variable bathymetry Serre-Green-Naghdi equations

.gitignore

@@ -8,3 +8,4 @@ out*/
 /docs/build/
 run
 run/*
+**/*.code-workspace

examples/serre_green_naghdi_1d/serre_green_naghdi_dingemans.jl

@@ -0,0 +1,49 @@
+using OrdinaryDiffEq
+using DispersiveShallowWater
+using SummationByPartsOperators: upwind_operators, periodic_derivative_operator
+
+###############################################################################
+# Semidiscretization of the Svärd-Kalisch equations
+
+bathymetry = bathymetry_variable # or bathymetry_mild_slope
+equations = SerreGreenNaghdiEquations1D(bathymetry;
+                                        gravity_constant = 9.81)
+
+initial_condition = initial_condition_dingemans
+boundary_conditions = boundary_condition_periodic
+
+# create homogeneous mesh
+coordinates_min = -140.0
+coordinates_max = 100.0
+N = 512
+mesh = Mesh1D(coordinates_min, coordinates_max, N)
+
+# create solver with periodic upwind SBP operators of accuracy order 4
+# (note that only central-type with even order are used)
+D1 = upwind_operators(periodic_derivative_operator;
+                      derivative_order = 1, accuracy_order = 3,
+                      xmin = xmin(mesh), xmax = xmax(mesh),
+                      N = nnodes(mesh))
+solver = Solver(D1, nothing)
+
+# 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, 70.0)
+ode = semidiscretize(semi, tspan)
+summary_callback = SummaryCallback()
+analysis_callback = AnalysisCallback(semi; interval = 10,
+                                     extra_analysis_errors = (:conservation_error,),
+                                     extra_analysis_integrals = (waterheight_total,
+                                                                 momentum,
+                                                                 entropy,
+                                                                 entropy_modified))
+
+callbacks = CallbackSet(analysis_callback, summary_callback)
+
+saveat = range(tspan..., length = 500)
+sol = solve(ode, Tsit5(), abstol = 1e-7, reltol = 1e-7,
+            save_everystep = false, callback = callbacks, saveat = saveat)

src/DispersiveShallowWater.jl

@@ -65,7 +65,7 @@ export Semidiscretization, semidiscretize, grid
 
 export boundary_condition_periodic, boundary_condition_reflecting
 
-export bathymetry_flat
+export bathymetry_flat, bathymetry_mild_slope, bathymetry_variable
 
 export initial_condition_convergence_test,
        initial_condition_manufactured, source_terms_manufactured,

src/equations/equations.jl

@@ -325,14 +325,39 @@ Default analysis integrals used by the [`AnalysisCallback`](@ref).
 default_analysis_integrals(::AbstractEquations) = Symbol[]
 
 abstract type AbstractBathymetry end
+
 struct BathymetryFlat <: AbstractBathymetry end
 """
     bathymetry_flat = DispersiveShallowWater.BathymetryFlat()
 
 A singleton struct indicating a flat bathymetry.
+
+See also [`bathymetry_mild_slope`](@ref) and [`bathymetry_variable`](@ref).
 """
 const bathymetry_flat = BathymetryFlat()
 
+struct BathymetryMildSlope <: AbstractBathymetry end
+"""
+    bathymetry_mild_slope = DispersiveShallowWater.BathymetryMildSlope()
+
+A singleton struct indicating a variable bathymetry with mild-slope
+approximation.
+
+See also [`bathymetry_flat`](@ref) and [`bathymetry_variable`](@ref).
+"""
+const bathymetry_mild_slope = BathymetryMildSlope()
+
+struct BathymetryVariable <: AbstractBathymetry end
+"""
+    bathymetry_variable = DispersiveShallowWater.BathymetryVariable()
+
+A singleton struct indicating a variable bathymetry (without
+mild-slope approximation).
+
+See also [`bathymetry_flat`](@ref) and [`bathymetry_mild_slope`](@ref).
+"""
+const bathymetry_variable = BathymetryVariable()
+
 # BBM-BBM equations
 abstract type AbstractBBMBBMEquations{NDIMS, NVARS} <:
               AbstractShallowWaterEquations{NDIMS, NVARS} end
@@ -347,4 +372,4 @@ include("svaerd_kalisch_1d.jl")
 # Serre-Green-Naghdi equations
 abstract type AbstractSerreGreenNaghdiEquations{NDIMS, NVARS} <:
               AbstractShallowWaterEquations{NDIMS, NVARS} end
-include("serre_green_naghdi_flat_1d.jl")
+include("serre_green_naghdi_1d.jl")