Add shallow water dirichlet

examples/shallowwater_dirichlet_1d.jl

@@ -0,0 +1,79 @@
+using Trixi, TrixiGPU
+using OrdinaryDiffEq
+
+# The example is taken from the Trixi.jl
+
+###############################################################################
+# Semidiscretization of the shallow water equations
+
+equations = ShallowWaterEquations1D(gravity_constant = 1.0, H0 = 3.0)
+
+# An initial condition with constant total water height and zero velocities to test well-balancedness.
+function initial_condition_well_balancedness(x, t, equations::ShallowWaterEquations1D)
+    # Set the background values
+    H = equations.H0
+    v = 0.0
+
+    b = (1.5 / exp(0.5 * ((x[1] - 1.0)^2)) + 0.75 / exp(0.5 * ((x[1] + 1.0)^2)))
+
+    return prim2cons(SVector(H, v, b), equations)
+end
+
+initial_condition = initial_condition_well_balancedness
+
+boundary_condition = BoundaryConditionDirichlet(initial_condition)
+
+###############################################################################
+# Get the DG approximation space
+
+volume_flux = (flux_wintermeyer_etal, flux_nonconservative_wintermeyer_etal)
+solver = DGSEM(polydeg = 4,
+               surface_flux = (flux_hll,
+                               flux_nonconservative_fjordholm_etal),
+               volume_integral = VolumeIntegralFluxDifferencing(volume_flux))
+
+###############################################################################
+# Get the TreeMesh and setup a periodic mesh
+
+coordinates_min = 0.0
+coordinates_max = sqrt(2.0)
+mesh = TreeMesh(coordinates_min, coordinates_max,
+                initial_refinement_level = 3,
+                n_cells_max = 10_000,
+                periodicity = false)
+
+# create the semi discretization object
+semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver,
+                                    boundary_conditions = boundary_condition)
+
+###############################################################################
+# ODE solvers, callbacks etc.
+
+tspan = (0.0, 100.0)
+ode = semidiscretize_gpu(semi, tspan) # from TrixiGPU.jl
+
+summary_callback = SummaryCallback()
+
+analysis_interval = 1000
+analysis_callback = AnalysisCallback(semi, interval = analysis_interval,
+                                     save_analysis = true,
+                                     extra_analysis_integrals = (lake_at_rest_error,))
+
+alive_callback = AliveCallback(analysis_interval = analysis_interval)
+
+save_solution = SaveSolutionCallback(interval = 1000,
+                                     save_initial_solution = true,
+                                     save_final_solution = true)
+
+stepsize_callback = StepsizeCallback(cfl = 1.0)
+
+callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution,
+                        stepsize_callback)
+
+###############################################################################
+# run the simulation
+
+sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false),
+            dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback
+            save_everystep = false, callback = callbacks);
+summary_callback() # print the timer summary

examples/shallowwater_dirichlet_2d.jl

@@ -0,0 +1,63 @@
+using Trixi, TrixiGPU
+using OrdinaryDiffEq
+
+# The example is taken from the Trixi.jl
+
+###############################################################################
+# Semidiscretization of the shallow water equations
+
+equations = ShallowWaterEquations2D(gravity_constant = 9.81)
+
+initial_condition = initial_condition_convergence_test
+
+boundary_condition = BoundaryConditionDirichlet(initial_condition)
+
+###############################################################################
+# Get the DG approximation space
+
+volume_flux = (flux_wintermeyer_etal, flux_nonconservative_wintermeyer_etal)
+solver = DGSEM(polydeg = 3,
+               surface_flux = (flux_lax_friedrichs, flux_nonconservative_fjordholm_etal),
+               volume_integral = VolumeIntegralFluxDifferencing(volume_flux))
+
+###############################################################################
+# Get the TreeMesh and setup a periodic mesh
+
+coordinates_min = (0.0, 0.0)
+coordinates_max = (sqrt(2.0), sqrt(2.0))
+mesh = TreeMesh(coordinates_min, coordinates_max,
+                initial_refinement_level = 3,
+                n_cells_max = 10_000,
+                periodicity = false)
+
+# create the semi discretization object
+semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver,
+                                    boundary_conditions = boundary_condition,
+                                    source_terms = source_terms_convergence_test)
+
+###############################################################################
+# ODE solvers, callbacks etc.
+
+tspan = (0.0, 1.0)
+ode = semidiscretize_gpu(semi, tspan) # from TrixiGPU.jl
+
+summary_callback = SummaryCallback()
+
+analysis_interval = 500
+analysis_callback = AnalysisCallback(semi, interval = analysis_interval)
+
+alive_callback = AliveCallback(analysis_interval = analysis_interval)
+
+save_solution = SaveSolutionCallback(interval = 200,
+                                     save_initial_solution = true,
+                                     save_final_solution = true)
+
+callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution)
+
+###############################################################################
+# run the simulation
+
+# use a Runge-Kutta method with automatic (error based) time step size control
+sol = solve(ode, RDPK3SpFSAL49(); abstol = 1.0e-8, reltol = 1.0e-8,
+            ode_default_options()..., callback = callbacks);
+summary_callback() # print the timer summary