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examples/tree_1d_dgsem/elixir_shallowwater_twolayer_convergence.jl
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using OrdinaryDiffEq | ||
using Trixi | ||
using TrixiShallowWater | ||
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############################################################################### | ||
# Semidiscretization of the two-layer shallow water equations | ||
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equations = ShallowWaterTwoLayerEquations1D(gravity_constant = 10.0, rho_upper = 0.9, | ||
rho_lower = 1.0) | ||
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initial_condition = initial_condition_convergence_test | ||
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############################################################################### | ||
# Get the DG approximation space | ||
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volume_flux = (flux_wintermeyer_etal, flux_nonconservative_ersing_etal) | ||
solver = DGSEM(polydeg = 3, | ||
surface_flux = (flux_wintermeyer_etal, flux_nonconservative_ersing_etal), | ||
volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) | ||
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############################################################################### | ||
# Get the TreeMesh and setup a periodic mesh | ||
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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 = true) | ||
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# create the semi discretization object | ||
semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, | ||
source_terms = source_terms_convergence_test) | ||
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############################################################################### | ||
# ODE solvers, callbacks etc. | ||
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tspan = (0.0, 1.0) | ||
ode = semidiscretize(semi, tspan) | ||
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summary_callback = SummaryCallback() | ||
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analysis_interval = 500 | ||
analysis_callback = AnalysisCallback(semi, interval = analysis_interval) | ||
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alive_callback = AliveCallback(analysis_interval = analysis_interval) | ||
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save_solution = SaveSolutionCallback(interval = 500, | ||
save_initial_solution = true, | ||
save_final_solution = true) | ||
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callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution) | ||
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############################################################################### | ||
# run the simulation | ||
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# 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, | ||
save_everystep = false, callback = callbacks); | ||
summary_callback() # print the timer summary |
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examples/tree_1d_dgsem/elixir_shallowwater_twolayer_dam_break.jl
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using OrdinaryDiffEq | ||
using Trixi | ||
using TrixiShallowWater | ||
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############################################################################### | ||
# Semidiscretization of the two-layer shallow water equations for a dam break | ||
# test with a discontinuous bottom topography function to test entropy conservation | ||
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equations = ShallowWaterTwoLayerEquations1D(gravity_constant = 9.81, H0 = 2.0, | ||
rho_upper = 0.9, rho_lower = 1.0) | ||
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# Initial condition of a dam break with a discontinuous water heights and bottom topography. | ||
# Works as intended for TreeMesh1D with `initial_refinement_level=5`. If the mesh | ||
# refinement level is changed the initial condition below may need changed as well to | ||
# ensure that the discontinuities lie on an element interface. | ||
function initial_condition_dam_break(x, t, equations::ShallowWaterTwoLayerEquations1D) | ||
v1_upper = 0.0 | ||
v1_lower = 0.0 | ||
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# Set the discontinuity | ||
if x[1] <= 10.0 | ||
H_lower = 2.0 | ||
H_upper = 4.0 | ||
b = 0.0 | ||
else | ||
H_lower = 1.5 | ||
H_upper = 3.0 | ||
b = 0.5 | ||
end | ||
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return prim2cons(SVector(H_upper, v1_upper, H_lower, v1_lower, b), equations) | ||
end | ||
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initial_condition = initial_condition_dam_break | ||
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############################################################################### | ||
# Get the DG approximation space | ||
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volume_flux = (flux_wintermeyer_etal, flux_nonconservative_ersing_etal) | ||
solver = DGSEM(polydeg = 3, | ||
surface_flux = (flux_wintermeyer_etal, flux_nonconservative_ersing_etal), | ||
volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) | ||
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############################################################################### | ||
# Get the TreeMesh and setup a non-periodic mesh | ||
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coordinates_min = 0.0 | ||
coordinates_max = 20.0 | ||
mesh = TreeMesh(coordinates_min, coordinates_max, | ||
initial_refinement_level = 5, | ||
n_cells_max = 10000, | ||
periodicity = false) | ||
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boundary_condition = boundary_condition_slip_wall | ||
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# create the semidiscretization object | ||
semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, | ||
boundary_conditions = boundary_condition) | ||
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############################################################################### | ||
# ODE solvers | ||
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tspan = (0.0, 0.4) | ||
ode = semidiscretize(semi, tspan) | ||
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############################################################################### | ||
# Callbacks | ||
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summary_callback = SummaryCallback() | ||
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analysis_interval = 500 | ||
analysis_callback = AnalysisCallback(semi, interval = analysis_interval, | ||
save_analysis = false, | ||
extra_analysis_integrals = (energy_total, | ||
energy_kinetic, | ||
energy_internal)) | ||
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stepsize_callback = StepsizeCallback(cfl = 1.0) | ||
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alive_callback = AliveCallback(analysis_interval = analysis_interval) | ||
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save_solution = SaveSolutionCallback(interval = 500, | ||
save_initial_solution = true, | ||
save_final_solution = true) | ||
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callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution) | ||
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############################################################################### | ||
# run the simulation | ||
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# 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, | ||
save_everystep = false, callback = callbacks); | ||
summary_callback() # print the timer summary |
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examples/tree_1d_dgsem/elixir_shallowwater_twolayer_well_balanced.jl
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using OrdinaryDiffEq | ||
using Trixi | ||
using TrixiShallowWater | ||
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############################################################################### | ||
# Semidiscretization of the two-layer shallow water equations to test well-balancedness | ||
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equations = ShallowWaterTwoLayerEquations1D(gravity_constant = 1.0, H0 = 0.6, | ||
rho_upper = 0.9, rho_lower = 1.0) | ||
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""" | ||
initial_condition_fjordholm_well_balanced(x, t, equations::ShallowWaterTwoLayerEquations1D) | ||
Initial condition to test well balanced with a bottom topography from Fjordholm | ||
- Ulrik Skre Fjordholm (2012) | ||
Energy conservative and stable schemes for the two-layer shallow water equations. | ||
[DOI: 10.1142/9789814417099_0039](https://doi.org/10.1142/9789814417099_0039) | ||
""" | ||
function initial_condition_fjordholm_well_balanced(x, t, | ||
equations::ShallowWaterTwoLayerEquations1D) | ||
inicenter = 0.5 | ||
x_norm = x[1] - inicenter | ||
r = abs(x_norm) | ||
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H_lower = 0.5 | ||
H_upper = 0.6 | ||
v1_upper = 0.0 | ||
v1_lower = 0.0 | ||
b = r <= 0.1 ? 0.2 * (cos(10 * pi * (x[1] - 0.5)) + 1) : 0.0 | ||
return prim2cons(SVector(H_upper, v1_upper, H_lower, v1_lower, b), equations) | ||
end | ||
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initial_condition = initial_condition_fjordholm_well_balanced | ||
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############################################################################### | ||
# Get the DG approximation space | ||
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volume_flux = (flux_wintermeyer_etal, flux_nonconservative_ersing_etal) | ||
solver = DGSEM(polydeg = 3, | ||
surface_flux = (flux_es_ersing_etal, flux_nonconservative_ersing_etal), | ||
volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) | ||
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############################################################################### | ||
# Get the TreeMesh and setup a periodic mesh | ||
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coordinates_min = 0.0 | ||
coordinates_max = 1.0 | ||
mesh = TreeMesh(coordinates_min, coordinates_max, | ||
initial_refinement_level = 4, | ||
n_cells_max = 10_000, | ||
periodicity = true) | ||
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# create the semi discretization object | ||
semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) | ||
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############################################################################### | ||
# ODE solvers, callbacks etc. | ||
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tspan = (0.0, 10.0) | ||
ode = semidiscretize(semi, tspan) | ||
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summary_callback = SummaryCallback() | ||
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analysis_interval = 1000 | ||
analysis_callback = AnalysisCallback(semi, interval = analysis_interval, | ||
save_analysis = false, | ||
extra_analysis_integrals = (lake_at_rest_error,)) | ||
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stepsize_callback = StepsizeCallback(cfl = 1.0) | ||
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alive_callback = AliveCallback(analysis_interval = analysis_interval) | ||
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save_solution = SaveSolutionCallback(interval = 1000, | ||
save_initial_solution = true, | ||
save_final_solution = true) | ||
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callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, | ||
stepsize_callback) | ||
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############################################################################### | ||
# run the simulation | ||
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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 |
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examples/tree_2d_dgsem/elixir_shallowwater_twolayer_convergence.jl
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using OrdinaryDiffEq | ||
using Trixi | ||
using TrixiShallowWater | ||
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############################################################################### | ||
# Semidiscretization of the two-layer shallow water equations | ||
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equations = ShallowWaterTwoLayerEquations2D(gravity_constant = 10.0, rho_upper = 0.9, | ||
rho_lower = 1.0) | ||
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initial_condition = initial_condition_convergence_test | ||
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############################################################################### | ||
# Get the DG approximation space | ||
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volume_flux = (flux_wintermeyer_etal, flux_nonconservative_ersing_etal) | ||
solver = DGSEM(polydeg = 3, | ||
surface_flux = (flux_wintermeyer_etal, flux_nonconservative_ersing_etal), | ||
volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) | ||
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############################################################################### | ||
# Get the TreeMesh and setup a periodic mesh | ||
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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 = 20_000, | ||
periodicity = true) | ||
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# Create the semi discretization object | ||
semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, | ||
source_terms = source_terms_convergence_test) | ||
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############################################################################### | ||
# ODE solvers, callbacks etc. | ||
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tspan = (0.0, 1.0) | ||
ode = semidiscretize(semi, tspan) | ||
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summary_callback = SummaryCallback() | ||
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analysis_interval = 500 | ||
analysis_callback = AnalysisCallback(semi, interval = analysis_interval) | ||
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alive_callback = AliveCallback(analysis_interval = analysis_interval) | ||
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save_solution = SaveSolutionCallback(interval = 500, | ||
save_initial_solution = true, | ||
save_final_solution = true) | ||
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callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution) | ||
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############################################################################### | ||
# run the simulation | ||
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# 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, | ||
save_everystep = false, callback = callbacks); | ||
summary_callback() # print the timer summary |
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examples/tree_2d_dgsem/elixir_shallowwater_twolayer_well_balanced.jl
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using OrdinaryDiffEq | ||
using Trixi | ||
using TrixiShallowWater | ||
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############################################################################### | ||
# Semidiscretization of the two-layer shallow water equations with a bottom topography function | ||
# to test well-balancedness | ||
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equations = ShallowWaterTwoLayerEquations2D(gravity_constant = 9.81, H0 = 0.6, | ||
rho_upper = 0.9, rho_lower = 1.0) | ||
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# An initial condition with constant total water height, zero velocities and a bottom topography to | ||
# test well-balancedness | ||
function initial_condition_well_balanced(x, t, equations::ShallowWaterTwoLayerEquations2D) | ||
H_lower = 0.5 | ||
H_upper = 0.6 | ||
v1_upper = 0.0 | ||
v2_upper = 0.0 | ||
v1_lower = 0.0 | ||
v2_lower = 0.0 | ||
b = (((x[1] - 0.5)^2 + (x[2] - 0.5)^2) < 0.04 ? | ||
0.2 * (cos(4 * pi * sqrt((x[1] - 0.5)^2 + (x[2] + | ||
-0.5)^2)) + 1) : 0.0) | ||
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return prim2cons(SVector(H_upper, v1_upper, v2_upper, H_lower, v1_lower, v2_lower, b), | ||
equations) | ||
end | ||
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initial_condition = initial_condition_well_balanced | ||
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############################################################################### | ||
# Get the DG approximation space | ||
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volume_flux = (flux_wintermeyer_etal, flux_nonconservative_ersing_etal) | ||
surface_flux = (flux_es_ersing_etal, flux_nonconservative_ersing_etal) | ||
solver = DGSEM(polydeg = 3, surface_flux = surface_flux, | ||
volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) | ||
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############################################################################### | ||
# Get the TreeMesh and setup a periodic mesh | ||
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coordinates_min = (0.0, 0.0) | ||
coordinates_max = (1.0, 1.0) | ||
mesh = TreeMesh(coordinates_min, coordinates_max, | ||
initial_refinement_level = 3, | ||
n_cells_max = 10_000, | ||
periodicity = true) | ||
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# Create the semi discretization object | ||
semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) | ||
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############################################################################### | ||
# ODE solver | ||
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tspan = (0.0, 10.0) | ||
ode = semidiscretize(semi, tspan) | ||
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summary_callback = SummaryCallback() | ||
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analysis_interval = 1000 | ||
analysis_callback = AnalysisCallback(semi, interval = analysis_interval, | ||
extra_analysis_integrals = (lake_at_rest_error,)) | ||
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stepsize_callback = StepsizeCallback(cfl = 1.0) | ||
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alive_callback = AliveCallback(analysis_interval = analysis_interval) | ||
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save_solution = SaveSolutionCallback(interval = 1000, | ||
save_initial_solution = true, | ||
save_final_solution = true) | ||
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callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, | ||
stepsize_callback) | ||
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############################################################################### | ||
# run the simulation | ||
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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 |
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