Add BBMEquation1D

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

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).

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).

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)

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)

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)

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)

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
 

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"