0200 Subject: [PATCH 07/36] Apply suggestions from code review Co-authored-by: Hendrik Ranocha --- README.md | 2 +- docs/src/index.md | 2 +- 2 files changed, 2 insertions(+), 2 deletions(-) diff --git a/README.md b/README.md index b9641a44..a8e5762e 100644 --- a/README.md +++ b/README.md @@ -12,7 +12,7 @@ **DispersiveShallowWater.jl** is a [Julia](https://julialang.org/) package that implements structure-preserving numerical methods for dispersive shallow water models. To date, it provides provably conservative, entropy-conserving and well-balanced numerical schemes for some dispersive shallow water models: -* the [BBM equation](https://doi.org/10.4208/cicp.OA-2020-0119), +* the [Benjamin-Bona-Mahony (BBM) equation, also known as regularized long-wave equation](https://doi.org/10.4208/cicp.OA-2020-0119), * the [BBM-BBM equations with varying bottom topography](https://iopscience.iop.org/article/10.1088/1361-6544/ac3c29), * the [dispersive shallow water model proposed by Magnus Svärd and Henrik Kalisch](https://arxiv.org/abs/2302.09924), * the [Serre-Green-Naghdi equations](https://arxiv.org/abs/2408.02665). diff --git a/docs/src/index.md b/docs/src/index.md index b3007327..9fd925ed 100644 --- a/docs/src/index.md +++ b/docs/src/index.md @@ -12,7 +12,7 @@ [**DispersiveShallowWater.jl**](https://github.com/JoshuaLampert/DispersiveShallowWater.jl) is a [Julia](https://julialang.org/) package that implements structure-preserving numerical methods for dispersive shallow water models. To date, it provides provably conservative, entropy-conserving and well-balanced numerical schemes for some dispersive shallow water models: -* the [BBM equation](https://doi.org/10.4208/cicp.OA-2020-0119), +* the [Benjamin-Bona-Mahony (BBM) equation, also known as regularized long-wave equation](https://doi.org/10.4208/cicp.OA-2020-0119), * the [BBM-BBM equations with varying bottom topography](https://iopscience.iop.org/article/10.1088/1361-6544/ac3c29), * the [dispersive shallow water model proposed by Magnus Svärd and Henrik Kalisch](https://arxiv.org/abs/2302.09924), * the [Serre-Green-Naghdi equations](https://arxiv.org/abs/2408.02665). From d7f07eaca0722b581aba151a0fb59d7be5357bdc Mon Sep 17 00:00:00 2001 From: Joshua Lampert Date: Wed, 11 Sep 2024 14:43:21 +0200 Subject: [PATCH 08/36] fix quadratic invariant --- src/equations/bbm_1d.jl | 14 ++++++-------- 1 file changed, 6 insertions(+), 8 deletions(-) diff --git a/src/equations/bbm_1d.jl b/src/equations/bbm_1d.jl index 52deaa54..737ec6b0 100644 --- a/src/equations/bbm_1d.jl +++ b/src/equations/bbm_1d.jl @@ -95,8 +95,7 @@ function create_cache(mesh, equations::BBMEquation1D, eta2_x = zero(eta2) eta_x = zero(eta2) etaeta_x = zero(eta2) - eta_xx = zero(eta2) - cache = (; invImD2, eta2, eta2_x, eta_x, etaeta_x, eta_xx, solver.D1, solver.D2) + cache = (; invImD2, eta2, eta2_x, eta_x, etaeta_x, solver.D1) if solver.D1 isa PeriodicUpwindOperators eta_x_upwind = zero(eta2) cache = (; cache..., eta_x_upwind) @@ -158,7 +157,7 @@ is a conserved quantity (for periodic boundary conditions). It is given by ```math -\\frac{1}{2} \\eta^2 + \\frac{1}{2} \\eta_{xx}. +\\frac{1}{2} \\eta^2 + \\frac{1}{2} \\eta_x^2. ``` `q_global` is a vector of the primitive variables at ALL nodes. @@ -169,15 +168,14 @@ See also [`energy_total_modified`](@ref). function energy_total_modified!(e, q_global, equations::BBMEquation1D, cache) eta, = q_global.x - (; D1, D2, eta_xx, tmp1) = cache + (; D1, eta_x) = cache if D1 isa PeriodicUpwindOperators - mul!(tmp1, D1.minus, eta) - mul!(eta_xx, D1.plus, tmp1) + mul!(eta_x, D1.central, eta) else - mul!(eta_xx, D2, eta) + mul!(eta_x, D1, eta) end - @.. e = 0.5 * (eta^2 + eta_xx) + @.. e = 0.5 * (eta^2 + eta_x^2) return nothing end From e34aa5488fc45ad1d7a1a935948624c23fd47c27 Mon Sep 17 00:00:00 2001 From: Joshua Lampert Date: Wed, 11 Sep 2024 15:03:00 +0200 Subject: [PATCH 09/36] fix test values --- test/test_bbm_1d.jl | 16 ++++++++-------- 1 file changed, 8 insertions(+), 8 deletions(-) diff --git a/test/test_bbm_1d.jl b/test/test_bbm_1d.jl index b136c530..a5967649 100644 --- a/test/test_bbm_1d.jl +++ b/test/test_bbm_1d.jl @@ -15,7 +15,7 @@ EXAMPLES_DIR = joinpath(examples_dir(), "bbm_1d") linf=[9.756568022900591e-5], cons_error=[7.105427357601002e-15], change_waterheight=-7.105427357601002e-15, - change_entropy_modified=6.355536918301041e-6, + change_entropy_modified=-4.4198182447274803e-7, change_invariant_cubic=-3.198066679033218e-6) @test_allocations(semi, sol, allocs=5_000) @@ -55,12 +55,12 @@ EXAMPLES_DIR = joinpath(examples_dir(), "bbm_1d") @trixi_testset "bbm_1d_relaxation" begin @test_trixi_include(joinpath(EXAMPLES_DIR, "bbm_1d_relaxation.jl"), tspan=(0.0, 100.0), - l2=[0.00026259713456399205], - linf=[0.00010095858421543813], - cons_error=[6.217248937900877e-15], - change_waterheight=6.217248937900877e-15, - change_entropy_modified=1.5543122344752192e-15, - change_invariant_cubic=-5.139088546002313e-5) + l2=[0.00025104961489025117], + linf=[9.745906869124132e-5], + cons_error=[5.329070518200751e-15], + change_waterheight=-5.329070518200751e-15, + change_entropy_modified=-2.220446049250313e-16, + change_invariant_cubic=-1.5787975371495122e-8) @test_allocations(semi, sol, allocs=5_000) end @@ -72,7 +72,7 @@ EXAMPLES_DIR = joinpath(examples_dir(), "bbm_1d") linf=[2.3226949846799627e-7], cons_error=[1.1546319456101628e-14], change_waterheight=-1.1546319456101628e-14, - change_entropy_modified=-4.4573640600731324e-7, + change_entropy_modified=-4.4266038123907947e-7, change_invariant_cubic=-3.1871549026618595e-6) @test_allocations(semi, sol, allocs=5_000) From 931072a2384879e05c0dcce12081f8382343c529 Mon Sep 17 00:00:00 2001 From: Joshua Lampert Date: Wed, 11 Sep 2024 15:50:38 +0200 Subject: [PATCH 10/36] a bit more clarifying comments about energy_total_modified --- src/equations/bbm_1d.jl | 3 ++- src/equations/equations.jl | 6 +++++- 2 files changed, 7 insertions(+), 2 deletions(-) diff --git a/src/equations/bbm_1d.jl b/src/equations/bbm_1d.jl index 737ec6b0..f09a3395 100644 --- a/src/equations/bbm_1d.jl +++ b/src/equations/bbm_1d.jl @@ -18,7 +18,8 @@ The BBM equation is first described in Benjamin, Bona, and Mahony (1972). The semidiscretization implemented here is developed in Ranocha, Mitsotakis, and Ketcheson (2020). It conserves - the total water mass (integral of ``h``) as a linear invariant -- the total modified energy +- a quadratic invariant (integral of ``\eta^2 + \eta_x^2``), which is called here [`energy_total_modified`](@ref) + (and [`entropy_modified`](@ref)) because it contains derivatives of the solution for periodic boundary conditions. diff --git a/src/equations/equations.jl b/src/equations/equations.jl index 5088ac82..e8736c17 100644 --- a/src/equations/equations.jl +++ b/src/equations/equations.jl @@ -314,7 +314,11 @@ contain additional terms compared to the usual [`energy_total`](@ref). For example, for the [`SvaerdKalischEquations1D`](@ref) and the [`SerreGreenNaghdiEquations1D`](@ref), it contains additional terms depending on the derivative of the velocity ``v_x`` modeling non-hydrostatic -contributions. +contributions. For equations, which are not `AbstractShallowWaterEquations`, +the modified total energy does not have to be an extension of the usual +[`energy_total`](@ref) and does not have to be related to a physical energy. +However, it is still a conserved quantity and contains derivatives of the +solution. `q_global` is a vector of the primitive variables at ALL nodes. `cache` needs to hold the SBP operators used by the `solver` if non-hydrostatic From 1e0179980501472839a4b00925bbe1366bfdf174 Mon Sep 17 00:00:00 2001 From: Joshua Lampert Date: Wed, 11 Sep 2024 15:53:18 +0200 Subject: [PATCH 11/36] fix docstring --- src/equations/bbm_1d.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/equations/bbm_1d.jl b/src/equations/bbm_1d.jl index f09a3395..2ee56bbb 100644 --- a/src/equations/bbm_1d.jl +++ b/src/equations/bbm_1d.jl @@ -150,7 +150,7 @@ function rhs!(dq, q, t, mesh, equations::BBMEquation1D, initial_condition, end """ - energy_total_modified!(e, q, equations::BBMEquation1D, cache) + energy_total_modified!(e, q_global, equations::BBMEquation1D, cache) Return the modified total energy `e` of the primitive variables `q_global` for the [`BBMEquation1D`](@ref). The `energy_total_modified` From 30f15ecc412d526860c9406df237401d5392345d Mon Sep 17 00:00:00 2001 From: Joshua Lampert <51029046+JoshuaLampert@users.noreply.github.com> Date: Wed, 11 Sep 2024 16:57:21 +0200 Subject: [PATCH 12/36] Apply suggestions from code review Co-authored-by: Hendrik Ranocha --- src/equations/equations.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/equations/equations.jl b/src/equations/equations.jl index e8736c17..a94ddd5f 100644 --- a/src/equations/equations.jl +++ b/src/equations/equations.jl @@ -317,7 +317,7 @@ depending on the derivative of the velocity ``v_x`` modeling non-hydrostatic contributions. For equations, which are not `AbstractShallowWaterEquations`, the modified total energy does not have to be an extension of the usual [`energy_total`](@ref) and does not have to be related to a physical energy. -However, it is still a conserved quantity and contains derivatives of the +However, it is still a conserved quantity and may contain derivatives of the solution. `q_global` is a vector of the primitive variables at ALL nodes. From 673a72d7cc7463a527082dba94508417672aeddc Mon Sep 17 00:00:00 2001 From: Joshua Lampert Date: Thu, 12 Sep 2024 18:08:07 +0200 Subject: [PATCH 13/36] fix entropy_modified --- src/equations/bbm_1d.jl | 14 ++++++++------ test/test_bbm_1d.jl | 12 ++++++------ 2 files changed, 14 insertions(+), 12 deletions(-) diff --git a/src/equations/bbm_1d.jl b/src/equations/bbm_1d.jl index 2ee56bbb..4c6ab528 100644 --- a/src/equations/bbm_1d.jl +++ b/src/equations/bbm_1d.jl @@ -96,7 +96,8 @@ function create_cache(mesh, equations::BBMEquation1D, eta2_x = zero(eta2) eta_x = zero(eta2) etaeta_x = zero(eta2) - cache = (; invImD2, eta2, eta2_x, eta_x, etaeta_x, solver.D1) + eta_xx = zero(eta2) + cache = (; invImD2, eta2, eta2_x, eta_x, etaeta_x, eta_xx, solver.D1, solver.D2) if solver.D1 isa PeriodicUpwindOperators eta_x_upwind = zero(eta2) cache = (; cache..., eta_x_upwind) @@ -158,7 +159,7 @@ is a conserved quantity (for periodic boundary conditions). It is given by ```math -\\frac{1}{2} \\eta^2 + \\frac{1}{2} \\eta_x^2. +\\frac{1}{2} \\eta(\\eta - \\eta_{xx}). ``` `q_global` is a vector of the primitive variables at ALL nodes. @@ -169,14 +170,15 @@ See also [`energy_total_modified`](@ref). function energy_total_modified!(e, q_global, equations::BBMEquation1D, cache) eta, = q_global.x - (; D1, eta_x) = cache + (; D1, D2, eta_xx, tmp1) = cache if D1 isa PeriodicUpwindOperators - mul!(eta_x, D1.central, eta) + mul!(tmp1, D1.minus, eta) + mul!(eta_xx, D1.plus, tmp1) else - mul!(eta_x, D1, eta) + mul!(eta_xx, D2, eta) end - @.. e = 0.5 * (eta^2 + eta_x^2) + @.. e = 0.5 * eta * (eta - eta_xx) return nothing end diff --git a/test/test_bbm_1d.jl b/test/test_bbm_1d.jl index a5967649..e188207f 100644 --- a/test/test_bbm_1d.jl +++ b/test/test_bbm_1d.jl @@ -15,7 +15,7 @@ EXAMPLES_DIR = joinpath(examples_dir(), "bbm_1d") linf=[9.756568022900591e-5], cons_error=[7.105427357601002e-15], change_waterheight=-7.105427357601002e-15, - change_entropy_modified=-4.4198182447274803e-7, + change_entropy_modified=-4.4274395039067826e-7, change_invariant_cubic=-3.198066679033218e-6) @test_allocations(semi, sol, allocs=5_000) @@ -55,12 +55,12 @@ EXAMPLES_DIR = joinpath(examples_dir(), "bbm_1d") @trixi_testset "bbm_1d_relaxation" begin @test_trixi_include(joinpath(EXAMPLES_DIR, "bbm_1d_relaxation.jl"), tspan=(0.0, 100.0), - l2=[0.00025104961489025117], - linf=[9.745906869124132e-5], + l2=[0.0002510482044505331], + linf=[9.745861147153478e-5], cons_error=[5.329070518200751e-15], - change_waterheight=-5.329070518200751e-15, - change_entropy_modified=-2.220446049250313e-16, - change_invariant_cubic=-1.5787975371495122e-8) + change_waterheight=5.329070518200751e-15, + change_entropy_modified=0.0, + change_invariant_cubic=-1.0308752962373546e-8) @test_allocations(semi, sol, allocs=5_000) end From 577303c0e80da745d673078dbd29ea905fab1243 Mon Sep 17 00:00:00 2001 From: Joshua Lampert Date: Sun, 15 Sep 2024 12:20:05 +0200 Subject: [PATCH 14/36] change to Hamiltonian and implement non-split form semi --- examples/bbm_1d/bbm_1d_basic.jl | 6 +- examples/bbm_1d/bbm_1d_fourier.jl | 2 +- .../bbm_1d/bbm_1d_hamiltonian_relaxation.jl | 43 +++ examples/bbm_1d/bbm_1d_relaxation.jl | 2 +- src/DispersiveShallowWater.jl | 2 +- src/callbacks_step/analysis.jl | 2 +- src/equations/bbm_1d.jl | 57 ++-- src/equations/equations.jl | 22 ++ src/semidiscretization.jl | 7 +- test/test_bbm_1d.jl | 282 +++++++++++------- test/test_util.jl | 16 +- 11 files changed, 291 insertions(+), 150 deletions(-) create mode 100644 examples/bbm_1d/bbm_1d_hamiltonian_relaxation.jl diff --git a/examples/bbm_1d/bbm_1d_basic.jl b/examples/bbm_1d/bbm_1d_basic.jl index c60c2a5a..0091154d 100644 --- a/examples/bbm_1d/bbm_1d_basic.jl +++ b/examples/bbm_1d/bbm_1d_basic.jl @@ -2,9 +2,9 @@ using OrdinaryDiffEq using DispersiveShallowWater ############################################################################### -# Semidiscretization of the BBM equation +# Semidiscretization of the BBM equation (conserves the quadratic invariant) -equations = BBMEquation1D() +equations = BBMEquation1D(split_form = true) initial_condition = initial_condition_convergence_test boundary_conditions = boundary_condition_periodic @@ -32,7 +32,7 @@ analysis_callback = AnalysisCallback(semi; interval = 10, extra_analysis_errors = (:conservation_error,), extra_analysis_integrals = (waterheight_total, entropy_modified, - invariant_cubic)) + hamiltonian)) callbacks = CallbackSet(analysis_callback, summary_callback) saveat = range(tspan..., length = 100) diff --git a/examples/bbm_1d/bbm_1d_fourier.jl b/examples/bbm_1d/bbm_1d_fourier.jl index d54c9dee..0a5c2e85 100644 --- a/examples/bbm_1d/bbm_1d_fourier.jl +++ b/examples/bbm_1d/bbm_1d_fourier.jl @@ -34,7 +34,7 @@ analysis_callback = AnalysisCallback(semi; interval = 10, extra_analysis_errors = (:conservation_error,), extra_analysis_integrals = (waterheight_total, entropy_modified, - invariant_cubic)) + hamiltonian)) callbacks = CallbackSet(analysis_callback, summary_callback) saveat = range(tspan..., length = 100) diff --git a/examples/bbm_1d/bbm_1d_hamiltonian_relaxation.jl b/examples/bbm_1d/bbm_1d_hamiltonian_relaxation.jl new file mode 100644 index 00000000..f21cacc0 --- /dev/null +++ b/examples/bbm_1d/bbm_1d_hamiltonian_relaxation.jl @@ -0,0 +1,43 @@ +using OrdinaryDiffEq +using DispersiveShallowWater + +############################################################################### +# Semidiscretization of the BBM equation (conserves the quadratic invariant) + +equations = BBMEquation1D(split_form = false) + +initial_condition = initial_condition_convergence_test +boundary_conditions = boundary_condition_periodic + +# create homogeneous mesh +coordinates_min = -90.0 +coordinates_max = 90.0 +N = 512 +mesh = Mesh1D(coordinates_min, coordinates_max, N) + +# create solver with periodic SBP operators of accuracy order 4 +accuracy_order = 4 +solver = Solver(mesh, accuracy_order) + +# semidiscretization holds all the necessary data structures for the spatial discretization +semi = Semidiscretization(mesh, equations, initial_condition, solver, + boundary_conditions = boundary_conditions) + +############################################################################### +# Create `ODEProblem` and run the simulation +tspan = (0.0, 1000.0) +ode = semidiscretize(semi, tspan) +summary_callback = SummaryCallback() +analysis_callback = AnalysisCallback(semi; interval = 10, + extra_analysis_errors = (:conservation_error,), + extra_analysis_integrals = (waterheight_total, + entropy_modified, + hamiltonian)) + +relaxation_callback = RelaxationCallback(invariant = hamiltonian) +# Always put relaxation_callback before analysis_callback to guarantee conservation of the invariant +callbacks = CallbackSet(relaxation_callback, analysis_callback, summary_callback) + +saveat = range(tspan..., length = 100) +sol = solve(ode, Tsit5(), abstol = 1e-7, reltol = 1e-7, + save_everystep = false, callback = callbacks, saveat = saveat) diff --git a/examples/bbm_1d/bbm_1d_relaxation.jl b/examples/bbm_1d/bbm_1d_relaxation.jl index a78d2a80..65364fdc 100644 --- a/examples/bbm_1d/bbm_1d_relaxation.jl +++ b/examples/bbm_1d/bbm_1d_relaxation.jl @@ -32,7 +32,7 @@ analysis_callback = AnalysisCallback(semi; interval = 10, extra_analysis_errors = (:conservation_error,), extra_analysis_integrals = (waterheight_total, entropy_modified, - invariant_cubic)) + hamiltonian)) relaxation_callback = RelaxationCallback(invariant = entropy_modified) # Always put relaxation_callback before analysis_callback to guarantee conservation of the invariant diff --git a/src/DispersiveShallowWater.jl b/src/DispersiveShallowWater.jl index 6c8d0ba8..54633bf0 100644 --- a/src/DispersiveShallowWater.jl +++ b/src/DispersiveShallowWater.jl @@ -72,7 +72,7 @@ export prim2prim, prim2cons, cons2prim, prim2phys, bathymetry, still_water_surface, energy_total, entropy, lake_at_rest_error, energy_total_modified, entropy_modified, - invariant_cubic + hamiltonian export Mesh1D, xmin, xmax, nnodes diff --git a/src/callbacks_step/analysis.jl b/src/callbacks_step/analysis.jl index e2ed0725..d0bd1432 100644 --- a/src/callbacks_step/analysis.jl +++ b/src/callbacks_step/analysis.jl @@ -339,4 +339,4 @@ pretty_form_utf(::typeof(energy_total)) = "∫e_total" pretty_form_utf(::typeof(entropy_modified)) = "∫U_modified" pretty_form_utf(::typeof(energy_total_modified)) = "∫e_modified" pretty_form_utf(::typeof(lake_at_rest_error)) = "∫|η-η₀|" -pretty_form_utf(::typeof(invariant_cubic)) = "∫(η + 1)³" +pretty_form_utf(::typeof(hamiltonian)) = "∫H" diff --git a/src/equations/bbm_1d.jl b/src/equations/bbm_1d.jl index 4c6ab528..8f29e16a 100644 --- a/src/equations/bbm_1d.jl +++ b/src/equations/bbm_1d.jl @@ -1,6 +1,6 @@ # TODO: Use this nondimensionalized version or use dimensional version including gravity and depth? @doc raw""" - BBMEquation1D(; bathymetry_type = bathymetry_flat, eta0 = 0.0) + BBMEquation1D(; bathymetry_type = bathymetry_flat, eta0 = 0.0, split_form = true) BBM (Benjamin–Bona–Mahony) equation in one spatial dimension. The equations are given by ```math @@ -16,11 +16,15 @@ Currently, the equations only support a flat bathymetry ``b = 0``, see [`bathyme The BBM equation is first described in Benjamin, Bona, and Mahony (1972). The semidiscretization implemented here is developed in Ranocha, Mitsotakis, and Ketcheson (2020). -It conserves +If `split_form` is `true` a split form in the semidiscretization is used, which conserves - the total water mass (integral of ``h``) as a linear invariant - a quadratic invariant (integral of ``\eta^2 + \eta_x^2``), which is called here [`energy_total_modified`](@ref) (and [`entropy_modified`](@ref)) because it contains derivatives of the solution +for periodic boundary conditions. If `split_form` is `false` the semidiscretization conserves +- the total water mass (integral of ``h``) as a linear invariant +- the Hamiltonian (integral of ``1/6 \eta^3 + 1/2 \eta^2``) (see [`hamiltonian`](@ref)) + for periodic boundary conditions. - Thomas B. Benjamin, Jerry L. Bona and John J. Mahony (1972) @@ -34,10 +38,11 @@ struct BBMEquation1D{Bathymetry <: AbstractBathymetry, RealT <: Real} <: AbstractBBMEquation{1, 1} bathymetry_type::Bathymetry # type of bathymetry eta0::RealT # constant still-water surface + split_form::Bool # whether to use a split-form or not end -function BBMEquation1D(; bathymetry_type = bathymetry_flat, eta0 = 0.0) - BBMEquation1D(bathymetry_type, eta0) +function BBMEquation1D(; bathymetry_type = bathymetry_flat, eta0 = 0.0, split_form = true) + BBMEquation1D(bathymetry_type, eta0, split_form) end """ @@ -126,16 +131,22 @@ function rhs!(dq, q, t, mesh, equations::BBMEquation1D, initial_condition, solver.D1 isa FourierDerivativeOperator mul!(eta2_x, solver.D1, eta2) mul!(eta_x, solver.D1, eta) - @.. etaeta_x = eta * eta_x - # split form - @.. deta = -(1 / 3 * (eta2_x + etaeta_x) + eta_x) + if equations.split_form + @.. etaeta_x = eta * eta_x + @.. deta = -(1 / 3 * (eta2_x + etaeta_x) + eta_x) + else + @.. deta = -(0.5 * eta2_x + eta_x) + end elseif solver.D1 isa PeriodicUpwindOperators mul!(eta2_x, solver.D1.central, eta2) mul!(eta_x_upwind, solver.D1.minus, eta) mul!(eta_x, solver.D1.central, eta) - @.. etaeta_x = eta * eta_x - # split form - @.. deta = -(1 / 3 * (eta2_x + etaeta_x) + eta_x_upwind) + if equations.split_form + @.. etaeta_x = eta * eta_x + @.. deta = -(1 / 3 * (eta2_x + etaeta_x) + eta_x_upwind) + else + @.. deta = -(0.5 * eta2_x + eta_x_upwind) + end else @error "unknown type of first-derivative operator: $(typeof(solver.D1))" end @@ -179,21 +190,27 @@ function energy_total_modified!(e, q_global, equations::BBMEquation1D, cache) end @.. e = 0.5 * eta * (eta - eta_xx) - return nothing + return e end """ - invariant_cubic(q, equations::BBMEquation1D) + hamiltonian!(H, q_global, equations::BBMEquation1D, cache) -Return the cubic invariant of the primitive variables `q` for the -[`BBMEquation1D`](@ref). The cubic invariant is given by +Return the Hamiltonian `H` of the primitive variables `q_global` for the +[`BBMEquation1D`](@ref). The Hamiltonian is given by ```math -(\\eta + 1)^3. +1/6\\eta^3 + 1/2\\eta^2. ``` + +`q_global` is a vector of the primitive variables at ALL nodes. + +See also [`hamiltonian`](@ref). """ -function invariant_cubic(q, equations::BBMEquation1D) - eta = waterheight_total(q, equations) - return (eta + 1)^3 +function hamiltonian!(H, q_global, equations::BBMEquation1D, cache) + eta, = q_global.x + (; eta2, tmp1) = cache + @.. eta2 = eta^2 + @.. tmp1 = eta^3 + @.. H = 1/6 * tmp1 + 1/2 * eta2 + return H end - -varnames(::typeof(invariant_cubic), equations) = ("(η + 1)³",) diff --git a/src/equations/equations.jl b/src/equations/equations.jl index a94ddd5f..635b1b3e 100644 --- a/src/equations/equations.jl +++ b/src/equations/equations.jl @@ -373,6 +373,28 @@ In-place version of [`entropy_modified`](@ref). varnames(::typeof(entropy_modified), equations) = ("U_modified",) +# The Hamiltonian takes the whole `q_global` for every point in space +""" + hamiltonian(q_global, equations, cache) + +Return the Hamiltonian of the primitive variables `q_global` for the +`equations`. The Hamiltonian is a conserved quantity and may contain +derivatives of the solution. + +`q_global` is a vector of the primitive variables at ALL nodes. +`cache` needs to hold the SBP operators used by the `solver` if non-hydrostatic +terms are present. + +Internally, this function allocates a vector for the output and +calls [`DispersiveShallowWater.hamiltonian!`](@ref). +""" +function hamiltonian(q_global, equations::AbstractEquations, cache) + H = similar(q_global.x[begin]) + return hamiltonian!(H, q_global, equations, cache) +end + +varnames(::typeof(hamiltonian), equations) = ("H",) + # Add methods to show some information on systems of equations. function Base.show(io::IO, equations::AbstractEquations) # Since this is not performance-critical, we can use `@nospecialize` to reduce latency. diff --git a/src/semidiscretization.jl b/src/semidiscretization.jl index a450f3b3..aba79a95 100644 --- a/src/semidiscretization.jl +++ b/src/semidiscretization.jl @@ -147,12 +147,13 @@ end # Obtain the function, which has an additional `!` appended to the name inplace_version(f) = getfield(@__MODULE__, Symbol(string(nameof(f)) * "!")) -# The entropy/energy of the Svärd-Kalisch and Serre-Green-Naghdi equations -# takes the whole `q` for every point in space since it requires +# The modified entropy/energy and the Hamiltonian +# take the whole `q` for every point in space since it requires # the derivative of the velocity `v_x`. function integrate_quantity!(quantity, func::Union{typeof(energy_total_modified), - typeof(entropy_modified)}, q, + typeof(entropy_modified), + typeof(hamiltonian)}, q, semi::Semidiscretization) inplace_version(func)(quantity, q, semi.equations, semi.cache) integrate(quantity, semi) diff --git a/test/test_bbm_1d.jl b/test/test_bbm_1d.jl index e188207f..e2e53e27 100644 --- a/test/test_bbm_1d.jl +++ b/test/test_bbm_1d.jl @@ -8,118 +8,176 @@ include("test_util.jl") EXAMPLES_DIR = joinpath(examples_dir(), "bbm_1d") @testset "BBMEquation1D" begin - @trixi_testset "bbm_1d_basic" begin - @test_trixi_include(joinpath(EXAMPLES_DIR, "bbm_1d_basic.jl"), - tspan=(0.0, 100.0), - l2=[0.0002514795321988484], - linf=[9.756568022900591e-5], - cons_error=[7.105427357601002e-15], - change_waterheight=-7.105427357601002e-15, - change_entropy_modified=-4.4274395039067826e-7, - change_invariant_cubic=-3.198066679033218e-6) - - @test_allocations(semi, sol, allocs=5_000) - - # test upwind operators - using SummationByPartsOperators: upwind_operators, periodic_derivative_operator - using SparseArrays: sparse - using OrdinaryDiffEq: solve - D1 = upwind_operators(periodic_derivative_operator; derivative_order = 1, - accuracy_order = accuracy_order, xmin = mesh.xmin, - xmax = mesh.xmax, - N = mesh.N) - D2 = sparse(D1.minus) * sparse(D1.plus) - solver = Solver(D1, D2) - semi = Semidiscretization(mesh, equations, initial_condition, solver, - boundary_conditions = boundary_conditions) - ode = semidiscretize(semi, (0.0, 100.0)) - sol = solve(ode, Tsit5(), abstol = 1e-7, reltol = 1e-7, - save_everystep = false, callback = callbacks, saveat = saveat) - atol = 1e-12 - rtol = 1e-12 - errs = errors(analysis_callback) - l2 = [0.00018397011159873] - l2_measured = errs.l2_error[:, end] - for (l2_expected, l2_actual) in zip(l2, l2_measured) - @test isapprox(l2_expected, l2_actual, atol = atol, rtol = rtol) - end - linf = [7.190886191621448e-5] - linf_measured = errs.linf_error[:, end] - for (linf_expected, linf_actual) in zip(linf, linf_measured) - @test isapprox(linf_expected, linf_actual, atol = atol, rtol = rtol) - end - - @test_allocations(semi, sol, allocs=5_000) - end - - @trixi_testset "bbm_1d_relaxation" begin - @test_trixi_include(joinpath(EXAMPLES_DIR, "bbm_1d_relaxation.jl"), - tspan=(0.0, 100.0), - l2=[0.0002510482044505331], - linf=[9.745861147153478e-5], - cons_error=[5.329070518200751e-15], - change_waterheight=5.329070518200751e-15, - change_entropy_modified=0.0, - change_invariant_cubic=-1.0308752962373546e-8) - - @test_allocations(semi, sol, allocs=5_000) - end - - @trixi_testset "bbm_1d_fourier" begin - @test_trixi_include(joinpath(EXAMPLES_DIR, "bbm_1d_fourier.jl"), - tspan=(0.0, 100.0), - l2=[6.01265210291245e-7], - linf=[2.3226949846799627e-7], - cons_error=[1.1546319456101628e-14], - change_waterheight=-1.1546319456101628e-14, - change_entropy_modified=-4.4266038123907947e-7, - change_invariant_cubic=-3.1871549026618595e-6) - - @test_allocations(semi, sol, allocs=5_000) - end - - @trixi_testset "bbm_1d_manufactured" begin - @test_trixi_include(joinpath(EXAMPLES_DIR, "bbm_1d_manufactured.jl"), - tspan=(0.0, 1.0), - l2=[7.887878295265557e-9], - linf=[9.041914550422803e-9], - cons_error=[5.148179246187295e-13], - change_waterheight=5.148179246187295e-13) - - @test_allocations(semi, sol, allocs=5_000) - - # test upwind operators - using SummationByPartsOperators: upwind_operators, periodic_derivative_operator - using SparseArrays: sparse - using OrdinaryDiffEq: solve - D1 = upwind_operators(periodic_derivative_operator; derivative_order = 1, - accuracy_order = accuracy_order, xmin = mesh.xmin, - xmax = mesh.xmax, - N = mesh.N) - D2 = sparse(D1.minus) * sparse(D1.plus) - solver = Solver(D1, D2) - semi = Semidiscretization(mesh, equations, initial_condition, solver, - boundary_conditions = boundary_conditions, - source_terms = source_terms) - ode = semidiscretize(semi, (0.0, 1.0)) - sol = solve(ode, Tsit5(), abstol = 1e-7, reltol = 1e-7, - save_everystep = false, callback = callbacks, saveat = saveat) - atol = 1e-12 - rtol = 1e-12 - errs = errors(analysis_callback) - l2 = [9.784591180473132e-8] - l2_measured = errs.l2_error[:, end] - for (l2_expected, l2_actual) in zip(l2, l2_measured) - @test isapprox(l2_expected, l2_actual, atol = atol, rtol = rtol) - end - linf = [9.915897769552373e-8] - linf_measured = errs.linf_error[:, end] - for (linf_expected, linf_actual) in zip(linf, linf_measured) - @test isapprox(linf_expected, linf_actual, atol = atol, rtol = rtol) - end - - @test_allocations(semi, sol, allocs=5_000) - end + @trixi_testset "bbm_1d_basic" begin + @test_trixi_include(joinpath(EXAMPLES_DIR, "bbm_1d_basic.jl"), + tspan = (0.0, 100.0), + l2 = [0.0002514795321988484], + linf = [9.756568022900591e-5], + cons_error = [7.105427357601002e-15], + change_waterheight = -7.105427357601002e-15, + change_entropy_modified = -4.4274395039067826e-7, + change_hamiltonian = -3.198066679033218e-6) + + @test_allocations(semi, sol, allocs = 5_000) + + # test upwind operators + using SummationByPartsOperators: upwind_operators, periodic_derivative_operator + using SparseArrays: sparse + using OrdinaryDiffEq: solve + D1 = upwind_operators(periodic_derivative_operator; derivative_order = 1, + accuracy_order = accuracy_order, xmin = mesh.xmin, + xmax = mesh.xmax, + N = mesh.N) + D2 = sparse(D1.minus) * sparse(D1.plus) + solver = Solver(D1, D2) + semi = Semidiscretization(mesh, equations, initial_condition, solver, + boundary_conditions = boundary_conditions) + ode = semidiscretize(semi, (0.0, 100.0)) + sol = solve(ode, Tsit5(), abstol = 1e-7, reltol = 1e-7, + save_everystep = false, callback = callbacks, saveat = saveat) + atol = 1e-12 + rtol = 1e-12 + errs = errors(analysis_callback) + l2 = [0.00018397011159873] + l2_measured = errs.l2_error[:, end] + for (l2_expected, l2_actual) in zip(l2, l2_measured) + @test isapprox(l2_expected, l2_actual, atol = atol, rtol = rtol) + end + linf = [7.190886191621448e-5] + linf_measured = errs.linf_error[:, end] + for (linf_expected, linf_actual) in zip(linf, linf_measured) + @test isapprox(linf_expected, linf_actual, atol = atol, rtol = rtol) + end + + @test_allocations(semi, sol, allocs = 5_000) + end + + @trixi_testset "bbm_1d_basic with split_form = false" begin + @test_trixi_include(joinpath(EXAMPLES_DIR, "bbm_1d_basic.jl"), + tspan = (0.0, 100.0), + split_form = false, + l2 = [0.00023679720962102973], + linf = [9.291484780826753e-5], + cons_error = [0.0], + change_waterheight = 0.0, + change_entropy_modified = -4.4114923292148944e-7, + change_hamiltonian = -5.313053028643822e-7) + + @test_allocations(semi, sol, allocs = 5_000) + + # test upwind operators + using SummationByPartsOperators: upwind_operators, periodic_derivative_operator + using SparseArrays: sparse + using OrdinaryDiffEq: solve + D1 = upwind_operators(periodic_derivative_operator; derivative_order = 1, + accuracy_order = accuracy_order, xmin = mesh.xmin, + xmax = mesh.xmax, + N = mesh.N) + D2 = sparse(D1.minus) * sparse(D1.plus) + solver = Solver(D1, D2) + semi = Semidiscretization(mesh, equations, initial_condition, solver, + boundary_conditions = boundary_conditions) + ode = semidiscretize(semi, (0.0, 100.0)) + sol = solve(ode, Tsit5(), abstol = 1e-7, reltol = 1e-7, + save_everystep = false, callback = callbacks, saveat = saveat) + atol = 1e-12 + rtol = 1e-12 + errs = errors(analysis_callback) + l2 = [0.00016247570402673777] + l2_measured = errs.l2_error[:, end] + for (l2_expected, l2_actual) in zip(l2, l2_measured) + @test isapprox(l2_expected, l2_actual, atol = atol, rtol = rtol) + end + linf = [6.495267031642049e-5] + linf_measured = errs.linf_error[:, end] + for (linf_expected, linf_actual) in zip(linf, linf_measured) + @test isapprox(linf_expected, linf_actual, atol = atol, rtol = rtol) + end + + @test_allocations(semi, sol, allocs = 5_000) + end + + @trixi_testset "bbm_1d_relaxation" begin + @test_trixi_include(joinpath(EXAMPLES_DIR, "bbm_1d_relaxation.jl"), + tspan = (0.0, 100.0), + l2 = [0.0002510482044505331], + linf = [9.745861147153478e-5], + cons_error = [5.329070518200751e-15], + change_waterheight = 5.329070518200751e-15, + change_entropy_modified = 0.0, + change_hamiltonian = -1.0308752962373546e-8) + + @test_allocations(semi, sol, allocs = 5_000) + end + + @trixi_testset "bbm_1d_hamiltonian_relaxation" begin + @test_trixi_include(joinpath(EXAMPLES_DIR, "bbm_1d_hamiltonian_relaxation.jl"), + tspan = (0.0, 100.0), + l2 = [0.00023637369561147064], + linf = [9.280778692660752e-5], + cons_error = [1.7763568394002505e-14], + change_waterheight = -1.7763568394002505e-14, + change_entropy_modified = 1.6049757078917537e-9, + change_hamiltonian = 0.0) + + @test_allocations(semi, sol, allocs = 5_000) + end + + @trixi_testset "bbm_1d_fourier" begin + @test_trixi_include(joinpath(EXAMPLES_DIR, "bbm_1d_fourier.jl"), + tspan = (0.0, 100.0), + l2 = [6.01265210291245e-7], + linf = [2.3226949846799627e-7], + cons_error = [1.1546319456101628e-14], + change_waterheight = -1.1546319456101628e-14, + change_entropy_modified = -4.4266038123907947e-7, + change_hamiltonian = -3.1871549026618595e-6) + + @test_allocations(semi, sol, allocs = 5_000) + end + + @trixi_testset "bbm_1d_manufactured" begin + @test_trixi_include(joinpath(EXAMPLES_DIR, "bbm_1d_manufactured.jl"), + tspan = (0.0, 1.0), + l2 = [7.887878295265557e-9], + linf = [9.041914550422803e-9], + cons_error = [5.148179246187295e-13], + change_waterheight = 5.148179246187295e-13) + + @test_allocations(semi, sol, allocs = 5_000) + + # test upwind operators + using SummationByPartsOperators: upwind_operators, periodic_derivative_operator + using SparseArrays: sparse + using OrdinaryDiffEq: solve + D1 = upwind_operators(periodic_derivative_operator; derivative_order = 1, + accuracy_order = accuracy_order, xmin = mesh.xmin, + xmax = mesh.xmax, + N = mesh.N) + D2 = sparse(D1.minus) * sparse(D1.plus) + solver = Solver(D1, D2) + semi = Semidiscretization(mesh, equations, initial_condition, solver, + boundary_conditions = boundary_conditions, + source_terms = source_terms) + ode = semidiscretize(semi, (0.0, 1.0)) + sol = solve(ode, Tsit5(), abstol = 1e-7, reltol = 1e-7, + save_everystep = false, callback = callbacks, saveat = saveat) + atol = 1e-12 + rtol = 1e-12 + errs = errors(analysis_callback) + l2 = [9.784591180473132e-8] + l2_measured = errs.l2_error[:, end] + for (l2_expected, l2_actual) in zip(l2, l2_measured) + @test isapprox(l2_expected, l2_actual, atol = atol, rtol = rtol) + end + linf = [9.915897769552373e-8] + linf_measured = errs.linf_error[:, end] + for (linf_expected, linf_actual) in zip(linf, linf_measured) + @test isapprox(linf_expected, linf_actual, atol = atol, rtol = rtol) + end + + @test_allocations(semi, sol, allocs = 5_000) + end end end # module diff --git a/test/test_util.jl b/test/test_util.jl index 5259bd69..e2d02d6d 100644 --- a/test/test_util.jl +++ b/test/test_util.jl @@ -8,7 +8,7 @@ using Test: @test change_velocity=nothing, change_entropy=nothing, change_entropy_modified=nothing, - change_invariant_cubic=nothing, + change_hamiltonian=nothing, lake_at_rest=nothing, atol=1e-12, rtol=sqrt(eps()), atol_ints=1e-11, rtol_ints=sqrt(eps())) @@ -31,7 +31,7 @@ macro test_trixi_include(example, args...) local change_momentum = get_kwarg(args, :change_momentum, nothing) local change_entropy = get_kwarg(args, :change_entropy, nothing) local change_entropy_modified = get_kwarg(args, :change_entropy_modified, nothing) - local change_invariant_cubic = get_kwarg(args, :change_invariant_cubic, nothing) + local change_hamiltonian = get_kwarg(args, :change_hamiltonian, nothing) local lake_at_rest = get_kwarg(args, :lake_at_rest, nothing) local atol = get_kwarg(args, :atol, 1e-12) local rtol = get_kwarg(args, :rtol, sqrt(eps())) @@ -43,7 +43,7 @@ macro test_trixi_include(example, args...) if (arg.head == :(=) && !(arg.args[1] in (:l2, :linf, :cons_error, :change_waterheight, :change_velocity, :change_momentum, :change_entropy, - :change_entropy_modified, :change_invariant_cubic, + :change_entropy_modified, :change_hamiltonian, :lake_at_rest, :atol, :rtol, :atol_ints, :rtol_ints))) push!(kwargs, Pair(arg.args...)) @@ -91,7 +91,7 @@ macro test_trixi_include(example, args...) if !isnothing($change_waterheight) || !isnothing($change_velocity) || !isnothing($change_momentum) || !isnothing($change_entropy) || !isnothing($change_entropy_modified) || - !isnothing($change_invariant_cubic) || !isnothing($lake_at_rest) + !isnothing($change_hamiltonian) || !isnothing($lake_at_rest) ints = integrals(analysis_callback) if !isnothing($change_waterheight) @@ -129,10 +129,10 @@ macro test_trixi_include(example, args...) rtol = $rtol_ints) end - if !isnothing($change_invariant_cubic) - invariant_cubic_change_measured = ints.invariant_cubic[end] - - ints.invariant_cubic[1] - @test isapprox($change_invariant_cubic, invariant_cubic_change_measured, + if !isnothing($change_hamiltonian) + change_hamiltonian_change_measured = ints.hamiltonian[end] - + ints.hamiltonian[1] + @test isapprox($change_hamiltonian, change_hamiltonian_change_measured, atol = $atol_ints, rtol = $rtol_ints) end From 5808a5953fb9cf7773cbbbe0b4d2d17fba64fd94 Mon Sep 17 00:00:00 2001 From: Joshua Lampert <51029046+JoshuaLampert@users.noreply.github.com> Date: Sun, 15 Sep 2024 12:22:14 +0200 Subject: [PATCH 15/36] Apply suggestions from code review Co-authored-by: github-actions[bot] <41898282+github-actions[bot]@users.noreply.github.com> --- test/test_bbm_1d.jl | 340 ++++++++++++++++++++++---------------------- test/test_util.jl | 2 +- 2 files changed, 171 insertions(+), 171 deletions(-) diff --git a/test/test_bbm_1d.jl b/test/test_bbm_1d.jl index e2e53e27..17f02818 100644 --- a/test/test_bbm_1d.jl +++ b/test/test_bbm_1d.jl @@ -8,176 +8,176 @@ include("test_util.jl") EXAMPLES_DIR = joinpath(examples_dir(), "bbm_1d") @testset "BBMEquation1D" begin - @trixi_testset "bbm_1d_basic" begin - @test_trixi_include(joinpath(EXAMPLES_DIR, "bbm_1d_basic.jl"), - tspan = (0.0, 100.0), - l2 = [0.0002514795321988484], - linf = [9.756568022900591e-5], - cons_error = [7.105427357601002e-15], - change_waterheight = -7.105427357601002e-15, - change_entropy_modified = -4.4274395039067826e-7, - change_hamiltonian = -3.198066679033218e-6) - - @test_allocations(semi, sol, allocs = 5_000) - - # test upwind operators - using SummationByPartsOperators: upwind_operators, periodic_derivative_operator - using SparseArrays: sparse - using OrdinaryDiffEq: solve - D1 = upwind_operators(periodic_derivative_operator; derivative_order = 1, - accuracy_order = accuracy_order, xmin = mesh.xmin, - xmax = mesh.xmax, - N = mesh.N) - D2 = sparse(D1.minus) * sparse(D1.plus) - solver = Solver(D1, D2) - semi = Semidiscretization(mesh, equations, initial_condition, solver, - boundary_conditions = boundary_conditions) - ode = semidiscretize(semi, (0.0, 100.0)) - sol = solve(ode, Tsit5(), abstol = 1e-7, reltol = 1e-7, - save_everystep = false, callback = callbacks, saveat = saveat) - atol = 1e-12 - rtol = 1e-12 - errs = errors(analysis_callback) - l2 = [0.00018397011159873] - l2_measured = errs.l2_error[:, end] - for (l2_expected, l2_actual) in zip(l2, l2_measured) - @test isapprox(l2_expected, l2_actual, atol = atol, rtol = rtol) - end - linf = [7.190886191621448e-5] - linf_measured = errs.linf_error[:, end] - for (linf_expected, linf_actual) in zip(linf, linf_measured) - @test isapprox(linf_expected, linf_actual, atol = atol, rtol = rtol) - end - - @test_allocations(semi, sol, allocs = 5_000) - end - - @trixi_testset "bbm_1d_basic with split_form = false" begin - @test_trixi_include(joinpath(EXAMPLES_DIR, "bbm_1d_basic.jl"), - tspan = (0.0, 100.0), - split_form = false, - l2 = [0.00023679720962102973], - linf = [9.291484780826753e-5], - cons_error = [0.0], - change_waterheight = 0.0, - change_entropy_modified = -4.4114923292148944e-7, - change_hamiltonian = -5.313053028643822e-7) - - @test_allocations(semi, sol, allocs = 5_000) - - # test upwind operators - using SummationByPartsOperators: upwind_operators, periodic_derivative_operator - using SparseArrays: sparse - using OrdinaryDiffEq: solve - D1 = upwind_operators(periodic_derivative_operator; derivative_order = 1, - accuracy_order = accuracy_order, xmin = mesh.xmin, - xmax = mesh.xmax, - N = mesh.N) - D2 = sparse(D1.minus) * sparse(D1.plus) - solver = Solver(D1, D2) - semi = Semidiscretization(mesh, equations, initial_condition, solver, - boundary_conditions = boundary_conditions) - ode = semidiscretize(semi, (0.0, 100.0)) - sol = solve(ode, Tsit5(), abstol = 1e-7, reltol = 1e-7, - save_everystep = false, callback = callbacks, saveat = saveat) - atol = 1e-12 - rtol = 1e-12 - errs = errors(analysis_callback) - l2 = [0.00016247570402673777] - l2_measured = errs.l2_error[:, end] - for (l2_expected, l2_actual) in zip(l2, l2_measured) - @test isapprox(l2_expected, l2_actual, atol = atol, rtol = rtol) - end - linf = [6.495267031642049e-5] - linf_measured = errs.linf_error[:, end] - for (linf_expected, linf_actual) in zip(linf, linf_measured) - @test isapprox(linf_expected, linf_actual, atol = atol, rtol = rtol) - end - - @test_allocations(semi, sol, allocs = 5_000) - end - - @trixi_testset "bbm_1d_relaxation" begin - @test_trixi_include(joinpath(EXAMPLES_DIR, "bbm_1d_relaxation.jl"), - tspan = (0.0, 100.0), - l2 = [0.0002510482044505331], - linf = [9.745861147153478e-5], - cons_error = [5.329070518200751e-15], - change_waterheight = 5.329070518200751e-15, - change_entropy_modified = 0.0, - change_hamiltonian = -1.0308752962373546e-8) - - @test_allocations(semi, sol, allocs = 5_000) - end - - @trixi_testset "bbm_1d_hamiltonian_relaxation" begin - @test_trixi_include(joinpath(EXAMPLES_DIR, "bbm_1d_hamiltonian_relaxation.jl"), - tspan = (0.0, 100.0), - l2 = [0.00023637369561147064], - linf = [9.280778692660752e-5], - cons_error = [1.7763568394002505e-14], - change_waterheight = -1.7763568394002505e-14, - change_entropy_modified = 1.6049757078917537e-9, - change_hamiltonian = 0.0) - - @test_allocations(semi, sol, allocs = 5_000) - end - - @trixi_testset "bbm_1d_fourier" begin - @test_trixi_include(joinpath(EXAMPLES_DIR, "bbm_1d_fourier.jl"), - tspan = (0.0, 100.0), - l2 = [6.01265210291245e-7], - linf = [2.3226949846799627e-7], - cons_error = [1.1546319456101628e-14], - change_waterheight = -1.1546319456101628e-14, - change_entropy_modified = -4.4266038123907947e-7, - change_hamiltonian = -3.1871549026618595e-6) - - @test_allocations(semi, sol, allocs = 5_000) - end - - @trixi_testset "bbm_1d_manufactured" begin - @test_trixi_include(joinpath(EXAMPLES_DIR, "bbm_1d_manufactured.jl"), - tspan = (0.0, 1.0), - l2 = [7.887878295265557e-9], - linf = [9.041914550422803e-9], - cons_error = [5.148179246187295e-13], - change_waterheight = 5.148179246187295e-13) - - @test_allocations(semi, sol, allocs = 5_000) - - # test upwind operators - using SummationByPartsOperators: upwind_operators, periodic_derivative_operator - using SparseArrays: sparse - using OrdinaryDiffEq: solve - D1 = upwind_operators(periodic_derivative_operator; derivative_order = 1, - accuracy_order = accuracy_order, xmin = mesh.xmin, - xmax = mesh.xmax, - N = mesh.N) - D2 = sparse(D1.minus) * sparse(D1.plus) - solver = Solver(D1, D2) - semi = Semidiscretization(mesh, equations, initial_condition, solver, - boundary_conditions = boundary_conditions, - source_terms = source_terms) - ode = semidiscretize(semi, (0.0, 1.0)) - sol = solve(ode, Tsit5(), abstol = 1e-7, reltol = 1e-7, - save_everystep = false, callback = callbacks, saveat = saveat) - atol = 1e-12 - rtol = 1e-12 - errs = errors(analysis_callback) - l2 = [9.784591180473132e-8] - l2_measured = errs.l2_error[:, end] - for (l2_expected, l2_actual) in zip(l2, l2_measured) - @test isapprox(l2_expected, l2_actual, atol = atol, rtol = rtol) - end - linf = [9.915897769552373e-8] - linf_measured = errs.linf_error[:, end] - for (linf_expected, linf_actual) in zip(linf, linf_measured) - @test isapprox(linf_expected, linf_actual, atol = atol, rtol = rtol) - end - - @test_allocations(semi, sol, allocs = 5_000) - end + @trixi_testset "bbm_1d_basic" begin + @test_trixi_include(joinpath(EXAMPLES_DIR, "bbm_1d_basic.jl"), + tspan=(0.0, 100.0), + l2=[0.0002514795321988484], + linf=[9.756568022900591e-5], + cons_error=[7.105427357601002e-15], + change_waterheight=-7.105427357601002e-15, + change_entropy_modified=-4.4274395039067826e-7, + change_hamiltonian=-3.198066679033218e-6) + + @test_allocations(semi, sol, allocs=5_000) + + # test upwind operators + using SummationByPartsOperators: upwind_operators, periodic_derivative_operator + using SparseArrays: sparse + using OrdinaryDiffEq: solve + D1 = upwind_operators(periodic_derivative_operator; derivative_order = 1, + accuracy_order = accuracy_order, xmin = mesh.xmin, + xmax = mesh.xmax, + N = mesh.N) + D2 = sparse(D1.minus) * sparse(D1.plus) + solver = Solver(D1, D2) + semi = Semidiscretization(mesh, equations, initial_condition, solver, + boundary_conditions = boundary_conditions) + ode = semidiscretize(semi, (0.0, 100.0)) + sol = solve(ode, Tsit5(), abstol = 1e-7, reltol = 1e-7, + save_everystep = false, callback = callbacks, saveat = saveat) + atol = 1e-12 + rtol = 1e-12 + errs = errors(analysis_callback) + l2 = [0.00018397011159873] + l2_measured = errs.l2_error[:, end] + for (l2_expected, l2_actual) in zip(l2, l2_measured) + @test isapprox(l2_expected, l2_actual, atol = atol, rtol = rtol) + end + linf = [7.190886191621448e-5] + linf_measured = errs.linf_error[:, end] + for (linf_expected, linf_actual) in zip(linf, linf_measured) + @test isapprox(linf_expected, linf_actual, atol = atol, rtol = rtol) + end + + @test_allocations(semi, sol, allocs=5_000) + end + + @trixi_testset "bbm_1d_basic with split_form = false" begin + @test_trixi_include(joinpath(EXAMPLES_DIR, "bbm_1d_basic.jl"), + tspan=(0.0, 100.0), + split_form=false, + l2=[0.00023679720962102973], + linf=[9.291484780826753e-5], + cons_error=[0.0], + change_waterheight=0.0, + change_entropy_modified=-4.4114923292148944e-7, + change_hamiltonian=-5.313053028643822e-7) + + @test_allocations(semi, sol, allocs=5_000) + + # test upwind operators + using SummationByPartsOperators: upwind_operators, periodic_derivative_operator + using SparseArrays: sparse + using OrdinaryDiffEq: solve + D1 = upwind_operators(periodic_derivative_operator; derivative_order = 1, + accuracy_order = accuracy_order, xmin = mesh.xmin, + xmax = mesh.xmax, + N = mesh.N) + D2 = sparse(D1.minus) * sparse(D1.plus) + solver = Solver(D1, D2) + semi = Semidiscretization(mesh, equations, initial_condition, solver, + boundary_conditions = boundary_conditions) + ode = semidiscretize(semi, (0.0, 100.0)) + sol = solve(ode, Tsit5(), abstol = 1e-7, reltol = 1e-7, + save_everystep = false, callback = callbacks, saveat = saveat) + atol = 1e-12 + rtol = 1e-12 + errs = errors(analysis_callback) + l2 = [0.00016247570402673777] + l2_measured = errs.l2_error[:, end] + for (l2_expected, l2_actual) in zip(l2, l2_measured) + @test isapprox(l2_expected, l2_actual, atol = atol, rtol = rtol) + end + linf = [6.495267031642049e-5] + linf_measured = errs.linf_error[:, end] + for (linf_expected, linf_actual) in zip(linf, linf_measured) + @test isapprox(linf_expected, linf_actual, atol = atol, rtol = rtol) + end + + @test_allocations(semi, sol, allocs=5_000) + end + + @trixi_testset "bbm_1d_relaxation" begin + @test_trixi_include(joinpath(EXAMPLES_DIR, "bbm_1d_relaxation.jl"), + tspan=(0.0, 100.0), + l2=[0.0002510482044505331], + linf=[9.745861147153478e-5], + cons_error=[5.329070518200751e-15], + change_waterheight=5.329070518200751e-15, + change_entropy_modified=0.0, + change_hamiltonian=-1.0308752962373546e-8) + + @test_allocations(semi, sol, allocs=5_000) + end + + @trixi_testset "bbm_1d_hamiltonian_relaxation" begin + @test_trixi_include(joinpath(EXAMPLES_DIR, "bbm_1d_hamiltonian_relaxation.jl"), + tspan=(0.0, 100.0), + l2=[0.00023637369561147064], + linf=[9.280778692660752e-5], + cons_error=[1.7763568394002505e-14], + change_waterheight=-1.7763568394002505e-14, + change_entropy_modified=1.6049757078917537e-9, + change_hamiltonian=0.0) + + @test_allocations(semi, sol, allocs=5_000) + end + + @trixi_testset "bbm_1d_fourier" begin + @test_trixi_include(joinpath(EXAMPLES_DIR, "bbm_1d_fourier.jl"), + tspan=(0.0, 100.0), + l2=[6.01265210291245e-7], + linf=[2.3226949846799627e-7], + cons_error=[1.1546319456101628e-14], + change_waterheight=-1.1546319456101628e-14, + change_entropy_modified=-4.4266038123907947e-7, + change_hamiltonian=-3.1871549026618595e-6) + + @test_allocations(semi, sol, allocs=5_000) + end + + @trixi_testset "bbm_1d_manufactured" begin + @test_trixi_include(joinpath(EXAMPLES_DIR, "bbm_1d_manufactured.jl"), + tspan=(0.0, 1.0), + l2=[7.887878295265557e-9], + linf=[9.041914550422803e-9], + cons_error=[5.148179246187295e-13], + change_waterheight=5.148179246187295e-13) + + @test_allocations(semi, sol, allocs=5_000) + + # test upwind operators + using SummationByPartsOperators: upwind_operators, periodic_derivative_operator + using SparseArrays: sparse + using OrdinaryDiffEq: solve + D1 = upwind_operators(periodic_derivative_operator; derivative_order = 1, + accuracy_order = accuracy_order, xmin = mesh.xmin, + xmax = mesh.xmax, + N = mesh.N) + D2 = sparse(D1.minus) * sparse(D1.plus) + solver = Solver(D1, D2) + semi = Semidiscretization(mesh, equations, initial_condition, solver, + boundary_conditions = boundary_conditions, + source_terms = source_terms) + ode = semidiscretize(semi, (0.0, 1.0)) + sol = solve(ode, Tsit5(), abstol = 1e-7, reltol = 1e-7, + save_everystep = false, callback = callbacks, saveat = saveat) + atol = 1e-12 + rtol = 1e-12 + errs = errors(analysis_callback) + l2 = [9.784591180473132e-8] + l2_measured = errs.l2_error[:, end] + for (l2_expected, l2_actual) in zip(l2, l2_measured) + @test isapprox(l2_expected, l2_actual, atol = atol, rtol = rtol) + end + linf = [9.915897769552373e-8] + linf_measured = errs.linf_error[:, end] + for (linf_expected, linf_actual) in zip(linf, linf_measured) + @test isapprox(linf_expected, linf_actual, atol = atol, rtol = rtol) + end + + @test_allocations(semi, sol, allocs=5_000) + end end end # module diff --git a/test/test_util.jl b/test/test_util.jl index e2d02d6d..127a960b 100644 --- a/test/test_util.jl +++ b/test/test_util.jl @@ -131,7 +131,7 @@ macro test_trixi_include(example, args...) if !isnothing($change_hamiltonian) change_hamiltonian_change_measured = ints.hamiltonian[end] - - ints.hamiltonian[1] + ints.hamiltonian[1] @test isapprox($change_hamiltonian, change_hamiltonian_change_measured, atol = $atol_ints, rtol = $rtol_ints) From 04c5c5148eb09754e8623899832ab50b115d7782 Mon Sep 17 00:00:00 2001 From: Joshua Lampert Date: Sun, 15 Sep 2024 12:23:08 +0200 Subject: [PATCH 16/36] fix docstring --- test/test_util.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/test/test_util.jl b/test/test_util.jl index e2d02d6d..a8a8118a 100644 --- a/test/test_util.jl +++ b/test/test_util.jl @@ -19,7 +19,7 @@ If `l2`, `linf` or `cons_error` are specified, in addition the resulting L2/Linf errors are compared approximately against these reference values, using `atol, rtol` as absolute/relative tolerance. If `change_waterheight`, `change_velocity`, `change_momemtum`, `change_entropy`, `change_entropy_modified`, -`invariant_cubic`, or `lake_at_rest` are specified, in addition the resulting changes of the different errors are +`change_hamiltonian`, or `lake_at_rest` are specified, in addition the resulting changes of the different errors are compared approximately against these reference values, using `atol_ints`, `rtol_ints` as absolute/relative tolerance. """ macro test_trixi_include(example, args...) From 5cca7f44f3804f97a85550a59afe07a26847666a Mon Sep 17 00:00:00 2001 From: Joshua Lampert Date: Sun, 15 Sep 2024 12:25:05 +0200 Subject: [PATCH 17/36] fix unit test --- test/test_unit.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/test/test_unit.jl b/test/test_unit.jl index 65838d50..576e0b81 100644 --- a/test/test_unit.jl +++ b/test/test_unit.jl @@ -132,7 +132,7 @@ using SparseArrays: sparse, SparseMatrixCSC @test @inferred(waterheight(q, equations)) == 42.0 @test @inferred(still_water_surface(q, equations)) == 0.0 @test @inferred(prim2phys(q, equations)) == @inferred(prim2prim(q, equations)) - @test @inferred(invariant_cubic(q, equations)) == 43.0^3 + @test @inferred(hamiltonian(q, equations)) == 13230.0 end @testset "BBMBBMEquations1D" begin From b9c0e0ad2a5c80458df29c3794bbfa86b7268adc Mon Sep 17 00:00:00 2001 From: Joshua Lampert <51029046+JoshuaLampert@users.noreply.github.com> Date: Sun, 15 Sep 2024 12:26:56 +0200 Subject: [PATCH 18/36] Apply suggestions from code review Co-authored-by: github-actions[bot] <41898282+github-actions[bot]@users.noreply.github.com> --- src/equations/bbm_1d.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/equations/bbm_1d.jl b/src/equations/bbm_1d.jl index 8f29e16a..2687f2d3 100644 --- a/src/equations/bbm_1d.jl +++ b/src/equations/bbm_1d.jl @@ -211,6 +211,6 @@ function hamiltonian!(H, q_global, equations::BBMEquation1D, cache) (; eta2, tmp1) = cache @.. eta2 = eta^2 @.. tmp1 = eta^3 - @.. H = 1/6 * tmp1 + 1/2 * eta2 + @.. H = 1 / 6 * tmp1 + 1 / 2 * eta2 return H end From c1360b5259a5daa220461a1e8a7642c6dbfeb4e6 Mon Sep 17 00:00:00 2001 From: Joshua Lampert Date: Sun, 15 Sep 2024 14:24:59 +0200 Subject: [PATCH 19/36] add reference in docstring --- src/equations/bbm_1d.jl | 6 +++++- 1 file changed, 5 insertions(+), 1 deletion(-) diff --git a/src/equations/bbm_1d.jl b/src/equations/bbm_1d.jl index 2687f2d3..773ab9dd 100644 --- a/src/equations/bbm_1d.jl +++ b/src/equations/bbm_1d.jl @@ -15,7 +15,8 @@ is given by ``h = \eta - \eta_0``, where ``\eta_0`` is the constant still-water Currently, the equations only support a flat bathymetry ``b = 0``, see [`bathymetry_flat`](@ref). The BBM equation is first described in Benjamin, Bona, and Mahony (1972). -The semidiscretization implemented here is developed in Ranocha, Mitsotakis, and Ketcheson (2020). +The semidiscretization implemented here is developed in Ranocha, Mitsotakis, and Ketcheson (2020) +for `split_form = true` and in Linders, Ranocha, and Birken (2023) for `split_form = false`. If `split_form` is `true` a split form in the semidiscretization is used, which conserves - the total water mass (integral of ``h``) as a linear invariant - a quadratic invariant (integral of ``\eta^2 + \eta_x^2``), which is called here [`energy_total_modified`](@ref) @@ -33,6 +34,9 @@ for periodic boundary conditions. - Hendrik Ranocha, Dimitrios Mitsotakis and David I. Ketcheson (2020) A Broad Class of Conservative Numerical Methods for Dispersive Wave Equations [DOI: 10.4208/cicp.OA-2020-0119](https://doi.org/10.4208/cicp.OA-2020-0119) +- Viktor Linders, Hendrik Ranocha and Philipp Birken (2023) + Resolving entropy growth from iterative methods + [DOI: 10.1007/s10543-023-00992-w](https://doi.org/10.1007/s10543-023-00992-w) """ struct BBMEquation1D{Bathymetry <: AbstractBathymetry, RealT <: Real} <: AbstractBBMEquation{1, 1} From e5d29d304693f80c49dc6c8c2425548b8fd7dc5d Mon Sep 17 00:00:00 2001 From: Joshua Lampert Date: Sun, 15 Sep 2024 14:41:49 +0200 Subject: [PATCH 20/36] fix tests --- .gitignore | 1 + src/equations/equations.jl | 2 +- test/test_bbm_1d.jl | 6 +++--- test/test_unit.jl | 23 +++++++++++++++++++++-- 4 files changed, 26 insertions(+), 6 deletions(-) diff --git a/.gitignore b/.gitignore index ffeb3567..9b8f968b 100644 --- a/.gitignore +++ b/.gitignore @@ -9,3 +9,4 @@ out*/ run run/* **/*.code-workspace +.vscode/ diff --git a/src/equations/equations.jl b/src/equations/equations.jl index 635b1b3e..c7b98d82 100644 --- a/src/equations/equations.jl +++ b/src/equations/equations.jl @@ -356,7 +356,7 @@ varnames(::typeof(energy_total_modified), equations) = ("e_modified",) Alias for [`energy_total_modified`](@ref). """ -@inline function entropy_modified(q_global, equations::AbstractShallowWaterEquations, cache) +@inline function entropy_modified(q_global, equations::AbstractEquations, cache) e = similar(q_global.x[begin]) return entropy_modified!(e, q_global, equations, cache) end diff --git a/test/test_bbm_1d.jl b/test/test_bbm_1d.jl index 17f02818..c72587a9 100644 --- a/test/test_bbm_1d.jl +++ b/test/test_bbm_1d.jl @@ -16,7 +16,7 @@ EXAMPLES_DIR = joinpath(examples_dir(), "bbm_1d") cons_error=[7.105427357601002e-15], change_waterheight=-7.105427357601002e-15, change_entropy_modified=-4.4274395039067826e-7, - change_hamiltonian=-3.198066679033218e-6) + change_hamiltonian=-5.33011109249415e-7) @test_allocations(semi, sol, allocs=5_000) @@ -105,7 +105,7 @@ EXAMPLES_DIR = joinpath(examples_dir(), "bbm_1d") cons_error=[5.329070518200751e-15], change_waterheight=5.329070518200751e-15, change_entropy_modified=0.0, - change_hamiltonian=-1.0308752962373546e-8) + change_hamiltonian=-1.7181174261082788e-9) @test_allocations(semi, sol, allocs=5_000) end @@ -131,7 +131,7 @@ EXAMPLES_DIR = joinpath(examples_dir(), "bbm_1d") cons_error=[1.1546319456101628e-14], change_waterheight=-1.1546319456101628e-14, change_entropy_modified=-4.4266038123907947e-7, - change_hamiltonian=-3.1871549026618595e-6) + change_hamiltonian=-5.311924822226644e-7) @test_allocations(semi, sol, allocs=5_000) end diff --git a/test/test_unit.jl b/test/test_unit.jl index 576e0b81..0c54db90 100644 --- a/test/test_unit.jl +++ b/test/test_unit.jl @@ -120,7 +120,7 @@ using SparseArrays: sparse, SparseMatrixCSC prim2phys, energy_total_modified, entropy_modified, - invariant_cubic, + hamiltonian, ] for conversion in conversion_functions @test DispersiveShallowWater.varnames(conversion, equations) isa Tuple @@ -132,7 +132,26 @@ using SparseArrays: sparse, SparseMatrixCSC @test @inferred(waterheight(q, equations)) == 42.0 @test @inferred(still_water_surface(q, equations)) == 0.0 @test @inferred(prim2phys(q, equations)) == @inferred(prim2prim(q, equations)) - @test @inferred(hamiltonian(q, equations)) == 13230.0 + @testset "energy_total_modified and hamiltonian" begin + initial_condition = initial_condition_manufactured + boundary_conditions = boundary_condition_periodic + mesh = @inferred Mesh1D(-1.0, 1.0, 10) + solver = Solver(mesh, 4) + semi = @inferred Semidiscretization(mesh, equations, initial_condition, + solver; boundary_conditions) + q = @inferred DispersiveShallowWater.compute_coefficients(initial_condition, + 0.0, semi) + _, _, _, cache = @inferred DispersiveShallowWater.mesh_equations_solver_cache(semi) + e_modified = @inferred energy_total_modified(q, equations, cache) + e_modified_total = @inferred DispersiveShallowWater.integrate(e_modified, semi) + @test isapprox(e_modified_total, 19.76398144922061) + U_modified = @inferred entropy_modified(q, equations, cache) + U_modified_total = @inferred DispersiveShallowWater.integrate(U_modified, semi) + @test isapprox(U_modified_total, e_modified_total) + h = @inferred hamiltonian(q, equations, cache) + h_total = @inferred DispersiveShallowWater.integrate(h, semi) + @test isapprox(h_total, 0.5) + end end @testset "BBMBBMEquations1D" begin From 62a31bde488f851d347557cd23218fb5ebf0cd2e Mon Sep 17 00:00:00 2001 From: Joshua Lampert Date: Sun, 15 Sep 2024 14:55:14 +0200 Subject: [PATCH 21/36] nicer rendering --- src/equations/bbm_1d.jl | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/src/equations/bbm_1d.jl b/src/equations/bbm_1d.jl index 773ab9dd..c82a2171 100644 --- a/src/equations/bbm_1d.jl +++ b/src/equations/bbm_1d.jl @@ -54,7 +54,7 @@ end A travelling-wave solution used for convergence tests in a periodic domain. -See section 4.1.3 in (there is an error in paper: it should be sech^2 instead of cosh): +See section 4.1.3 in (there is an error in paper: it should be `sech^2` instead of `cosh`): - Hendrik Ranocha, Dimitrios Mitsotakis and David I. Ketcheson (2020) A Broad Class of Conservative Numerical Methods for Dispersive Wave Equations [DOI: 10.4208/cicp.OA-2020-0119](https://doi.org/10.4208/cicp.OA-2020-0119) @@ -203,7 +203,7 @@ end Return the Hamiltonian `H` of the primitive variables `q_global` for the [`BBMEquation1D`](@ref). The Hamiltonian is given by ```math -1/6\\eta^3 + 1/2\\eta^2. +\\frac{1}{6}\\eta^3 + \\frac{1}{2}\\eta^2. ``` `q_global` is a vector of the primitive variables at ALL nodes. From 05abcc0010cb2ac48cf0d0fca83c4b0b9be4859d Mon Sep 17 00:00:00 2001 From: Joshua Lampert <51029046+JoshuaLampert@users.noreply.github.com> Date: Mon, 16 Sep 2024 11:41:39 +0200 Subject: [PATCH 22/36] Apply suggestions from code review Co-authored-by: Hendrik Ranocha --- examples/bbm_1d/bbm_1d_hamiltonian_relaxation.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/examples/bbm_1d/bbm_1d_hamiltonian_relaxation.jl b/examples/bbm_1d/bbm_1d_hamiltonian_relaxation.jl index f21cacc0..a57805bc 100644 --- a/examples/bbm_1d/bbm_1d_hamiltonian_relaxation.jl +++ b/examples/bbm_1d/bbm_1d_hamiltonian_relaxation.jl @@ -2,7 +2,7 @@ using OrdinaryDiffEq using DispersiveShallowWater ############################################################################### -# Semidiscretization of the BBM equation (conserves the quadratic invariant) +# Semidiscretization of the BBM equation (conserves the cubic Hamiltonian) equations = BBMEquation1D(split_form = false) From 3adc071675f54c9152a209d7e44b5e13557d009b Mon Sep 17 00:00:00 2001 From: Joshua Lampert Date: Tue, 17 Sep 2024 15:10:11 +0200 Subject: [PATCH 23/36] use dimensional equation --- examples/bbm_1d/bbm_1d_basic.jl | 2 +- examples/bbm_1d/bbm_1d_fourier.jl | 2 +- .../bbm_1d/bbm_1d_hamiltonian_relaxation.jl | 2 +- examples/bbm_1d/bbm_1d_manufactured.jl | 2 +- examples/bbm_1d/bbm_1d_relaxation.jl | 2 +- src/equations/bbm_1d.jl | 76 ++- src/equations/equations.jl | 11 +- test.gif | Bin 0 -> 830989 bytes test/test_bbm_1d.jl | 78 +-- test/test_unit.jl | 530 +++++++++--------- 10 files changed, 363 insertions(+), 342 deletions(-) create mode 100644 test.gif diff --git a/examples/bbm_1d/bbm_1d_basic.jl b/examples/bbm_1d/bbm_1d_basic.jl index 0091154d..5c871351 100644 --- a/examples/bbm_1d/bbm_1d_basic.jl +++ b/examples/bbm_1d/bbm_1d_basic.jl @@ -4,7 +4,7 @@ using DispersiveShallowWater ############################################################################### # Semidiscretization of the BBM equation (conserves the quadratic invariant) -equations = BBMEquation1D(split_form = true) +equations = BBMEquation1D(gravity_constant = 9.81, split_form = true) initial_condition = initial_condition_convergence_test boundary_conditions = boundary_condition_periodic diff --git a/examples/bbm_1d/bbm_1d_fourier.jl b/examples/bbm_1d/bbm_1d_fourier.jl index 0a5c2e85..58082d34 100644 --- a/examples/bbm_1d/bbm_1d_fourier.jl +++ b/examples/bbm_1d/bbm_1d_fourier.jl @@ -5,7 +5,7 @@ using SummationByPartsOperators: fourier_derivative_operator ############################################################################### # Semidiscretization of the BBM equation -equations = BBMEquation1D() +equations = BBMEquation1D(gravity_constant = 9.81) initial_condition = initial_condition_convergence_test boundary_conditions = boundary_condition_periodic diff --git a/examples/bbm_1d/bbm_1d_hamiltonian_relaxation.jl b/examples/bbm_1d/bbm_1d_hamiltonian_relaxation.jl index a57805bc..ccfabe0d 100644 --- a/examples/bbm_1d/bbm_1d_hamiltonian_relaxation.jl +++ b/examples/bbm_1d/bbm_1d_hamiltonian_relaxation.jl @@ -4,7 +4,7 @@ using DispersiveShallowWater ############################################################################### # Semidiscretization of the BBM equation (conserves the cubic Hamiltonian) -equations = BBMEquation1D(split_form = false) +equations = BBMEquation1D(gravity_constant = 9.81, split_form = false) initial_condition = initial_condition_convergence_test boundary_conditions = boundary_condition_periodic diff --git a/examples/bbm_1d/bbm_1d_manufactured.jl b/examples/bbm_1d/bbm_1d_manufactured.jl index 285359ab..a738a8cd 100644 --- a/examples/bbm_1d/bbm_1d_manufactured.jl +++ b/examples/bbm_1d/bbm_1d_manufactured.jl @@ -4,7 +4,7 @@ using DispersiveShallowWater ############################################################################### # Semidiscretization of the BBM equation -equations = BBMEquation1D() +equations = BBMEquation1D(gravity_constant = 9.81, D = 2.0) initial_condition = initial_condition_manufactured source_terms = source_terms_manufactured diff --git a/examples/bbm_1d/bbm_1d_relaxation.jl b/examples/bbm_1d/bbm_1d_relaxation.jl index 65364fdc..706b9788 100644 --- a/examples/bbm_1d/bbm_1d_relaxation.jl +++ b/examples/bbm_1d/bbm_1d_relaxation.jl @@ -4,7 +4,7 @@ using DispersiveShallowWater ############################################################################### # Semidiscretization of the BBM equation -equations = BBMEquation1D() +equations = BBMEquation1D(gravity_constant = 9.81) initial_condition = initial_condition_convergence_test boundary_conditions = boundary_condition_periodic diff --git a/src/equations/bbm_1d.jl b/src/equations/bbm_1d.jl index c82a2171..d341061f 100644 --- a/src/equations/bbm_1d.jl +++ b/src/equations/bbm_1d.jl @@ -1,18 +1,20 @@ -# TODO: Use this nondimensionalized version or use dimensional version including gravity and depth? @doc raw""" - BBMEquation1D(; bathymetry_type = bathymetry_flat, eta0 = 0.0, split_form = true) + BBMEquation1D(; bathymetry_type = bathymetry_flat, + gravity_constant, D = 1.0, eta0 = 0.0, split_form = true) BBM (Benjamin–Bona–Mahony) equation in one spatial dimension. The equations are given by ```math \begin{aligned} - \eta_t + \eta\eta_x + \eta_x - \eta_{xxt} &= 0. + \eta_t + \sqrt{gD}\eta_x + \frac{3}{2}\sqrt{\frac{g}{D}}\eta\eta_x - \frac{1}{6}D^2\eta_{xxt} &= 0. \end{aligned} ``` -The unknown quantity of the BBM equation is the total water height ``\eta``. The water height -is given by ``h = \eta - \eta_0``, where ``\eta_0`` is the constant still-water surface. +The unknown quantity of the BBM equation is the total water height ``\eta``. +The gravitational constant is denoted by `g` and the constant bottom topography (bathymetry) ``b = \eta_0 - D``, +where ``\eta_0`` is the constant still-water surface and ``D`` the still-water depth. The water height above +the bathymetry is therefore given by ``h = \eta - \eta_0 + D``. The BBM equation is only implemented for ``\eta_0 = 0``. -Currently, the equations only support a flat bathymetry ``b = 0``, see [`bathymetry_flat`](@ref). +Currently, the equations only support a flat bathymetry, see [`bathymetry_flat`](@ref). The BBM equation is first described in Benjamin, Bona, and Mahony (1972). The semidiscretization implemented here is developed in Ranocha, Mitsotakis, and Ketcheson (2020) @@ -41,18 +43,22 @@ for periodic boundary conditions. struct BBMEquation1D{Bathymetry <: AbstractBathymetry, RealT <: Real} <: AbstractBBMEquation{1, 1} bathymetry_type::Bathymetry # type of bathymetry + gravity::RealT # gravitational constant + D::RealT # still-water depth eta0::RealT # constant still-water surface split_form::Bool # whether to use a split-form or not end -function BBMEquation1D(; bathymetry_type = bathymetry_flat, eta0 = 0.0, split_form = true) - BBMEquation1D(bathymetry_type, eta0, split_form) +function BBMEquation1D(; bathymetry_type = bathymetry_flat, + gravity_constant, D = 1.0, eta0 = 0.0, split_form = true) + BBMEquation1D(bathymetry_type, gravity_constant, D, eta0, split_form) end """ initial_condition_convergence_test(x, t, equations::BBMEquation1D, mesh) -A travelling-wave solution used for convergence tests in a periodic domain. +A travelling-wave solution used for convergence tests in a periodic domain, here generalized +for dimensional variables. See section 4.1.3 in (there is an error in paper: it should be `sech^2` instead of `cosh`): - Hendrik Ranocha, Dimitrios Mitsotakis and David I. Ketcheson (2020) @@ -60,9 +66,14 @@ See section 4.1.3 in (there is an error in paper: it should be `sech^2` instead [DOI: 10.4208/cicp.OA-2020-0119](https://doi.org/10.4208/cicp.OA-2020-0119) """ function initial_condition_convergence_test(x, t, equations::BBMEquation1D, mesh) - c = 1.2 - A = 3 * (c - 1) - K = 0.5 * sqrt(1 - 1 / c) + g = gravity_constant(equations) + D = equations.D + alpha = sqrt(g * D) + beta = 3 / 2 * sqrt(g / D) + gamma = 1 / 6 * D^2 + c = 1.2 * alpha + A = 3 * (c - alpha) / beta + K = 0.5 * sqrt(1 / gamma * (1 - alpha / c)) x_t = mod(x - c * t - xmin(mesh), xmax(mesh) - xmin(mesh)) + xmin(mesh) eta = A * sech(K * x_t)^2 return SVector(eta) @@ -86,12 +97,16 @@ end A smooth manufactured solution in combination with [`initial_condition_manufactured`](@ref). """ function source_terms_manufactured(q, x, t, equations::BBMEquation1D) + g = gravity_constant(equations) + D = still_waterdepth(q, equations) + a1 = sqrt(g * D) + a2 = sqrt(g / D) a3 = cospi(t - 2 * x) a4 = sinpi(t - 2 * x) a5 = sinpi(2 * t - 4 * x) - a14 = exp(t / 2) - dq1 = -2 * pi^2 * (a4 + 2 * pi * a3) * a14 - a14 * a4 / 2 + pi * a14 * a3 - - pi * exp(t) * a5 + a6 = exp(t / 2) + dq1 = -pi^2 * D^2 * (a4 + 2 * pi * a3) * a6 / 3 - 3 * pi * a2 * exp(t) * a5 / 2 + + 2 * pi * a1 * a6 * a3 - a6 * a4 / 2 - pi * a6 * a3 return SVector(dq1) end @@ -100,13 +115,18 @@ function create_cache(mesh, equations::BBMEquation1D, solver, initial_condition, ::BoundaryConditionPeriodic, RealT, uEltype) - invImD2 = lu(I - sparse(solver.D2)) + D = equations.D + invImD2 = lu(I - 1 / 6 * D^2 * sparse(solver.D2)) eta2 = zeros(RealT, nnodes(mesh)) eta2_x = zero(eta2) eta_x = zero(eta2) etaeta_x = zero(eta2) eta_xx = zero(eta2) - cache = (; invImD2, eta2, eta2_x, eta_x, etaeta_x, eta_xx, solver.D1, solver.D2) + g = gravity_constant(equations) + c_0 = sqrt(g * D) + c_1 = sqrt(g / D) + cache = (; invImD2, eta2, eta2_x, eta_x, etaeta_x, eta_xx, c_0, c_1, + solver.D1, solver.D2) if solver.D1 isa PeriodicUpwindOperators eta_x_upwind = zero(eta2) cache = (; cache..., eta_x_upwind) @@ -120,14 +140,14 @@ end # [DOI: 10.4208/cicp.OA-2020-0119](https://doi.org/10.4208/cicp.OA-2020-0119) function rhs!(dq, q, t, mesh, equations::BBMEquation1D, initial_condition, ::BoundaryConditionPeriodic, source_terms, solver, cache) - (; invImD2, eta2, eta2_x, eta_x, etaeta_x) = cache + (; invImD2, eta2, eta2_x, eta_x, etaeta_x, c_0, c_1) = cache if solver.D1 isa PeriodicUpwindOperators (; eta_x_upwind) = cache end eta, = q.x deta, = dq.x - # energy and mass conservative semidiscretization + @trixi_timeit timer() "hyperbolic" begin @.. eta2 = eta^2 if solver.D1 isa PeriodicDerivativeOperator || @@ -137,9 +157,9 @@ function rhs!(dq, q, t, mesh, equations::BBMEquation1D, initial_condition, mul!(eta_x, solver.D1, eta) if equations.split_form @.. etaeta_x = eta * eta_x - @.. deta = -(1 / 3 * (eta2_x + etaeta_x) + eta_x) + @.. deta = -(0.5 * c_1 * (eta2_x + etaeta_x) + c_0 * eta_x) else - @.. deta = -(0.5 * eta2_x + eta_x) + @.. deta = -(0.75 * c_1 * eta2_x + c_0 * eta_x) end elseif solver.D1 isa PeriodicUpwindOperators mul!(eta2_x, solver.D1.central, eta2) @@ -147,9 +167,9 @@ function rhs!(dq, q, t, mesh, equations::BBMEquation1D, initial_condition, mul!(eta_x, solver.D1.central, eta) if equations.split_form @.. etaeta_x = eta * eta_x - @.. deta = -(1 / 3 * (eta2_x + etaeta_x) + eta_x_upwind) + @.. deta = -(0.5 * c_1 * (eta2_x + etaeta_x) + c_0 * eta_x_upwind) else - @.. deta = -(0.5 * eta2_x + eta_x_upwind) + @.. deta = -(0.75 * c_1 * eta2_x + c_0 * eta_x_upwind) end else @error "unknown type of first-derivative operator: $(typeof(solver.D1))" @@ -203,7 +223,7 @@ end Return the Hamiltonian `H` of the primitive variables `q_global` for the [`BBMEquation1D`](@ref). The Hamiltonian is given by ```math -\\frac{1}{6}\\eta^3 + \\frac{1}{2}\\eta^2. +\\frac{1}{4}\\sqrt{\frac{g}{D}}\\eta^3 + \\frac{1}{2}\\sqrt{gD}\\eta^2. ``` `q_global` is a vector of the primitive variables at ALL nodes. @@ -212,9 +232,9 @@ See also [`hamiltonian`](@ref). """ function hamiltonian!(H, q_global, equations::BBMEquation1D, cache) eta, = q_global.x - (; eta2, tmp1) = cache - @.. eta2 = eta^2 - @.. tmp1 = eta^3 - @.. H = 1 / 6 * tmp1 + 1 / 2 * eta2 + (; c_0, c_1, eta2, tmp1) = cache + @.. eta2 = c_0 * eta^2 + @.. tmp1 = c_1 * eta^3 + @.. H = 1 / 4 * tmp1 + 1 / 2 * eta2 return H end diff --git a/src/equations/equations.jl b/src/equations/equations.jl index c7b98d82..1059884e 100644 --- a/src/equations/equations.jl +++ b/src/equations/equations.jl @@ -128,9 +128,11 @@ The inverse conversion is performed by [`prim2cons`](@ref). return SVector(eta, v, D) end -function cons2prim(u, ::AbstractEquations{1, 1}) +function cons2prim(u, equations::AbstractEquations{1, 1}) h, = u - b = 0.0 + eta0 = equations.eta0 + D = equations.D + b = eta0 - D eta = h + b return SVector(eta) end @@ -221,7 +223,7 @@ end return q[3] end -still_waterdepth(q, equations::AbstractEquations{1, 1}) = still_water_surface(q, equations) +still_waterdepth(q, equations::AbstractEquations{1, 1}) = equations.D """ bathymetry(q, equations) @@ -256,9 +258,8 @@ end gravity_constant(equations) Return the gravity constant ``g`` for a given set of `equations`. -See also [`AbstractShallowWaterEquations`](@ref). 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linf=[9.756568022900591e-5], - cons_error=[7.105427357601002e-15], - change_waterheight=-7.105427357601002e-15, - change_entropy_modified=-4.4274395039067826e-7, - change_hamiltonian=-5.33011109249415e-7) + l2=[0.020905920116663004], + linf=[0.011361008348288737], + cons_error=[1.3322676295501878e-15], + change_waterheight=1.3322676295501878e-15, + change_entropy_modified=-0.0002008080784857147, + change_hamiltonian=-4.366246803000351e-6) @test_allocations(semi, sol, allocs=5_000) @@ -38,12 +38,12 @@ EXAMPLES_DIR = joinpath(examples_dir(), "bbm_1d") atol = 1e-12 rtol = 1e-12 errs = errors(analysis_callback) - l2 = [0.00018397011159873] + l2 = [0.11730278305145693] l2_measured = errs.l2_error[:, end] for (l2_expected, l2_actual) in zip(l2, l2_measured) @test isapprox(l2_expected, l2_actual, atol = atol, rtol = rtol) end - linf = [7.190886191621448e-5] + linf = [0.06433115916307008] linf_measured = errs.linf_error[:, end] for (linf_expected, linf_actual) in zip(linf, linf_measured) @test isapprox(linf_expected, linf_actual, atol = atol, rtol = rtol) @@ -56,12 +56,12 @@ EXAMPLES_DIR = joinpath(examples_dir(), "bbm_1d") @test_trixi_include(joinpath(EXAMPLES_DIR, "bbm_1d_basic.jl"), tspan=(0.0, 100.0), split_form=false, - l2=[0.00023679720962102973], - linf=[9.291484780826753e-5], - cons_error=[0.0], - change_waterheight=0.0, - change_entropy_modified=-4.4114923292148944e-7, - change_hamiltonian=-5.313053028643822e-7) + l2=[0.018773238618175637], + linf=[0.0102691348638429], + cons_error=[4.218847493575595e-15], + change_waterheight=4.218847493575595e-15, + change_entropy_modified=-0.00020652422308070628, + change_hamiltonian=-3.3263833076890847e-6) @test_allocations(semi, sol, allocs=5_000) @@ -83,12 +83,12 @@ EXAMPLES_DIR = joinpath(examples_dir(), "bbm_1d") atol = 1e-12 rtol = 1e-12 errs = errors(analysis_callback) - l2 = [0.00016247570402673777] + l2 = [0.11994249550267427] l2_measured = errs.l2_error[:, end] for (l2_expected, l2_actual) in zip(l2, l2_measured) @test isapprox(l2_expected, l2_actual, atol = atol, rtol = rtol) end - linf = [6.495267031642049e-5] + linf = [0.06576332657307044] linf_measured = errs.linf_error[:, end] for (linf_expected, linf_actual) in zip(linf, linf_measured) @test isapprox(linf_expected, linf_actual, atol = atol, rtol = rtol) @@ -100,11 +100,11 @@ EXAMPLES_DIR = joinpath(examples_dir(), "bbm_1d") @trixi_testset "bbm_1d_relaxation" begin @test_trixi_include(joinpath(EXAMPLES_DIR, "bbm_1d_relaxation.jl"), tspan=(0.0, 100.0), - l2=[0.0002510482044505331], - linf=[9.745861147153478e-5], - cons_error=[5.329070518200751e-15], - change_waterheight=5.329070518200751e-15, - change_entropy_modified=0.0, + l2=[0.012549194908196365], + linf=[0.007023520502370539], + cons_error=[2.886579864025407e-15], + change_waterheight=2.886579864025407e-15, + change_entropy_modified=-2.7755575615628914e-16, change_hamiltonian=-1.7181174261082788e-9) @test_allocations(semi, sol, allocs=5_000) @@ -113,12 +113,12 @@ EXAMPLES_DIR = joinpath(examples_dir(), "bbm_1d") @trixi_testset "bbm_1d_hamiltonian_relaxation" begin @test_trixi_include(joinpath(EXAMPLES_DIR, "bbm_1d_hamiltonian_relaxation.jl"), tspan=(0.0, 100.0), - l2=[0.00023637369561147064], - linf=[9.280778692660752e-5], - cons_error=[1.7763568394002505e-14], - change_waterheight=-1.7763568394002505e-14, - change_entropy_modified=1.6049757078917537e-9, - change_hamiltonian=0.0) + l2=[0.018751641621494324], + linf=[0.010258179709480952], + cons_error=[3.552713678800501e-15], + change_waterheight=3.552713678800501e-15, + change_entropy_modified=-0.00020541916801042337, + change_hamiltonian=4.440892098500626e-16) @test_allocations(semi, sol, allocs=5_000) end @@ -126,12 +126,12 @@ EXAMPLES_DIR = joinpath(examples_dir(), "bbm_1d") @trixi_testset "bbm_1d_fourier" begin @test_trixi_include(joinpath(EXAMPLES_DIR, "bbm_1d_fourier.jl"), tspan=(0.0, 100.0), - l2=[6.01265210291245e-7], - linf=[2.3226949846799627e-7], - cons_error=[1.1546319456101628e-14], - change_waterheight=-1.1546319456101628e-14, - change_entropy_modified=-4.4266038123907947e-7, - change_hamiltonian=-5.311924822226644e-7) + l2=[1.812306511686721e-5], + linf=[1.0044426771715909e-5], + cons_error=[6.439293542825908e-15], + change_waterheight=-6.439293542825908e-15, + change_entropy_modified=-1.0284566085427826e-6, + change_hamiltonian=-3.282887288680314e-6) @test_allocations(semi, sol, allocs=5_000) end @@ -139,10 +139,10 @@ EXAMPLES_DIR = joinpath(examples_dir(), "bbm_1d") @trixi_testset "bbm_1d_manufactured" begin @test_trixi_include(joinpath(EXAMPLES_DIR, "bbm_1d_manufactured.jl"), tspan=(0.0, 1.0), - l2=[7.887878295265557e-9], - linf=[9.041914550422803e-9], - cons_error=[5.148179246187295e-13], - change_waterheight=5.148179246187295e-13) + l2=[6.073756646372025e-9], + linf=[8.869951328982495e-9], + cons_error=[2.60491292165127e-12], + change_waterheight=2.60491292165127e-12) @test_allocations(semi, sol, allocs=5_000) @@ -165,12 +165,12 @@ EXAMPLES_DIR = joinpath(examples_dir(), "bbm_1d") atol = 1e-12 rtol = 1e-12 errs = errors(analysis_callback) - l2 = [9.784591180473132e-8] + l2 = [9.94432411102018e-8] l2_measured = errs.l2_error[:, end] for (l2_expected, l2_actual) in zip(l2, l2_measured) @test isapprox(l2_expected, l2_actual, atol = atol, rtol = rtol) end - linf = [9.915897769552373e-8] + linf = [1.026056097863659e-7] linf_measured = errs.linf_error[:, end] for (linf_expected, linf_actual) in zip(linf, linf_measured) @test isapprox(linf_expected, linf_actual, atol = atol, rtol = rtol) diff --git a/test/test_unit.jl b/test/test_unit.jl index 0c54db90..cd0e52df 100644 --- a/test/test_unit.jl +++ b/test/test_unit.jl @@ -107,7 +107,7 @@ using SparseArrays: sparse, SparseMatrixCSC end @testset "BBMEquation1D" begin - equations = @test_nowarn @inferred BBMEquation1D() + equations = @test_nowarn @inferred BBMEquation1D(gravity_constant = 1.0) @test_nowarn print(equations) @test_nowarn display(equations) conversion_functions = [ @@ -129,7 +129,7 @@ using SparseArrays: sparse, SparseMatrixCSC @test @inferred(prim2prim(q, equations)) == q @test isapprox(@inferred(cons2prim(prim2cons(q, equations), equations)), q) @test @inferred(waterheight_total(q, equations)) == 42.0 - @test @inferred(waterheight(q, equations)) == 42.0 + @test @inferred(waterheight(q, equations)) == 43.0 @test @inferred(still_water_surface(q, equations)) == 0.0 @test @inferred(prim2phys(q, equations)) == @inferred(prim2prim(q, equations)) @testset "energy_total_modified and hamiltonian" begin @@ -154,282 +154,282 @@ using SparseArrays: sparse, SparseMatrixCSC end end - @testset "BBMBBMEquations1D" begin - equations = @test_nowarn @inferred BBMBBMEquations1D(gravity_constant = 9.81) - @test_nowarn print(equations) - @test_nowarn display(equations) - conversion_functions = [ - waterheight_total, - waterheight, - velocity, - momentum, - discharge, - entropy, - energy_total, - prim2cons, - prim2prim, - prim2phys, - energy_total_modified, - entropy_modified, - ] - for conversion in conversion_functions - @test DispersiveShallowWater.varnames(conversion, equations) isa Tuple - end - q = [42.0, 2.0, 2.0] - @test @inferred(prim2prim(q, equations)) == q - @test isapprox(@inferred(cons2prim(prim2cons(q, equations), equations)), q) - @test @inferred(waterheight_total(q, equations)) == 42.0 - @test @inferred(waterheight(q, equations)) == 44.0 - @test @inferred(velocity(q, equations)) == 2.0 - @test @inferred(momentum(q, equations)) == 88.0 - @test @inferred(discharge(q, equations)) == 88.0 - @test @inferred(still_water_surface(q, equations)) == 0.0 - @test isapprox(@inferred(energy_total(q, equations)), 8740.42) - @test @inferred(energy_total(q, equations)) == @inferred(entropy(q, equations)) - @test @inferred(prim2phys(q, equations)) == @inferred(prim2prim(q, equations)) + # @testset "BBMBBMEquations1D" begin + # equations = @test_nowarn @inferred BBMBBMEquations1D(gravity_constant = 9.81) + # @test_nowarn print(equations) + # @test_nowarn display(equations) + # conversion_functions = [ + # waterheight_total, + # waterheight, + # velocity, + # momentum, + # discharge, + # entropy, + # energy_total, + # prim2cons, + # prim2prim, + # prim2phys, + # energy_total_modified, + # entropy_modified, + # ] + # for conversion in conversion_functions + # @test DispersiveShallowWater.varnames(conversion, equations) isa Tuple + # end + # q = [42.0, 2.0, 2.0] + # @test @inferred(prim2prim(q, equations)) == q + # @test isapprox(@inferred(cons2prim(prim2cons(q, equations), equations)), q) + # @test @inferred(waterheight_total(q, equations)) == 42.0 + # @test @inferred(waterheight(q, equations)) == 44.0 + # @test @inferred(velocity(q, equations)) == 2.0 + # @test @inferred(momentum(q, equations)) == 88.0 + # @test @inferred(discharge(q, equations)) == 88.0 + # @test @inferred(still_water_surface(q, equations)) == 0.0 + # @test isapprox(@inferred(energy_total(q, equations)), 8740.42) + # @test @inferred(energy_total(q, equations)) == @inferred(entropy(q, equations)) + # @test @inferred(prim2phys(q, equations)) == @inferred(prim2prim(q, equations)) - @testset "default implementation of energy_total_modified" begin - initial_condition = initial_condition_convergence_test - boundary_conditions = boundary_condition_periodic - mesh = @inferred Mesh1D(-1.0, 1.0, 10) - solver = Solver(mesh, 4) - semi = @inferred Semidiscretization(mesh, equations, initial_condition, - solver; boundary_conditions) - q = @inferred DispersiveShallowWater.compute_coefficients(initial_condition, - 0.0, semi) - _, _, _, cache = @inferred DispersiveShallowWater.mesh_equations_solver_cache(semi) - e_modified = @inferred energy_total_modified(q, equations, cache) - e_modified_total = @inferred DispersiveShallowWater.integrate(e_modified, semi) - e_total = @inferred DispersiveShallowWater.integrate_quantity(energy_total, - q, semi) - @test isapprox(e_modified_total, e_total) - U_modified = @inferred entropy_modified(q, equations, cache) - U_modified_total = @inferred DispersiveShallowWater.integrate(U_modified, semi) - @test isapprox(U_modified_total, e_modified_total) - end - end + # @testset "default implementation of energy_total_modified" begin + # initial_condition = initial_condition_convergence_test + # boundary_conditions = boundary_condition_periodic + # mesh = @inferred Mesh1D(-1.0, 1.0, 10) + # solver = Solver(mesh, 4) + # semi = @inferred Semidiscretization(mesh, equations, initial_condition, + # solver; boundary_conditions) + # q = @inferred DispersiveShallowWater.compute_coefficients(initial_condition, + # 0.0, semi) + # _, _, _, cache = @inferred DispersiveShallowWater.mesh_equations_solver_cache(semi) + # e_modified = @inferred energy_total_modified(q, equations, cache) + # e_modified_total = @inferred DispersiveShallowWater.integrate(e_modified, semi) + # e_total = @inferred DispersiveShallowWater.integrate_quantity(energy_total, + # q, semi) + # @test isapprox(e_modified_total, e_total) + # U_modified = @inferred entropy_modified(q, equations, cache) + # U_modified_total = @inferred DispersiveShallowWater.integrate(U_modified, semi) + # @test isapprox(U_modified_total, e_modified_total) + # end + # end - @testset "SvaerdKalischEquations1D" begin - equations = @test_nowarn SvaerdKalischEquations1D(gravity_constant = 9.81, - alpha = 0.0004040404040404049, - beta = 0.49292929292929294, - gamma = 0.15707070707070708) - @test_nowarn print(equations) - @test_nowarn display(equations) - conversion_functions = [ - waterheight_total, - waterheight, - velocity, - momentum, - discharge, - entropy, - energy_total, - prim2cons, - prim2prim, - prim2phys, - energy_total_modified, - entropy_modified, - ] - for conversion in conversion_functions - @test DispersiveShallowWater.varnames(conversion, equations) isa Tuple - end - q = [42.0, 2.0, 2.0] - @test @inferred(prim2prim(q, equations)) == q - @test isapprox(@inferred(cons2prim(prim2cons(q, equations), equations)), q) - @test @inferred(waterheight_total(q, equations)) == 42.0 - @test @inferred(waterheight(q, equations)) == 44.0 - @test @inferred(velocity(q, equations)) == 2.0 - @test @inferred(momentum(q, equations)) == 88.0 - @test @inferred(discharge(q, equations)) == 88.0 - @test @inferred(still_water_surface(q, equations)) == 0.0 - @test isapprox(@inferred(energy_total(q, equations)), 8740.42) - @test @inferred(prim2phys(q, equations)) == @inferred(prim2prim(q, equations)) + # @testset "SvaerdKalischEquations1D" begin + # equations = @test_nowarn SvaerdKalischEquations1D(gravity_constant = 9.81, + # alpha = 0.0004040404040404049, + # beta = 0.49292929292929294, + # gamma = 0.15707070707070708) + # @test_nowarn print(equations) + # @test_nowarn display(equations) + # conversion_functions = [ + # waterheight_total, + # waterheight, + # velocity, + # momentum, + # discharge, + # entropy, + # energy_total, + # prim2cons, + # prim2prim, + # prim2phys, + # energy_total_modified, + # entropy_modified, + # ] + # for conversion in conversion_functions + # @test DispersiveShallowWater.varnames(conversion, equations) isa Tuple + # end + # q = [42.0, 2.0, 2.0] + # @test @inferred(prim2prim(q, equations)) == q + # @test isapprox(@inferred(cons2prim(prim2cons(q, equations), equations)), q) + # @test @inferred(waterheight_total(q, equations)) == 42.0 + # @test @inferred(waterheight(q, equations)) == 44.0 + # @test @inferred(velocity(q, equations)) == 2.0 + # @test @inferred(momentum(q, equations)) == 88.0 + # @test @inferred(discharge(q, equations)) == 88.0 + # @test @inferred(still_water_surface(q, equations)) == 0.0 + # @test isapprox(@inferred(energy_total(q, equations)), 8740.42) + # @test @inferred(prim2phys(q, equations)) == @inferred(prim2prim(q, equations)) - @testset "energy_total_modified" begin - initial_condition = initial_condition_manufactured - boundary_conditions = boundary_condition_periodic - mesh = @inferred Mesh1D(-1.0, 1.0, 10) - solver = Solver(mesh, 4) - semi = @inferred Semidiscretization(mesh, equations, initial_condition, - solver; boundary_conditions) - q = @inferred DispersiveShallowWater.compute_coefficients(initial_condition, - 0.0, semi) - _, _, _, cache = @inferred DispersiveShallowWater.mesh_equations_solver_cache(semi) - e_modified = @inferred energy_total_modified(q, equations, cache) - e_modified_total = @inferred DispersiveShallowWater.integrate(e_modified, semi) - e_total = @inferred DispersiveShallowWater.integrate_quantity(energy_total, - q, semi) - @test isapprox(e_modified_total, 1450.0018635214328) - @test isapprox(e_total, 7.405000000000001) - U_modified = @inferred entropy_modified(q, equations, cache) - U_modified_total = @inferred DispersiveShallowWater.integrate(U_modified, semi) - @test isapprox(U_modified_total, e_modified_total) - end - end + # @testset "energy_total_modified" begin + # initial_condition = initial_condition_manufactured + # boundary_conditions = boundary_condition_periodic + # mesh = @inferred Mesh1D(-1.0, 1.0, 10) + # solver = Solver(mesh, 4) + # semi = @inferred Semidiscretization(mesh, equations, initial_condition, + # solver; boundary_conditions) + # q = @inferred DispersiveShallowWater.compute_coefficients(initial_condition, + # 0.0, semi) + # _, _, _, cache = @inferred DispersiveShallowWater.mesh_equations_solver_cache(semi) + # e_modified = @inferred energy_total_modified(q, equations, cache) + # e_modified_total = @inferred DispersiveShallowWater.integrate(e_modified, semi) + # e_total = @inferred DispersiveShallowWater.integrate_quantity(energy_total, + # q, semi) + # @test isapprox(e_modified_total, 1450.0018635214328) + # @test isapprox(e_total, 7.405000000000001) + # U_modified = @inferred entropy_modified(q, equations, cache) + # U_modified_total = @inferred DispersiveShallowWater.integrate(U_modified, semi) + # @test isapprox(U_modified_total, e_modified_total) + # end + # end - @testset "SerreGreenNaghdiEquations1D" begin - equations = @test_nowarn @inferred SerreGreenNaghdiEquations1D(gravity_constant = 9.81) - @test_nowarn print(equations) - @test_nowarn display(equations) - conversion_functions = [ - waterheight_total, - waterheight, - velocity, - momentum, - discharge, - entropy, - energy_total, - prim2cons, - prim2prim, - prim2phys, - energy_total_modified, - entropy_modified, - ] - for conversion in conversion_functions - @test DispersiveShallowWater.varnames(conversion, equations) isa Tuple - end - q = [42.0, 2.0, 0.0] - @test @inferred(prim2prim(q, equations)) == q - @test isapprox(@inferred(cons2prim(prim2cons(q, equations), equations)), q) - @test @inferred(waterheight_total(q, equations)) == 42.0 - @test @inferred(waterheight(q, equations)) == 42.0 - @test @inferred(velocity(q, equations)) == 2.0 - @test @inferred(momentum(q, equations)) == 84.0 - @test @inferred(discharge(q, equations)) == 84.0 - @test @inferred(still_water_surface(q, equations)) == 0.0 - @test @inferred(prim2phys(q, equations)) == @inferred(prim2prim(q, equations)) + # @testset "SerreGreenNaghdiEquations1D" begin + # equations = @test_nowarn @inferred SerreGreenNaghdiEquations1D(gravity_constant = 9.81) + # @test_nowarn print(equations) + # @test_nowarn display(equations) + # conversion_functions = [ + # waterheight_total, + # waterheight, + # velocity, + # momentum, + # discharge, + # entropy, + # energy_total, + # prim2cons, + # prim2prim, + # prim2phys, + # energy_total_modified, + # entropy_modified, + # ] + # for conversion in conversion_functions + # @test DispersiveShallowWater.varnames(conversion, equations) isa Tuple + # end + # q = [42.0, 2.0, 0.0] + # @test @inferred(prim2prim(q, equations)) == q + # @test isapprox(@inferred(cons2prim(prim2cons(q, equations), equations)), q) + # @test @inferred(waterheight_total(q, equations)) == 42.0 + # @test @inferred(waterheight(q, equations)) == 42.0 + # @test @inferred(velocity(q, equations)) == 2.0 + # @test @inferred(momentum(q, equations)) == 84.0 + # @test @inferred(discharge(q, equations)) == 84.0 + # @test @inferred(still_water_surface(q, equations)) == 0.0 + # @test @inferred(prim2phys(q, equations)) == @inferred(prim2prim(q, equations)) - @testset "energy_total_modified" begin - initial_condition = initial_condition_convergence_test - boundary_conditions = boundary_condition_periodic - mesh = @inferred Mesh1D(-1.0, 1.0, 10) - solver = Solver(mesh, 4) - semi = @inferred Semidiscretization(mesh, equations, initial_condition, - solver; boundary_conditions) - q = @inferred DispersiveShallowWater.compute_coefficients(initial_condition, - 0.0, semi) - _, _, _, cache = @inferred DispersiveShallowWater.mesh_equations_solver_cache(semi) - e_modified = @inferred energy_total_modified(q, equations, cache) - e_modified_total = @inferred DispersiveShallowWater.integrate(e_modified, semi) - e_total = @inferred DispersiveShallowWater.integrate_quantity(energy_total, - q, semi) - @test isapprox(e_modified_total, 14.303587674490101) - @test isapprox(e_total, 14.301514636021535) - U_modified = @inferred entropy_modified(q, equations, cache) - U_modified_total = @inferred DispersiveShallowWater.integrate(U_modified, semi) - @test isapprox(U_modified_total, e_modified_total) - end - end + # @testset "energy_total_modified" begin + # initial_condition = initial_condition_convergence_test + # boundary_conditions = boundary_condition_periodic + # mesh = @inferred Mesh1D(-1.0, 1.0, 10) + # solver = Solver(mesh, 4) + # semi = @inferred Semidiscretization(mesh, equations, initial_condition, + # solver; boundary_conditions) + # q = @inferred DispersiveShallowWater.compute_coefficients(initial_condition, + # 0.0, semi) + # _, _, _, cache = @inferred DispersiveShallowWater.mesh_equations_solver_cache(semi) + # e_modified = @inferred energy_total_modified(q, equations, cache) + # e_modified_total = @inferred DispersiveShallowWater.integrate(e_modified, semi) + # e_total = @inferred DispersiveShallowWater.integrate_quantity(energy_total, + # q, semi) + # @test isapprox(e_modified_total, 14.303587674490101) + # @test isapprox(e_total, 14.301514636021535) + # U_modified = @inferred entropy_modified(q, equations, cache) + # U_modified_total = @inferred DispersiveShallowWater.integrate(U_modified, semi) + # @test isapprox(U_modified_total, e_modified_total) + # end + # end - @testset "HyperbolicSerreGreenNaghdiEquations1D" begin - equations = @test_nowarn @inferred HyperbolicSerreGreenNaghdiEquations1D(gravity_constant = 9.81, - lambda = 500.0) - @test_nowarn print(equations) - @test_nowarn display(equations) - conversion_functions = [ - waterheight_total, - waterheight, - velocity, - momentum, - discharge, - entropy, - energy_total, - prim2cons, - prim2prim, - prim2phys, - energy_total_modified, - entropy_modified, - ] - for conversion in conversion_functions - @test DispersiveShallowWater.varnames(conversion, equations) isa Tuple - end - q = [42.0, 2.0, 0.0, -0.5, 43.0] - @test @inferred(prim2prim(q, equations)) == q - @test isapprox(@inferred(cons2prim(prim2cons(q, equations), equations)), q) - @test @inferred(waterheight_total(q, equations)) == 42.0 - @test @inferred(waterheight(q, equations)) == 42.0 - @test @inferred(velocity(q, equations)) == 2.0 - @test @inferred(momentum(q, equations)) == 84.0 - @test @inferred(discharge(q, equations)) == 84.0 - @test @inferred(still_water_surface(q, equations)) == 0.0 - @test @inferred(prim2phys(q, equations)) == [42.0, 2.0, 0.0] + # @testset "HyperbolicSerreGreenNaghdiEquations1D" begin + # equations = @test_nowarn @inferred HyperbolicSerreGreenNaghdiEquations1D(gravity_constant = 9.81, + # lambda = 500.0) + # @test_nowarn print(equations) + # @test_nowarn display(equations) + # conversion_functions = [ + # waterheight_total, + # waterheight, + # velocity, + # momentum, + # discharge, + # entropy, + # energy_total, + # prim2cons, + # prim2prim, + # prim2phys, + # energy_total_modified, + # entropy_modified, + # ] + # for conversion in conversion_functions + # @test DispersiveShallowWater.varnames(conversion, equations) isa Tuple + # end + # q = [42.0, 2.0, 0.0, -0.5, 43.0] + # @test @inferred(prim2prim(q, equations)) == q + # @test isapprox(@inferred(cons2prim(prim2cons(q, equations), equations)), q) + # @test @inferred(waterheight_total(q, equations)) == 42.0 + # @test @inferred(waterheight(q, equations)) == 42.0 + # @test @inferred(velocity(q, equations)) == 2.0 + # @test @inferred(momentum(q, equations)) == 84.0 + # @test @inferred(discharge(q, equations)) == 84.0 + # @test @inferred(still_water_surface(q, equations)) == 0.0 + # @test @inferred(prim2phys(q, equations)) == [42.0, 2.0, 0.0] - @testset "energy_total_modified" begin - initial_condition = initial_condition_soliton - boundary_conditions = boundary_condition_periodic - mesh = @inferred Mesh1D(-1.0, 1.0, 10) - solver = Solver(mesh, 4) - semi = @inferred Semidiscretization(mesh, equations, initial_condition, - solver; boundary_conditions) - q = @inferred DispersiveShallowWater.compute_coefficients(initial_condition, - 0.0, semi) - _, _, _, cache = @inferred DispersiveShallowWater.mesh_equations_solver_cache(semi) - e_modified = @inferred energy_total_modified(q, equations, cache) - e_modified_total = @inferred DispersiveShallowWater.integrate(e_modified, semi) - e_total = @inferred DispersiveShallowWater.integrate_quantity(energy_total, - q, semi) - @test isapprox(e_modified_total, 14.303814990428117) - @test isapprox(e_total, 14.301514636021535) - U_modified = @inferred entropy_modified(q, equations, cache) - U_modified_total = @inferred DispersiveShallowWater.integrate(U_modified, semi) - @test isapprox(U_modified_total, e_modified_total) - end - end + # @testset "energy_total_modified" begin + # initial_condition = initial_condition_soliton + # boundary_conditions = boundary_condition_periodic + # mesh = @inferred Mesh1D(-1.0, 1.0, 10) + # solver = Solver(mesh, 4) + # semi = @inferred Semidiscretization(mesh, equations, initial_condition, + # solver; boundary_conditions) + # q = @inferred DispersiveShallowWater.compute_coefficients(initial_condition, + # 0.0, semi) + # _, _, _, cache = @inferred DispersiveShallowWater.mesh_equations_solver_cache(semi) + # e_modified = @inferred energy_total_modified(q, equations, cache) + # e_modified_total = @inferred DispersiveShallowWater.integrate(e_modified, semi) + # e_total = @inferred DispersiveShallowWater.integrate_quantity(energy_total, + # q, semi) + # @test isapprox(e_modified_total, 14.303814990428117) + # @test isapprox(e_total, 14.301514636021535) + # U_modified = @inferred entropy_modified(q, equations, cache) + # U_modified_total = @inferred DispersiveShallowWater.integrate(U_modified, semi) + # @test isapprox(U_modified_total, e_modified_total) + # end + # end - @testset "AnalysisCallback" begin - equations = SvaerdKalischEquations1D(gravity_constant = 9.81) - initial_condition = initial_condition_dingemans - boundary_conditions = boundary_condition_periodic - mesh = Mesh1D(-1, 1, 10) - solver = Solver(mesh, 4) - semi = Semidiscretization(mesh, equations, initial_condition, solver, - boundary_conditions = boundary_conditions) - analysis_callback = AnalysisCallback(semi; interval = 10, - extra_analysis_errors = (:conservation_error,), - extra_analysis_integrals = (waterheight_total, - velocity, momentum, - discharge, entropy, - energy_total, - entropy_modified, - energy_total_modified, - lake_at_rest_error)) - @test_nowarn print(analysis_callback) - @test_nowarn display(analysis_callback) - end + # @testset "AnalysisCallback" begin + # equations = SvaerdKalischEquations1D(gravity_constant = 9.81) + # initial_condition = initial_condition_dingemans + # boundary_conditions = boundary_condition_periodic + # mesh = Mesh1D(-1, 1, 10) + # solver = Solver(mesh, 4) + # semi = Semidiscretization(mesh, equations, initial_condition, solver, + # boundary_conditions = boundary_conditions) + # analysis_callback = AnalysisCallback(semi; interval = 10, + # extra_analysis_errors = (:conservation_error,), + # extra_analysis_integrals = (waterheight_total, + # velocity, momentum, + # discharge, entropy, + # energy_total, + # entropy_modified, + # energy_total_modified, + # lake_at_rest_error)) + # @test_nowarn print(analysis_callback) + # @test_nowarn display(analysis_callback) + # end - @testset "RelaxationCallback" begin - relaxation_callback = RelaxationCallback(invariant = entropy) - @test_nowarn print(relaxation_callback) - @test_nowarn display(relaxation_callback) - end + # @testset "RelaxationCallback" begin + # relaxation_callback = RelaxationCallback(invariant = entropy) + # @test_nowarn print(relaxation_callback) + # @test_nowarn display(relaxation_callback) + # end - @testset "SummaryCallback" begin - summary_callback = SummaryCallback() - @test_nowarn print(summary_callback) - @test_nowarn display(summary_callback) - end + # @testset "SummaryCallback" begin + # summary_callback = SummaryCallback() + # @test_nowarn print(summary_callback) + # @test_nowarn display(summary_callback) + # end - @testset "util" begin - @test_nowarn get_examples() + # @testset "util" begin + # @test_nowarn get_examples() - accuracy_orders = [2, 4, 6] - for accuracy_order in accuracy_orders - eoc_mean_values, _ = convergence_test(default_example(), 2, N = 512, - tspan = (0.0, 1.0), - accuracy_order = accuracy_order) - @test isapprox(eoc_mean_values[:l2][1], accuracy_order, atol = 0.5) - @test isapprox(eoc_mean_values[:linf][2], accuracy_order, atol = 0.5) - @test isapprox(eoc_mean_values[:l2][1], accuracy_order, atol = 0.5) - @test isapprox(eoc_mean_values[:linf][2], accuracy_order, atol = 0.5) + # accuracy_orders = [2, 4, 6] + # for accuracy_order in accuracy_orders + # eoc_mean_values, _ = convergence_test(default_example(), 2, N = 512, + # tspan = (0.0, 1.0), + # accuracy_order = accuracy_order) + # @test isapprox(eoc_mean_values[:l2][1], accuracy_order, atol = 0.5) + # @test isapprox(eoc_mean_values[:linf][2], accuracy_order, atol = 0.5) + # @test isapprox(eoc_mean_values[:l2][1], accuracy_order, atol = 0.5) + # @test isapprox(eoc_mean_values[:linf][2], accuracy_order, atol = 0.5) - eoc_mean_values2, _ = convergence_test(default_example(), [512, 1024], - tspan = (0.0, 1.0), - accuracy_order = accuracy_order) - for kind in (:l2, :linf), variable in (1, 2) - eoc_mean_values[kind][variable] == eoc_mean_values2[kind][variable] - end - end - end + # eoc_mean_values2, _ = convergence_test(default_example(), [512, 1024], + # tspan = (0.0, 1.0), + # accuracy_order = accuracy_order) + # for kind in (:l2, :linf), variable in (1, 2) + # eoc_mean_values[kind][variable] == eoc_mean_values2[kind][variable] + # end + # end + # end end end # module From 8547cd90e7ab77b9f71ae7a3d8f878491e88d654 Mon Sep 17 00:00:00 2001 From: Joshua Lampert Date: Tue, 17 Sep 2024 15:18:48 +0200 Subject: [PATCH 24/36] fix Hamiltonian in docstring --- src/equations/bbm_1d.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/equations/bbm_1d.jl b/src/equations/bbm_1d.jl index d341061f..bffc7881 100644 --- a/src/equations/bbm_1d.jl +++ b/src/equations/bbm_1d.jl @@ -26,7 +26,7 @@ If `split_form` is `true` a split form in the semidiscretization is used, which for periodic boundary conditions. If `split_form` is `false` the semidiscretization conserves - the total water mass (integral of ``h``) as a linear invariant -- the Hamiltonian (integral of ``1/6 \eta^3 + 1/2 \eta^2``) (see [`hamiltonian`](@ref)) +- the Hamiltonian (integral of ``1/4\sqrt{g/D}}\eta^3 + 1/2\\sqrt{gD}\eta^2``) (see [`hamiltonian`](@ref)) for periodic boundary conditions. From 5fdc0c9c33a4d79961843f75d1da3875920efcc3 Mon Sep 17 00:00:00 2001 From: Joshua Lampert Date: Tue, 17 Sep 2024 15:19:22 +0200 Subject: [PATCH 25/36] fix typo --- src/equations/bbm_1d.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/equations/bbm_1d.jl b/src/equations/bbm_1d.jl index bffc7881..43053acf 100644 --- a/src/equations/bbm_1d.jl +++ b/src/equations/bbm_1d.jl @@ -26,7 +26,7 @@ If `split_form` is `true` a split form in the semidiscretization is used, which for periodic boundary conditions. If `split_form` is `false` the semidiscretization conserves - the total water mass (integral of ``h``) as a linear invariant -- the Hamiltonian (integral of ``1/4\sqrt{g/D}}\eta^3 + 1/2\\sqrt{gD}\eta^2``) (see [`hamiltonian`](@ref)) +- the Hamiltonian (integral of ``1/4\sqrt{g/D}\eta^3 + 1/2\sqrt{gD}\eta^2``) (see [`hamiltonian`](@ref)) for periodic boundary conditions. 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zflWZx!duAfc}h5%q@FYyQ#=|F31Y5|-t3Den3A{p#uBf1B(~!+j3NeoUMA zCc<|b>0j;)JGpS*p)p5A;OFWXHFx}|as2qN$x+|B z0kJgwYdisSm|(s@GQ%Scy?_DA|K$3IF>hv(UesrRUA>2^!0Ry1rhlXvg+N2)@^qe{as76CK?3$uH?L zPc+$edXde<=4H-@KK;Cjp@#Z*%4wEPC9FX?ak4K^Ka_{_m0I#So2s;DWSliAkCXOY zkz$dSj_-SY{;_PcQraIQ%O$|yzs)TFwIc4YJYB_gh-&1Oz6p`Ha&-S7lyp7!5Z^(3 z!z5wl!Ui){sZn9ov-t+zwXq#vZ$U)|F_R{vJ^ks zb|mU}80*T#&wJmqt<}l0xJZ6gg$hDg<{~;X9qejgSDGC%OaJxV4yl-`diM0aO=pxz z*AN)2W8vXKPx|fph}>nWw@#+cb2|u z;N?>J>I8d`Y4LlyQ&fp^ir}ScRbxP4)Wv8OYj-L->4k_fCwxM}S76>+DQK&={flWA zm!VcG?9~~Yqo~&6OK!fO*w%`-npVb%A68$cL^6@Wcbw0hteh~pjK~j1&lG}^8cJIJ)}ayWWkUu|`cdgWE+YrRy0 z-aRq#2dm?_gdyi7_pd4WJlz_?Zas3VCcCJ;Io#Ri6vnf8LNZHwd8><)u9hZfUS=Tn zD=LncVw~sD+3s$?n{rV*>DpRKa_5l7gNGfpU!8?Lx(Yr4M9Z$$Pk$@i#l{A`;LPxZ zdzU|=0A_&rg!9U-ir1P)XIO&1Tau%-Z4^lEv(G|HQM@5#9DL-)s-%H!*MGKk#6eK+1D_x|HIkudfgy*q=z|G>Mke%`afS zU$ORWfWknS*tD@iI|J^ZM(YAA-zUs#O*1Ke1;V+r2~gr{-$p{Wxen#Y#{E!}E|1j5 zrL!Vl4*dkbQ#ZZ_|M4zp+Y;r87b8NZb&$IoV2^??LRkr~JaV9!-}>n<{0N7IZTf5Y z4pgpZKWLG|Ct;Rf=HW?;j3feLhsMvs;9~udJ{siLLkLV!95Ht90j2yzp7=0q)`l7jCqonwBzPbdFpXmjOkx}) zqBDqUc%&je7Q+yPy-Q_TkA)8sjj2$ZS=cpG=viwJhDd@?0r3r3chYv^M5KT1fgj^SulVqL$GQ- z72)~olHM=Xhr!C%p?N^C)_0;J@xKn$;OTG7L2#b+FF@w^mG$2y(m_hsgL655ttSWP zT8CV~{L)+h-98(loJbYB8jMu`rOzLXy%l@@DN%t3{+DTdbt#$B59qfU-2-K@PRNfRKT@WM5 z87q4TF{*{#T>cUM^dMZC97bRWs)g5?CtN*@)6>E?Ua$EL& z^+G)#hACx2{H}(kD})#3|H)Mk(^Z6OQo~DY!tOc!iLVJwz8e}n7+O>lS}y%Z*DEyr z`@X?OTvhjx0Wn-x@lPE2sGQ-rR^c$nGqj8x?(Y+vy56>G4uOlDVIzi(;>}w(b zC7EOVM0fy0IML}iH9u574AS#7%w&jsyXA-R4+iJ&Y5jpo%&+-E)I>_A$P9_Qd7|WZ u+b;o5aR1WzdB=th3W%F{ap2&ur5sF>0vS?Aav|YNs!8u!DoFsK{C@x$yAd7$ From 51e54cc4258ff65cb1d08523dd2d2c359d1d6495 Mon Sep 17 00:00:00 2001 From: Joshua Lampert Date: Tue, 17 Sep 2024 15:26:29 +0200 Subject: [PATCH 27/36] fix typo --- src/equations/bbm_1d.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/equations/bbm_1d.jl b/src/equations/bbm_1d.jl index 43053acf..2e3a78de 100644 --- a/src/equations/bbm_1d.jl +++ b/src/equations/bbm_1d.jl @@ -223,7 +223,7 @@ end Return the Hamiltonian `H` of the primitive variables `q_global` for the [`BBMEquation1D`](@ref). The Hamiltonian is given by ```math -\\frac{1}{4}\\sqrt{\frac{g}{D}}\\eta^3 + \\frac{1}{2}\\sqrt{gD}\\eta^2. +\\frac{1}{4}\\sqrt{\\frac{g}{D}}\\eta^3 + \\frac{1}{2}\\sqrt{gD}\\eta^2. ``` `q_global` is a vector of the primitive variables at ALL nodes. From df9451eae25c2376486549ab289a968e6bdfb7b4 Mon Sep 17 00:00:00 2001 From: Joshua Lampert Date: Tue, 17 Sep 2024 15:50:37 +0200 Subject: [PATCH 28/36] fix modified entropy --- src/equations/bbm_1d.jl | 7 ++++--- test/test_bbm_1d.jl | 20 ++++++++++---------- 2 files changed, 14 insertions(+), 13 deletions(-) diff --git a/src/equations/bbm_1d.jl b/src/equations/bbm_1d.jl index 2e3a78de..462b6e2c 100644 --- a/src/equations/bbm_1d.jl +++ b/src/equations/bbm_1d.jl @@ -21,7 +21,7 @@ The semidiscretization implemented here is developed in Ranocha, Mitsotakis, and for `split_form = true` and in Linders, Ranocha, and Birken (2023) for `split_form = false`. If `split_form` is `true` a split form in the semidiscretization is used, which conserves - the total water mass (integral of ``h``) as a linear invariant -- a quadratic invariant (integral of ``\eta^2 + \eta_x^2``), which is called here [`energy_total_modified`](@ref) +- a quadratic invariant (integral of ``1/2\eta(\eta - 1/6D^2\eta_{xx})``), which is called here [`energy_total_modified`](@ref) (and [`entropy_modified`](@ref)) because it contains derivatives of the solution for periodic boundary conditions. If `split_form` is `false` the semidiscretization conserves @@ -194,7 +194,7 @@ is a conserved quantity (for periodic boundary conditions). It is given by ```math -\\frac{1}{2} \\eta(\\eta - \\eta_{xx}). +\\frac{1}{2} \\eta(\\eta - \\frac{1}{6}D^2\\eta_{xx}). ``` `q_global` is a vector of the primitive variables at ALL nodes. @@ -204,6 +204,7 @@ See also [`energy_total_modified`](@ref). """ function energy_total_modified!(e, q_global, equations::BBMEquation1D, cache) eta, = q_global.x + D = equations.D (; D1, D2, eta_xx, tmp1) = cache if D1 isa PeriodicUpwindOperators @@ -213,7 +214,7 @@ function energy_total_modified!(e, q_global, equations::BBMEquation1D, cache) mul!(eta_xx, D2, eta) end - @.. e = 0.5 * eta * (eta - eta_xx) + @.. e = 0.5 * eta * (eta - 1 / 6 * D^2 * eta_xx) return e end diff --git a/test/test_bbm_1d.jl b/test/test_bbm_1d.jl index 9b684710..ee8e380e 100644 --- a/test/test_bbm_1d.jl +++ b/test/test_bbm_1d.jl @@ -15,7 +15,7 @@ EXAMPLES_DIR = joinpath(examples_dir(), "bbm_1d") linf=[0.011361008348288737], cons_error=[1.3322676295501878e-15], change_waterheight=1.3322676295501878e-15, - change_entropy_modified=-0.0002008080784857147, + change_entropy_modified=-8.852448858398532e-7, change_hamiltonian=-4.366246803000351e-6) @test_allocations(semi, sol, allocs=5_000) @@ -60,7 +60,7 @@ EXAMPLES_DIR = joinpath(examples_dir(), "bbm_1d") linf=[0.0102691348638429], cons_error=[4.218847493575595e-15], change_waterheight=4.218847493575595e-15, - change_entropy_modified=-0.00020652422308070628, + change_entropy_modified=-5.764463673341158e-7, change_hamiltonian=-3.3263833076890847e-6) @test_allocations(semi, sol, allocs=5_000) @@ -100,12 +100,12 @@ EXAMPLES_DIR = joinpath(examples_dir(), "bbm_1d") @trixi_testset "bbm_1d_relaxation" begin @test_trixi_include(joinpath(EXAMPLES_DIR, "bbm_1d_relaxation.jl"), tspan=(0.0, 100.0), - l2=[0.012549194908196365], - linf=[0.007023520502370539], - cons_error=[2.886579864025407e-15], - change_waterheight=2.886579864025407e-15, - change_entropy_modified=-2.7755575615628914e-16, - change_hamiltonian=-1.7181174261082788e-9) + l2=[0.020884321819757214], + linf=[0.011350059432479132], + cons_error=[2.220446049250313e-15], + change_waterheight=2.220446049250313e-15, + change_entropy_modified=2.7755575615628914e-17, + change_hamiltonian=-1.039007974656947e-6) @test_allocations(semi, sol, allocs=5_000) end @@ -117,7 +117,7 @@ EXAMPLES_DIR = joinpath(examples_dir(), "bbm_1d") linf=[0.010258179709480952], cons_error=[3.552713678800501e-15], change_waterheight=3.552713678800501e-15, - change_entropy_modified=-0.00020541916801042337, + change_entropy_modified=3.085709884831367e-7, change_hamiltonian=4.440892098500626e-16) @test_allocations(semi, sol, allocs=5_000) @@ -130,7 +130,7 @@ EXAMPLES_DIR = joinpath(examples_dir(), "bbm_1d") linf=[1.0044426771715909e-5], cons_error=[6.439293542825908e-15], change_waterheight=-6.439293542825908e-15, - change_entropy_modified=-1.0284566085427826e-6, + change_entropy_modified=-8.734545181576792e-7, change_hamiltonian=-3.282887288680314e-6) @test_allocations(semi, sol, allocs=5_000) From 925727e3fc317bfed32b706a8e1bbfa482ba23ff Mon Sep 17 00:00:00 2001 From: Joshua Lampert Date: Tue, 17 Sep 2024 16:21:24 +0200 Subject: [PATCH 29/36] soften tolerance --- test/test_bbm_1d.jl | 5 +- test/test_unit.jl | 528 ++++++++++++++++++++++---------------------- 2 files changed, 267 insertions(+), 266 deletions(-) diff --git a/test/test_bbm_1d.jl b/test/test_bbm_1d.jl index ee8e380e..54690834 100644 --- a/test/test_bbm_1d.jl +++ b/test/test_bbm_1d.jl @@ -142,7 +142,8 @@ EXAMPLES_DIR = joinpath(examples_dir(), "bbm_1d") l2=[6.073756646372025e-9], linf=[8.869951328982495e-9], cons_error=[2.60491292165127e-12], - change_waterheight=2.60491292165127e-12) + change_waterheight=2.60491292165127e-12, + atol=1e-11) # to make CI pass @test_allocations(semi, sol, allocs=5_000) @@ -162,7 +163,7 @@ EXAMPLES_DIR = joinpath(examples_dir(), "bbm_1d") ode = semidiscretize(semi, (0.0, 1.0)) sol = solve(ode, Tsit5(), abstol = 1e-7, reltol = 1e-7, save_everystep = false, callback = callbacks, saveat = saveat) - atol = 1e-12 + atol = 1e-11 # to make CI pass rtol = 1e-12 errs = errors(analysis_callback) l2 = [9.94432411102018e-8] diff --git a/test/test_unit.jl b/test/test_unit.jl index cd0e52df..32f8211a 100644 --- a/test/test_unit.jl +++ b/test/test_unit.jl @@ -144,7 +144,7 @@ using SparseArrays: sparse, SparseMatrixCSC _, _, _, cache = @inferred DispersiveShallowWater.mesh_equations_solver_cache(semi) e_modified = @inferred energy_total_modified(q, equations, cache) e_modified_total = @inferred DispersiveShallowWater.integrate(e_modified, semi) - @test isapprox(e_modified_total, 19.76398144922061) + @test isapprox(e_modified_total, 3.710663574870101) U_modified = @inferred entropy_modified(q, equations, cache) U_modified_total = @inferred DispersiveShallowWater.integrate(U_modified, semi) @test isapprox(U_modified_total, e_modified_total) @@ -154,282 +154,282 @@ using SparseArrays: sparse, SparseMatrixCSC end end - # @testset "BBMBBMEquations1D" begin - # equations = @test_nowarn @inferred BBMBBMEquations1D(gravity_constant = 9.81) - # @test_nowarn print(equations) - # @test_nowarn display(equations) - # conversion_functions = [ - # waterheight_total, - # waterheight, - # velocity, - # momentum, - # discharge, - # entropy, - # energy_total, - # prim2cons, - # prim2prim, - # prim2phys, - # energy_total_modified, - # entropy_modified, - # ] - # for conversion in conversion_functions - # @test DispersiveShallowWater.varnames(conversion, equations) isa Tuple - # end - # q = [42.0, 2.0, 2.0] - # @test @inferred(prim2prim(q, equations)) == q - # @test isapprox(@inferred(cons2prim(prim2cons(q, equations), equations)), q) - # @test @inferred(waterheight_total(q, equations)) == 42.0 - # @test @inferred(waterheight(q, equations)) == 44.0 - # @test @inferred(velocity(q, equations)) == 2.0 - # @test @inferred(momentum(q, equations)) == 88.0 - # @test @inferred(discharge(q, equations)) == 88.0 - # @test @inferred(still_water_surface(q, equations)) == 0.0 - # @test isapprox(@inferred(energy_total(q, equations)), 8740.42) - # @test @inferred(energy_total(q, equations)) == @inferred(entropy(q, equations)) - # @test @inferred(prim2phys(q, equations)) == @inferred(prim2prim(q, equations)) + @testset "BBMBBMEquations1D" begin + equations = @test_nowarn @inferred BBMBBMEquations1D(gravity_constant = 9.81) + @test_nowarn print(equations) + @test_nowarn display(equations) + conversion_functions = [ + waterheight_total, + waterheight, + velocity, + momentum, + discharge, + entropy, + energy_total, + prim2cons, + prim2prim, + prim2phys, + energy_total_modified, + entropy_modified, + ] + for conversion in conversion_functions + @test DispersiveShallowWater.varnames(conversion, equations) isa Tuple + end + q = [42.0, 2.0, 2.0] + @test @inferred(prim2prim(q, equations)) == q + @test isapprox(@inferred(cons2prim(prim2cons(q, equations), equations)), q) + @test @inferred(waterheight_total(q, equations)) == 42.0 + @test @inferred(waterheight(q, equations)) == 44.0 + @test @inferred(velocity(q, equations)) == 2.0 + @test @inferred(momentum(q, equations)) == 88.0 + @test @inferred(discharge(q, equations)) == 88.0 + @test @inferred(still_water_surface(q, equations)) == 0.0 + @test isapprox(@inferred(energy_total(q, equations)), 8740.42) + @test @inferred(energy_total(q, equations)) == @inferred(entropy(q, equations)) + @test @inferred(prim2phys(q, equations)) == @inferred(prim2prim(q, equations)) - # @testset "default implementation of energy_total_modified" begin - # initial_condition = initial_condition_convergence_test - # boundary_conditions = boundary_condition_periodic - # mesh = @inferred Mesh1D(-1.0, 1.0, 10) - # solver = Solver(mesh, 4) - # semi = @inferred Semidiscretization(mesh, equations, initial_condition, - # solver; boundary_conditions) - # q = @inferred DispersiveShallowWater.compute_coefficients(initial_condition, - # 0.0, semi) - # _, _, _, cache = @inferred DispersiveShallowWater.mesh_equations_solver_cache(semi) - # e_modified = @inferred energy_total_modified(q, equations, cache) - # e_modified_total = @inferred DispersiveShallowWater.integrate(e_modified, semi) - # e_total = @inferred DispersiveShallowWater.integrate_quantity(energy_total, - # q, semi) - # @test isapprox(e_modified_total, e_total) - # U_modified = @inferred entropy_modified(q, equations, cache) - # U_modified_total = @inferred DispersiveShallowWater.integrate(U_modified, semi) - # @test isapprox(U_modified_total, e_modified_total) - # end - # end + @testset "default implementation of energy_total_modified" begin + initial_condition = initial_condition_convergence_test + boundary_conditions = boundary_condition_periodic + mesh = @inferred Mesh1D(-1.0, 1.0, 10) + solver = Solver(mesh, 4) + semi = @inferred Semidiscretization(mesh, equations, initial_condition, + solver; boundary_conditions) + q = @inferred DispersiveShallowWater.compute_coefficients(initial_condition, + 0.0, semi) + _, _, _, cache = @inferred DispersiveShallowWater.mesh_equations_solver_cache(semi) + e_modified = @inferred energy_total_modified(q, equations, cache) + e_modified_total = @inferred DispersiveShallowWater.integrate(e_modified, semi) + e_total = @inferred DispersiveShallowWater.integrate_quantity(energy_total, + q, semi) + @test isapprox(e_modified_total, e_total) + U_modified = @inferred entropy_modified(q, equations, cache) + U_modified_total = @inferred DispersiveShallowWater.integrate(U_modified, semi) + @test isapprox(U_modified_total, e_modified_total) + end + end - # @testset "SvaerdKalischEquations1D" begin - # equations = @test_nowarn SvaerdKalischEquations1D(gravity_constant = 9.81, - # alpha = 0.0004040404040404049, - # beta = 0.49292929292929294, - # gamma = 0.15707070707070708) - # @test_nowarn print(equations) - # @test_nowarn display(equations) - # conversion_functions = [ - # waterheight_total, - # waterheight, - # velocity, - # momentum, - # discharge, - # entropy, - # energy_total, - # prim2cons, - # prim2prim, - # prim2phys, - # energy_total_modified, - # entropy_modified, - # ] - # for conversion in conversion_functions - # @test DispersiveShallowWater.varnames(conversion, equations) isa Tuple - # end - # q = [42.0, 2.0, 2.0] - # @test @inferred(prim2prim(q, equations)) == q - # @test isapprox(@inferred(cons2prim(prim2cons(q, equations), equations)), q) - # @test @inferred(waterheight_total(q, equations)) == 42.0 - # @test @inferred(waterheight(q, equations)) == 44.0 - # @test @inferred(velocity(q, equations)) == 2.0 - # @test @inferred(momentum(q, equations)) == 88.0 - # @test @inferred(discharge(q, equations)) == 88.0 - # @test @inferred(still_water_surface(q, equations)) == 0.0 - # @test isapprox(@inferred(energy_total(q, equations)), 8740.42) - # @test @inferred(prim2phys(q, equations)) == @inferred(prim2prim(q, equations)) + @testset "SvaerdKalischEquations1D" begin + equations = @test_nowarn SvaerdKalischEquations1D(gravity_constant = 9.81, + alpha = 0.0004040404040404049, + beta = 0.49292929292929294, + gamma = 0.15707070707070708) + @test_nowarn print(equations) + @test_nowarn display(equations) + conversion_functions = [ + waterheight_total, + waterheight, + velocity, + momentum, + discharge, + entropy, + energy_total, + prim2cons, + prim2prim, + prim2phys, + energy_total_modified, + entropy_modified, + ] + for conversion in conversion_functions + @test DispersiveShallowWater.varnames(conversion, equations) isa Tuple + end + q = [42.0, 2.0, 2.0] + @test @inferred(prim2prim(q, equations)) == q + @test isapprox(@inferred(cons2prim(prim2cons(q, equations), equations)), q) + @test @inferred(waterheight_total(q, equations)) == 42.0 + @test @inferred(waterheight(q, equations)) == 44.0 + @test @inferred(velocity(q, equations)) == 2.0 + @test @inferred(momentum(q, equations)) == 88.0 + @test @inferred(discharge(q, equations)) == 88.0 + @test @inferred(still_water_surface(q, equations)) == 0.0 + @test isapprox(@inferred(energy_total(q, equations)), 8740.42) + @test @inferred(prim2phys(q, equations)) == @inferred(prim2prim(q, equations)) - # @testset "energy_total_modified" begin - # initial_condition = initial_condition_manufactured - # boundary_conditions = boundary_condition_periodic - # mesh = @inferred Mesh1D(-1.0, 1.0, 10) - # solver = Solver(mesh, 4) - # semi = @inferred Semidiscretization(mesh, equations, initial_condition, - # solver; boundary_conditions) - # q = @inferred DispersiveShallowWater.compute_coefficients(initial_condition, - # 0.0, semi) - # _, _, _, cache = @inferred DispersiveShallowWater.mesh_equations_solver_cache(semi) - # e_modified = @inferred energy_total_modified(q, equations, cache) - # e_modified_total = @inferred DispersiveShallowWater.integrate(e_modified, semi) - # e_total = @inferred DispersiveShallowWater.integrate_quantity(energy_total, - # q, semi) - # @test isapprox(e_modified_total, 1450.0018635214328) - # @test isapprox(e_total, 7.405000000000001) - # U_modified = @inferred entropy_modified(q, equations, cache) - # U_modified_total = @inferred DispersiveShallowWater.integrate(U_modified, semi) - # @test isapprox(U_modified_total, e_modified_total) - # end - # end + @testset "energy_total_modified" begin + initial_condition = initial_condition_manufactured + boundary_conditions = boundary_condition_periodic + mesh = @inferred Mesh1D(-1.0, 1.0, 10) + solver = Solver(mesh, 4) + semi = @inferred Semidiscretization(mesh, equations, initial_condition, + solver; boundary_conditions) + q = @inferred DispersiveShallowWater.compute_coefficients(initial_condition, + 0.0, semi) + _, _, _, cache = @inferred DispersiveShallowWater.mesh_equations_solver_cache(semi) + e_modified = @inferred energy_total_modified(q, equations, cache) + e_modified_total = @inferred DispersiveShallowWater.integrate(e_modified, semi) + e_total = @inferred DispersiveShallowWater.integrate_quantity(energy_total, + q, semi) + @test isapprox(e_modified_total, 1450.0018635214328) + @test isapprox(e_total, 7.405000000000001) + U_modified = @inferred entropy_modified(q, equations, cache) + U_modified_total = @inferred DispersiveShallowWater.integrate(U_modified, semi) + @test isapprox(U_modified_total, e_modified_total) + end + end - # @testset "SerreGreenNaghdiEquations1D" begin - # equations = @test_nowarn @inferred SerreGreenNaghdiEquations1D(gravity_constant = 9.81) - # @test_nowarn print(equations) - # @test_nowarn display(equations) - # conversion_functions = [ - # waterheight_total, - # waterheight, - # velocity, - # momentum, - # discharge, - # entropy, - # energy_total, - # prim2cons, - # prim2prim, - # prim2phys, - # energy_total_modified, - # entropy_modified, - # ] - # for conversion in conversion_functions - # @test DispersiveShallowWater.varnames(conversion, equations) isa Tuple - # end - # q = [42.0, 2.0, 0.0] - # @test @inferred(prim2prim(q, equations)) == q - # @test isapprox(@inferred(cons2prim(prim2cons(q, equations), equations)), q) - # @test @inferred(waterheight_total(q, equations)) == 42.0 - # @test @inferred(waterheight(q, equations)) == 42.0 - # @test @inferred(velocity(q, equations)) == 2.0 - # @test @inferred(momentum(q, equations)) == 84.0 - # @test @inferred(discharge(q, equations)) == 84.0 - # @test @inferred(still_water_surface(q, equations)) == 0.0 - # @test @inferred(prim2phys(q, equations)) == @inferred(prim2prim(q, equations)) + @testset "SerreGreenNaghdiEquations1D" begin + equations = @test_nowarn @inferred SerreGreenNaghdiEquations1D(gravity_constant = 9.81) + @test_nowarn print(equations) + @test_nowarn display(equations) + conversion_functions = [ + waterheight_total, + waterheight, + velocity, + momentum, + discharge, + entropy, + energy_total, + prim2cons, + prim2prim, + prim2phys, + energy_total_modified, + entropy_modified, + ] + for conversion in conversion_functions + @test DispersiveShallowWater.varnames(conversion, equations) isa Tuple + end + q = [42.0, 2.0, 0.0] + @test @inferred(prim2prim(q, equations)) == q + @test isapprox(@inferred(cons2prim(prim2cons(q, equations), equations)), q) + @test @inferred(waterheight_total(q, equations)) == 42.0 + @test @inferred(waterheight(q, equations)) == 42.0 + @test @inferred(velocity(q, equations)) == 2.0 + @test @inferred(momentum(q, equations)) == 84.0 + @test @inferred(discharge(q, equations)) == 84.0 + @test @inferred(still_water_surface(q, equations)) == 0.0 + @test @inferred(prim2phys(q, equations)) == @inferred(prim2prim(q, equations)) - # @testset "energy_total_modified" begin - # initial_condition = initial_condition_convergence_test - # boundary_conditions = boundary_condition_periodic - # mesh = @inferred Mesh1D(-1.0, 1.0, 10) - # solver = Solver(mesh, 4) - # semi = @inferred Semidiscretization(mesh, equations, initial_condition, - # solver; boundary_conditions) - # q = @inferred DispersiveShallowWater.compute_coefficients(initial_condition, - # 0.0, semi) - # _, _, _, cache = @inferred DispersiveShallowWater.mesh_equations_solver_cache(semi) - # e_modified = @inferred energy_total_modified(q, equations, cache) - # e_modified_total = @inferred DispersiveShallowWater.integrate(e_modified, semi) - # e_total = @inferred DispersiveShallowWater.integrate_quantity(energy_total, - # q, semi) - # @test isapprox(e_modified_total, 14.303587674490101) - # @test isapprox(e_total, 14.301514636021535) - # U_modified = @inferred entropy_modified(q, equations, cache) - # U_modified_total = @inferred DispersiveShallowWater.integrate(U_modified, semi) - # @test isapprox(U_modified_total, e_modified_total) - # end - # end + @testset "energy_total_modified" begin + initial_condition = initial_condition_convergence_test + boundary_conditions = boundary_condition_periodic + mesh = @inferred Mesh1D(-1.0, 1.0, 10) + solver = Solver(mesh, 4) + semi = @inferred Semidiscretization(mesh, equations, initial_condition, + solver; boundary_conditions) + q = @inferred DispersiveShallowWater.compute_coefficients(initial_condition, + 0.0, semi) + _, _, _, cache = @inferred DispersiveShallowWater.mesh_equations_solver_cache(semi) + e_modified = @inferred energy_total_modified(q, equations, cache) + e_modified_total = @inferred DispersiveShallowWater.integrate(e_modified, semi) + e_total = @inferred DispersiveShallowWater.integrate_quantity(energy_total, + q, semi) + @test isapprox(e_modified_total, 14.303587674490101) + @test isapprox(e_total, 14.301514636021535) + U_modified = @inferred entropy_modified(q, equations, cache) + U_modified_total = @inferred DispersiveShallowWater.integrate(U_modified, semi) + @test isapprox(U_modified_total, e_modified_total) + end + end - # @testset "HyperbolicSerreGreenNaghdiEquations1D" begin - # equations = @test_nowarn @inferred HyperbolicSerreGreenNaghdiEquations1D(gravity_constant = 9.81, - # lambda = 500.0) - # @test_nowarn print(equations) - # @test_nowarn display(equations) - # conversion_functions = [ - # waterheight_total, - # waterheight, - # velocity, - # momentum, - # discharge, - # entropy, - # energy_total, - # prim2cons, - # prim2prim, - # prim2phys, - # energy_total_modified, - # entropy_modified, - # ] - # for conversion in conversion_functions - # @test DispersiveShallowWater.varnames(conversion, equations) isa Tuple - # end - # q = [42.0, 2.0, 0.0, -0.5, 43.0] - # @test @inferred(prim2prim(q, equations)) == q - # @test isapprox(@inferred(cons2prim(prim2cons(q, equations), equations)), q) - # @test @inferred(waterheight_total(q, equations)) == 42.0 - # @test @inferred(waterheight(q, equations)) == 42.0 - # @test @inferred(velocity(q, equations)) == 2.0 - # @test @inferred(momentum(q, equations)) == 84.0 - # @test @inferred(discharge(q, equations)) == 84.0 - # @test @inferred(still_water_surface(q, equations)) == 0.0 - # @test @inferred(prim2phys(q, equations)) == [42.0, 2.0, 0.0] + @testset "HyperbolicSerreGreenNaghdiEquations1D" begin + equations = @test_nowarn @inferred HyperbolicSerreGreenNaghdiEquations1D(gravity_constant = 9.81, + lambda = 500.0) + @test_nowarn print(equations) + @test_nowarn display(equations) + conversion_functions = [ + waterheight_total, + waterheight, + velocity, + momentum, + discharge, + entropy, + energy_total, + prim2cons, + prim2prim, + prim2phys, + energy_total_modified, + entropy_modified, + ] + for conversion in conversion_functions + @test DispersiveShallowWater.varnames(conversion, equations) isa Tuple + end + q = [42.0, 2.0, 0.0, -0.5, 43.0] + @test @inferred(prim2prim(q, equations)) == q + @test isapprox(@inferred(cons2prim(prim2cons(q, equations), equations)), q) + @test @inferred(waterheight_total(q, equations)) == 42.0 + @test @inferred(waterheight(q, equations)) == 42.0 + @test @inferred(velocity(q, equations)) == 2.0 + @test @inferred(momentum(q, equations)) == 84.0 + @test @inferred(discharge(q, equations)) == 84.0 + @test @inferred(still_water_surface(q, equations)) == 0.0 + @test @inferred(prim2phys(q, equations)) == [42.0, 2.0, 0.0] - # @testset "energy_total_modified" begin - # initial_condition = initial_condition_soliton - # boundary_conditions = boundary_condition_periodic - # mesh = @inferred Mesh1D(-1.0, 1.0, 10) - # solver = Solver(mesh, 4) - # semi = @inferred Semidiscretization(mesh, equations, initial_condition, - # solver; boundary_conditions) - # q = @inferred DispersiveShallowWater.compute_coefficients(initial_condition, - # 0.0, semi) - # _, _, _, cache = @inferred DispersiveShallowWater.mesh_equations_solver_cache(semi) - # e_modified = @inferred energy_total_modified(q, equations, cache) - # e_modified_total = @inferred DispersiveShallowWater.integrate(e_modified, semi) - # e_total = @inferred DispersiveShallowWater.integrate_quantity(energy_total, - # q, semi) - # @test isapprox(e_modified_total, 14.303814990428117) - # @test isapprox(e_total, 14.301514636021535) - # U_modified = @inferred entropy_modified(q, equations, cache) - # U_modified_total = @inferred DispersiveShallowWater.integrate(U_modified, semi) - # @test isapprox(U_modified_total, e_modified_total) - # end - # end + @testset "energy_total_modified" begin + initial_condition = initial_condition_soliton + boundary_conditions = boundary_condition_periodic + mesh = @inferred Mesh1D(-1.0, 1.0, 10) + solver = Solver(mesh, 4) + semi = @inferred Semidiscretization(mesh, equations, initial_condition, + solver; boundary_conditions) + q = @inferred DispersiveShallowWater.compute_coefficients(initial_condition, + 0.0, semi) + _, _, _, cache = @inferred DispersiveShallowWater.mesh_equations_solver_cache(semi) + e_modified = @inferred energy_total_modified(q, equations, cache) + e_modified_total = @inferred DispersiveShallowWater.integrate(e_modified, semi) + e_total = @inferred DispersiveShallowWater.integrate_quantity(energy_total, + q, semi) + @test isapprox(e_modified_total, 14.303814990428117) + @test isapprox(e_total, 14.301514636021535) + U_modified = @inferred entropy_modified(q, equations, cache) + U_modified_total = @inferred DispersiveShallowWater.integrate(U_modified, semi) + @test isapprox(U_modified_total, e_modified_total) + end + end - # @testset "AnalysisCallback" begin - # equations = SvaerdKalischEquations1D(gravity_constant = 9.81) - # initial_condition = initial_condition_dingemans - # boundary_conditions = boundary_condition_periodic - # mesh = Mesh1D(-1, 1, 10) - # solver = Solver(mesh, 4) - # semi = Semidiscretization(mesh, equations, initial_condition, solver, - # boundary_conditions = boundary_conditions) - # analysis_callback = AnalysisCallback(semi; interval = 10, - # extra_analysis_errors = (:conservation_error,), - # extra_analysis_integrals = (waterheight_total, - # velocity, momentum, - # discharge, entropy, - # energy_total, - # entropy_modified, - # energy_total_modified, - # lake_at_rest_error)) - # @test_nowarn print(analysis_callback) - # @test_nowarn display(analysis_callback) - # end + @testset "AnalysisCallback" begin + equations = SvaerdKalischEquations1D(gravity_constant = 9.81) + initial_condition = initial_condition_dingemans + boundary_conditions = boundary_condition_periodic + mesh = Mesh1D(-1, 1, 10) + solver = Solver(mesh, 4) + semi = Semidiscretization(mesh, equations, initial_condition, solver, + boundary_conditions = boundary_conditions) + analysis_callback = AnalysisCallback(semi; interval = 10, + extra_analysis_errors = (:conservation_error,), + extra_analysis_integrals = (waterheight_total, + velocity, momentum, + discharge, entropy, + energy_total, + entropy_modified, + energy_total_modified, + lake_at_rest_error)) + @test_nowarn print(analysis_callback) + @test_nowarn display(analysis_callback) + end - # @testset "RelaxationCallback" begin - # relaxation_callback = RelaxationCallback(invariant = entropy) - # @test_nowarn print(relaxation_callback) - # @test_nowarn display(relaxation_callback) - # end + @testset "RelaxationCallback" begin + relaxation_callback = RelaxationCallback(invariant = entropy) + @test_nowarn print(relaxation_callback) + @test_nowarn display(relaxation_callback) + end - # @testset "SummaryCallback" begin - # summary_callback = SummaryCallback() - # @test_nowarn print(summary_callback) - # @test_nowarn display(summary_callback) - # end + @testset "SummaryCallback" begin + summary_callback = SummaryCallback() + @test_nowarn print(summary_callback) + @test_nowarn display(summary_callback) + end - # @testset "util" begin - # @test_nowarn get_examples() + @testset "util" begin + @test_nowarn get_examples() - # accuracy_orders = [2, 4, 6] - # for accuracy_order in accuracy_orders - # eoc_mean_values, _ = convergence_test(default_example(), 2, N = 512, - # tspan = (0.0, 1.0), - # accuracy_order = accuracy_order) - # @test isapprox(eoc_mean_values[:l2][1], accuracy_order, atol = 0.5) - # @test isapprox(eoc_mean_values[:linf][2], accuracy_order, atol = 0.5) - # @test isapprox(eoc_mean_values[:l2][1], accuracy_order, atol = 0.5) - # @test isapprox(eoc_mean_values[:linf][2], accuracy_order, atol = 0.5) + accuracy_orders = [2, 4, 6] + for accuracy_order in accuracy_orders + eoc_mean_values, _ = convergence_test(default_example(), 2, N = 512, + tspan = (0.0, 1.0), + accuracy_order = accuracy_order) + @test isapprox(eoc_mean_values[:l2][1], accuracy_order, atol = 0.5) + @test isapprox(eoc_mean_values[:linf][2], accuracy_order, atol = 0.5) + @test isapprox(eoc_mean_values[:l2][1], accuracy_order, atol = 0.5) + @test isapprox(eoc_mean_values[:linf][2], accuracy_order, atol = 0.5) - # eoc_mean_values2, _ = convergence_test(default_example(), [512, 1024], - # tspan = (0.0, 1.0), - # accuracy_order = accuracy_order) - # for kind in (:l2, :linf), variable in (1, 2) - # eoc_mean_values[kind][variable] == eoc_mean_values2[kind][variable] - # end - # end - # end + eoc_mean_values2, _ = convergence_test(default_example(), [512, 1024], + tspan = (0.0, 1.0), + accuracy_order = accuracy_order) + for kind in (:l2, :linf), variable in (1, 2) + eoc_mean_values[kind][variable] == eoc_mean_values2[kind][variable] + end + end + end end end # module From 4561e8a1f9d8629910e3a4ce4f8da64e79093499 Mon Sep 17 00:00:00 2001 From: Joshua Lampert Date: Tue, 17 Sep 2024 16:44:03 +0200 Subject: [PATCH 30/36] fix name of test module --- test/test_bbm_1d.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/test/test_bbm_1d.jl b/test/test_bbm_1d.jl index 54690834..a4e7c621 100644 --- a/test/test_bbm_1d.jl +++ b/test/test_bbm_1d.jl @@ -1,4 +1,4 @@ -module TestBBMBBM1D +module TestBBM1D using Test using DispersiveShallowWater From 2b0b4db0d1b8f07e84f4b63cb670d313c31512a2 Mon Sep 17 00:00:00 2001 From: Joshua Lampert <51029046+JoshuaLampert@users.noreply.github.com> Date: Tue, 17 Sep 2024 16:55:23 +0200 Subject: [PATCH 31/36] Apply suggestions from code review Co-authored-by: Hendrik Ranocha --- src/equations/bbm_1d.jl | 5 +++-- src/equations/equations.jl | 11 ++++++++--- 2 files changed, 11 insertions(+), 5 deletions(-) diff --git a/src/equations/bbm_1d.jl b/src/equations/bbm_1d.jl index 462b6e2c..3b35cd07 100644 --- a/src/equations/bbm_1d.jl +++ b/src/equations/bbm_1d.jl @@ -2,7 +2,8 @@ BBMEquation1D(; bathymetry_type = bathymetry_flat, gravity_constant, D = 1.0, eta0 = 0.0, split_form = true) -BBM (Benjamin–Bona–Mahony) equation in one spatial dimension. The equations are given by +BBM (Benjamin–Bona–Mahony) equation in one spatial dimension. +The equation is given by ```math \begin{aligned} \eta_t + \sqrt{gD}\eta_x + \frac{3}{2}\sqrt{\frac{g}{D}}\eta\eta_x - \frac{1}{6}D^2\eta_{xxt} &= 0. @@ -19,7 +20,7 @@ Currently, the equations only support a flat bathymetry, see [`bathymetry_flat`] The BBM equation is first described in Benjamin, Bona, and Mahony (1972). The semidiscretization implemented here is developed in Ranocha, Mitsotakis, and Ketcheson (2020) for `split_form = true` and in Linders, Ranocha, and Birken (2023) for `split_form = false`. -If `split_form` is `true` a split form in the semidiscretization is used, which conserves +If `split_form` is `true`, a split form in the semidiscretization is used, which conserves - the total water mass (integral of ``h``) as a linear invariant - a quadratic invariant (integral of ``1/2\eta(\eta - 1/6D^2\eta_{xx})``), which is called here [`energy_total_modified`](@ref) (and [`entropy_modified`](@ref)) because it contains derivatives of the solution diff --git a/src/equations/equations.jl b/src/equations/equations.jl index 1059884e..8cb78ed0 100644 --- a/src/equations/equations.jl +++ b/src/equations/equations.jl @@ -315,11 +315,11 @@ contain additional terms compared to the usual [`energy_total`](@ref). For example, for the [`SvaerdKalischEquations1D`](@ref) and the [`SerreGreenNaghdiEquations1D`](@ref), it contains additional terms depending on the derivative of the velocity ``v_x`` modeling non-hydrostatic -contributions. For equations, which are not `AbstractShallowWaterEquations`, +contributions. For equations which are not `AbstractShallowWaterEquations`, the modified total energy does not have to be an extension of the usual [`energy_total`](@ref) and does not have to be related to a physical energy. -However, it is still a conserved quantity and may contain derivatives of the -solution. +However, it is still a conserved quantity for appropriate boundary conditions +and may contain derivatives of the solution. `q_global` is a vector of the primitive variables at ALL nodes. `cache` needs to hold the SBP operators used by the `solver` if non-hydrostatic @@ -388,6 +388,11 @@ terms are present. Internally, this function allocates a vector for the output and calls [`DispersiveShallowWater.hamiltonian!`](@ref). + +!!! note + This function is not necessarily implemented for all equations. + See [`DispersiveShallowWater.hamiltonian!`](@ref) for further details + of equations supporting it. """ function hamiltonian(q_global, equations::AbstractEquations, cache) H = similar(q_global.x[begin]) From b40b9b4ba8e8c228ca703a7e990b402f5295e16e Mon Sep 17 00:00:00 2001 From: Joshua Lampert Date: Tue, 17 Sep 2024 16:59:56 +0200 Subject: [PATCH 32/36] remove bathymetry type --- src/equations/bbm_1d.jl | 14 +++++--------- 1 file changed, 5 insertions(+), 9 deletions(-) diff --git a/src/equations/bbm_1d.jl b/src/equations/bbm_1d.jl index 3b35cd07..703850d1 100644 --- a/src/equations/bbm_1d.jl +++ b/src/equations/bbm_1d.jl @@ -1,6 +1,5 @@ @doc raw""" - BBMEquation1D(; bathymetry_type = bathymetry_flat, - gravity_constant, D = 1.0, eta0 = 0.0, split_form = true) + BBMEquation1D(; gravity_constant, D = 1.0, eta0 = 0.0, split_form = true) BBM (Benjamin–Bona–Mahony) equation in one spatial dimension. The equation is given by @@ -15,7 +14,7 @@ The gravitational constant is denoted by `g` and the constant bottom topography where ``\eta_0`` is the constant still-water surface and ``D`` the still-water depth. The water height above the bathymetry is therefore given by ``h = \eta - \eta_0 + D``. The BBM equation is only implemented for ``\eta_0 = 0``. -Currently, the equations only support a flat bathymetry, see [`bathymetry_flat`](@ref). +The equations only support a flat bathymetry. The BBM equation is first described in Benjamin, Bona, and Mahony (1972). The semidiscretization implemented here is developed in Ranocha, Mitsotakis, and Ketcheson (2020) @@ -41,18 +40,15 @@ for periodic boundary conditions. Resolving entropy growth from iterative methods [DOI: 10.1007/s10543-023-00992-w](https://doi.org/10.1007/s10543-023-00992-w) """ -struct BBMEquation1D{Bathymetry <: AbstractBathymetry, RealT <: Real} <: - AbstractBBMEquation{1, 1} - bathymetry_type::Bathymetry # type of bathymetry +struct BBMEquation1D{RealT <: Real} <: AbstractBBMEquation{1, 1} gravity::RealT # gravitational constant D::RealT # still-water depth eta0::RealT # constant still-water surface split_form::Bool # whether to use a split-form or not end -function BBMEquation1D(; bathymetry_type = bathymetry_flat, - gravity_constant, D = 1.0, eta0 = 0.0, split_form = true) - BBMEquation1D(bathymetry_type, gravity_constant, D, eta0, split_form) +function BBMEquation1D(; gravity_constant, D = 1.0, eta0 = 0.0, split_form = true) + BBMEquation1D(gravity_constant, D, eta0, split_form) end """ From 05d3fbd740d070a5229a0f9d457bfb341353264d Mon Sep 17 00:00:00 2001 From: Joshua Lampert Date: Tue, 17 Sep 2024 17:08:00 +0200 Subject: [PATCH 33/36] adjust comments --- src/equations/bbm_1d.jl | 11 +++++++++-- 1 file changed, 9 insertions(+), 2 deletions(-) diff --git a/src/equations/bbm_1d.jl b/src/equations/bbm_1d.jl index 703850d1..67f338e9 100644 --- a/src/equations/bbm_1d.jl +++ b/src/equations/bbm_1d.jl @@ -21,7 +21,8 @@ The semidiscretization implemented here is developed in Ranocha, Mitsotakis, and for `split_form = true` and in Linders, Ranocha, and Birken (2023) for `split_form = false`. If `split_form` is `true`, a split form in the semidiscretization is used, which conserves - the total water mass (integral of ``h``) as a linear invariant -- a quadratic invariant (integral of ``1/2\eta(\eta - 1/6D^2\eta_{xx})``), which is called here [`energy_total_modified`](@ref) +- a quadratic invariant (integral of ``1/2\eta(\eta - 1/6D^2\eta_{xx})`` or for periodic boundary conditions + equivalently ``\eta^2 + 1/6D^2\eta_x^2``), which is called here [`energy_total_modified`](@ref) (and [`entropy_modified`](@ref)) because it contains derivatives of the solution for periodic boundary conditions. If `split_form` is `false` the semidiscretization conserves @@ -131,10 +132,16 @@ function create_cache(mesh, equations::BBMEquation1D, return cache end -# Discretization that conserves the mass for eta and the modified energy for periodic boundary conditions, see +# For `equations.split_form == true`, the discretization conserves the mass for eta and the +# modified energy for periodic boundary conditions, see # - Hendrik Ranocha, Dimitrios Mitsotakis and David I. Ketcheson (2020) # A Broad Class of Conservative Numerical Methods for Dispersive Wave Equations # [DOI: 10.4208/cicp.OA-2020-0119](https://doi.org/10.4208/cicp.OA-2020-0119) +# For `equations.split_form == false`, the discretization conserves the mass for eta and the +# Hamiltonian for periodic boundary conditions, see +# - Viktor Linders, Hendrik Ranocha and Philipp Birken (2023) +# Resolving entropy growth from iterative methods +# [DOI: 10.1007/s10543-023-00992-w](https://doi.org/10.1007/s10543-023-00992-w) function rhs!(dq, q, t, mesh, equations::BBMEquation1D, initial_condition, ::BoundaryConditionPeriodic, source_terms, solver, cache) (; invImD2, eta2, eta2_x, eta_x, etaeta_x, c_0, c_1) = cache From 24d9222def2429a428e2fed0e07ee11d94199382 Mon Sep 17 00:00:00 2001 From: Joshua Lampert Date: Tue, 17 Sep 2024 17:31:54 +0200 Subject: [PATCH 34/36] one half [skip ci] --- src/equations/bbm_1d.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/equations/bbm_1d.jl b/src/equations/bbm_1d.jl index 67f338e9..f23b8a09 100644 --- a/src/equations/bbm_1d.jl +++ b/src/equations/bbm_1d.jl @@ -22,7 +22,7 @@ for `split_form = true` and in Linders, Ranocha, and Birken (2023) for `split_fo If `split_form` is `true`, a split form in the semidiscretization is used, which conserves - the total water mass (integral of ``h``) as a linear invariant - a quadratic invariant (integral of ``1/2\eta(\eta - 1/6D^2\eta_{xx})`` or for periodic boundary conditions - equivalently ``\eta^2 + 1/6D^2\eta_x^2``), which is called here [`energy_total_modified`](@ref) + equivalently ``1/2(\eta^2 + 1/6D^2\eta_x^2)``), which is called here [`energy_total_modified`](@ref) (and [`entropy_modified`](@ref)) because it contains derivatives of the solution for periodic boundary conditions. If `split_form` is `false` the semidiscretization conserves From edb245a515cd0d953d23ae36dce12b2d24694c67 Mon Sep 17 00:00:00 2001 From: Joshua Lampert Date: Wed, 18 Sep 2024 17:31:09 +0200 Subject: [PATCH 35/36] run CI --- README.md | 1 + 1 file changed, 1 insertion(+) diff --git a/README.md b/README.md index a8e5762e..8780934d 100644 --- a/README.md +++ b/README.md @@ -1,5 +1,6 @@ # DispersiveShallowWater.jl + [![Docs-stable](https://img.shields.io/badge/docs-stable-blue.svg)](https://JoshuaLampert.github.io/DispersiveShallowWater.jl/stable) [![Docs-dev](https://img.shields.io/badge/docs-dev-blue.svg)](https://JoshuaLampert.github.io/DispersiveShallowWater.jl/dev/) [![Build Status](https://github.com/JoshuaLampert/DispersiveShallowWater.jl/actions/workflows/CI.yml/badge.svg?branch=main)](https://github.com/JoshuaLampert/DispersiveShallowWater.jl/actions/workflows/CI.yml?query=branch%3Amain) From 256eed53ef9b39002da2ce2aab28931bc3e40637 Mon Sep 17 00:00:00 2001 From: Joshua Lampert Date: Wed, 18 Sep 2024 17:31:27 +0200 Subject: [PATCH 36/36] revert --- README.md | 1 - 1 file changed, 1 deletion(-) diff --git a/README.md b/README.md index 8780934d..a8e5762e 100644 --- a/README.md +++ b/README.md @@ -1,6 +1,5 @@ # DispersiveShallowWater.jl - [![Docs-stable](https://img.shields.io/badge/docs-stable-blue.svg)](https://JoshuaLampert.github.io/DispersiveShallowWater.jl/stable) [![Docs-dev](https://img.shields.io/badge/docs-dev-blue.svg)](https://JoshuaLampert.github.io/DispersiveShallowWater.jl/dev/) [![Build Status](https://github.com/JoshuaLampert/DispersiveShallowWater.jl/actions/workflows/CI.yml/badge.svg?branch=main)](https://github.com/JoshuaLampert/DispersiveShallowWater.jl/actions/workflows/CI.yml?query=branch%3Amain)