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Add wet/dry functionality for the 2D Multilayer-SWE (#44)
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* add wet/dry functionality

* add elixirs and tests

* fix tests

* fix 2d indicator

* improve dry dam break test

* fix typo

* update coverage test settings

* fix some comments

* fix hydrostatic reconstruction

* remove unused bc from elixir

* Apply suggestions from code review

Co-authored-by: Andrew Winters <andrew.ross.winters@liu.se>

---------

Co-authored-by: Andrew Winters <andrew.ross.winters@liu.se>
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@patrickersing @andrewwinters5000
patrickersing and andrewwinters5000 committed May 7, 2024
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163 changes: 163 additions & 0 deletions examples/tree_2d_dgsem/elixir_shallowwater_multilayer_dam_break_dry.jl
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using OrdinaryDiffEq
using Trixi
using TrixiShallowWater

###############################################################################
# Semidiscretization of the multilayer shallow water equations for a dam break test over a dry domain
# with a discontinuous bottom topography function.
equations = ShallowWaterMultiLayerEquations2D(gravity_constant = 1.0,
rhos = (0.9, 0.95, 1.0))

function initial_condition_dam_break(x, t, equations::ShallowWaterMultiLayerEquations2D)
# Bottom topography
b = 1.4 * exp(-10.0 * (x[1]^2 + x[2]^2))
if x[1] > 0.0
b += 0.1
end

if x[1] < -0.5
H = [1.0, 0.8, 0.6]
else
H = [b, b, b]
end

v1 = zero(H)
v2 = zero(H)

# It is mandatory to shift the water level at dry areas to make sure the water height h
# stays positive. The system would not be stable for h set to a hard 0 due to division by h in
# the computation of velocity, e.g., (h v) / h. Therefore, a small dry state threshold
# with a default value of 5*eps() ≈ 1e-15 in double precision, is set in the constructor above
# for the ShallowWaterMultiLayerEquations2D and added to the initial condition if h = 0.
# This default value can be changed within the constructor call depending on the simulation setup.
for i in reverse(eachlayer(equations))
if i == nlayers(equations)
H[i] = max(H[i], b + equations.threshold_limiter)
else
H[i] = max(H[i], H[i + 1] + equations.threshold_limiter)
end
end

return prim2cons(SVector(H..., v1..., v2..., b),
equations)
end

initial_condition = initial_condition_dam_break

boundary_conditions = boundary_condition_slip_wall

###############################################################################
# Get the DG approximation space
volume_flux = (flux_ersing_etal, flux_nonconservative_ersing_etal)
surface_flux = (FluxHydrostaticReconstruction(FluxPlusDissipation(flux_ersing_etal,
DissipationLocalLaxFriedrichs()),
hydrostatic_reconstruction_ersing_etal),
FluxHydrostaticReconstruction(flux_nonconservative_ersing_etal,
hydrostatic_reconstruction_ersing_etal))

basis = LobattoLegendreBasis(3)

indicator_sc = IndicatorHennemannGassnerShallowWater(equations, basis,
alpha_max = 0.5,
alpha_min = 0.001,
alpha_smooth = true,
variable = waterheight_pressure)
volume_integral = VolumeIntegralShockCapturingHG(indicator_sc;
volume_flux_dg = volume_flux,
volume_flux_fv = surface_flux)

solver = DGSEM(basis, surface_flux, volume_integral)

###############################################################################
# Get the TreeMesh and setup a non-periodic mesh with wall boundary conditions

coordinates_min = (-1.0, -1.0)
coordinates_max = (1.0, 1.0)
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_conditions)
###############################################################################
# ODE solver

tspan = (0.0, 2.0)
ode = semidiscretize(semi, tspan)
###############################################################################
#=
Workaround for TreeMesh2D to set true discontinuities for debugging and testing.
Essentially, this is a slight augmentation of the `compute_coefficients` where the `x` node values
passed here are slightly perturbed in order to set a true discontinuity that avoids the doubled
value of the LGL nodes at a particular element interface.
=#

# Point to the data we want to augment
u = Trixi.wrap_array(ode.u0, semi)
# Reset the initial condition
for element in eachelement(semi.solver, semi.cache)
for i in eachnode(semi.solver), j in eachnode(semi.solver)
x_node = Trixi.get_node_coords(semi.cache.elements.node_coordinates, equations,
semi.solver, i, j, element)
# Changing the node positions passed to the initial condition by the minimum
# amount possible with the current type of floating point numbers allows setting
# discontinuous initial data in a simple way. In particular, a check like `if x < x_jump`
# works if the jump location `x_jump` is at the position of an interface.
if i == 1 && j == 1 # bottom left corner
x_node = SVector(nextfloat(x_node[1]), nextfloat(x_node[2]))
elseif i == 1 && j == nnodes(semi.solver) # top left corner
x_node = SVector(nextfloat(x_node[1]), prevfloat(x_node[2]))
elseif i == nnodes(semi.solver) && j == 1 # bottom right corner
x_node = SVector(prevfloat(x_node[1]), nextfloat(x_node[2]))
elseif i == nnodes(semi.solver) && j == nnodes(semi.solver) # top right corner
x_node = SVector(prevfloat(x_node[1]), prevfloat(x_node[2]))
elseif i == 1 # left boundary
x_node = SVector(nextfloat(x_node[1]), x_node[2])
elseif j == 1 # bottom boundary
x_node = SVector(x_node[1], nextfloat(x_node[2]))
elseif i == nnodes(semi.solver) # right boundary
x_node = SVector(prevfloat(x_node[1]), x_node[2])
elseif j == nnodes(semi.solver) # top boundary
x_node = SVector(x_node[1], prevfloat(x_node[2]))
end

u_node = initial_condition_dam_break(x_node, first(tspan), equations)
Trixi.set_node_vars!(u, u_node, equations, semi.solver, i, j, element)
end
end

###############################################################################
# Callbacks

summary_callback = SummaryCallback()

analysis_interval = 50
analysis_callback = AnalysisCallback(semi, interval = analysis_interval,
save_analysis = false,
extra_analysis_integrals = (energy_total,
energy_kinetic,
energy_internal))

alive_callback = AliveCallback(analysis_interval = analysis_interval)

save_solution = SaveSolutionCallback(interval = 100,
save_initial_solution = true,
save_final_solution = true)

stepsize_callback = StepsizeCallback(cfl = 0.3)

callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution,
stepsize_callback)

stage_limiter! = PositivityPreservingLimiterShallowWater(variables = (Trixi.waterheight,))

###############################################################################
# run the simulation

# use a Runge-Kutta method with CFL-based time step
sol = solve(ode, SSPRK43(stage_limiter!);
ode_default_options()..., callback = callbacks, adaptive = false, dt = 1.0);
summary_callback() # print the timer summary
182 changes: 182 additions & 0 deletions examples/unstructured_2d_dgsem/elixir_shallowwater_multilayer_dam_break_dry.jl
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using OrdinaryDiffEq
using Trixi
using TrixiShallowWater

###############################################################################
# Semidiscretization of the multilayer shallow water equations for a dam break test over a dry domain
# with a discontinuous bottom topography function
equations = ShallowWaterMultiLayerEquations2D(gravity_constant = 1.0,
rhos = (0.9, 0.95, 1.0))

# This test case uses a special work around to setup a truly discontinuous bottom topography
# function and initial condition. First, a dummy initial_condition_dam_break is introduced to create
# the semidiscretization. Then the initial condition is reset with the true discontinuous values
# from initial_condition_discontinuous_dam_break.

function initial_condition_dam_break(x, t, equations::ShallowWaterMultiLayerEquations2D)
# Bottom topography
b = 1.4 * exp(-10.0 * ((x[1] - sqrt(2) / 2)^2 + (x[2] - sqrt(2) / 2)^2))

if x[1] < sqrt(2) / 2
H = [1.0, 0.8, 0.6]
else
b += 0.1
H = [b, b, b]
end

v1 = zero(H)
v2 = zero(H)

# It is mandatory to shift the water level at dry areas to make sure the water height h
# stays positive. The system would not be stable for h set to a hard 0 due to division by h in
# the computation of velocity, e.g., (h v) / h. Therefore, a small dry state threshold
# with a default value of 5*eps() ≈ 1e-15 in double precision, is set in the constructor above
# for the ShallowWaterMultiLayerEquations2D and added to the initial condition if h = 0.
# This default value can be changed within the constructor call depending on the simulation setup.
for i in reverse(eachlayer(equations))
if i == nlayers(equations)
H[i] = max(H[i], b + equations.threshold_limiter)
else
H[i] = max(H[i], H[i + 1] + equations.threshold_limiter)
end
end

return prim2cons(SVector(H..., v1..., v2..., b),
equations)
end

initial_condition = initial_condition_dam_break

###############################################################################
# Get the DG approximation space

volume_flux = (flux_ersing_etal, flux_nonconservative_ersing_etal)
surface_flux = (FluxHydrostaticReconstruction(FluxPlusDissipation(flux_ersing_etal,
DissipationLocalLaxFriedrichs()),
hydrostatic_reconstruction_ersing_etal),
FluxHydrostaticReconstruction(flux_nonconservative_ersing_etal,
hydrostatic_reconstruction_ersing_etal))
basis = LobattoLegendreBasis(6)

indicator_sc = IndicatorHennemannGassnerShallowWater(equations, basis,
alpha_max = 0.5,
alpha_min = 0.001,
alpha_smooth = true,
variable = waterheight_pressure)
volume_integral = VolumeIntegralShockCapturingHG(indicator_sc;
volume_flux_dg = volume_flux,
volume_flux_fv = surface_flux)

solver = DGSEM(basis, surface_flux, volume_integral)

###############################################################################
# Get the unstructured quad mesh from a file (downloads the file if not available locally)
mesh_file = Trixi.download("https://gist.githubusercontent.com/andrewwinters5000/8f8cd23df27fcd494553f2a89f3c1ba4/raw/85e3c8d976bbe57ca3d559d653087b0889535295/mesh_alfven_wave_with_twist_and_flip.mesh",
joinpath(@__DIR__, "mesh_alfven_wave_with_twist_and_flip.mesh"))

mesh = UnstructuredMesh2D(mesh_file, periodicity = false)

# Boundary conditions
boundary_condition = Dict(:Top => boundary_condition_slip_wall,
:Left => boundary_condition_slip_wall,
:Right => boundary_condition_slip_wall,
:Bottom => boundary_condition_slip_wall)

# Create the semi discretization object
semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition,
solver, boundary_conditions = boundary_condition)

###############################################################################
# ODE solver

tspan = (0.0, 2.0)
ode = semidiscretize(semi, tspan)

###############################################################################
# Workaround to set a discontinuous bottom topography and initial condition.

# alternative version of the initial conditinon used to setup a truly discontinuous
# test case and initial condition.
# In contrast to the usual signature of initial conditions, this one get passed the
# `element_id` explicitly. In particular, this initial conditions works as intended
# only for the specific mesh loaded above!
function initial_condition_discontinuous_dam_break(x, t, element_id,
equations::ShallowWaterMultiLayerEquations2D)
# Bottom topography
b = 1.4 * exp(-10.0 * ((x[1] - sqrt(2) / 2)^2 + (x[2] - sqrt(2) / 2)^2))

# Left side of discontinuity
IDs = [1, 2, 5, 6, 9, 10, 13, 14]
if element_id in IDs
H = [1.0, 0.8, 0.6]
else # Right side of discontinuity
b += 0.1
H = [b, b, b]
end

v1 = zero(H)
v2 = zero(H)

# It is mandatory to shift the water level at dry areas to make sure the water height h
# stays positive. The system would not be stable for h set to a hard 0 due to division by h in
# the computation of velocity, e.g., (h v) / h. Therefore, a small dry state threshold
# with a default value of 5*eps() ≈ 1e-15 in double precision, is set in the constructor above
# for the ShallowWaterMultiLayerEquations2D and added to the initial condition if h = 0.
# This default value can be changed within the constructor call depending on the simulation setup.
for i in reverse(eachlayer(equations))
if i == nlayers(equations)
H[i] = max(H[i], b + equations.threshold_limiter)
else
H[i] = max(H[i], H[i + 1] + equations.threshold_limiter)
end
end

return prim2cons(SVector(H..., v1..., v2..., b),
equations)
end

# point to the data we want to augment
u = Trixi.wrap_array(ode.u0, semi)
# reset the initial condition
for element in eachelement(semi.solver, semi.cache)
for j in eachnode(semi.solver), i in eachnode(semi.solver)
x_node = Trixi.get_node_coords(semi.cache.elements.node_coordinates, equations,
semi.solver, i, j, element)
u_node = initial_condition_discontinuous_dam_break(x_node, first(tspan), element,
equations)
Trixi.set_node_vars!(u, u_node, equations, semi.solver, i, j, element)
end
end

###############################################################################
# Callbacks

summary_callback = SummaryCallback()

analysis_interval = 10
analysis_callback = AnalysisCallback(semi, interval = analysis_interval,
save_analysis = false,
extra_analysis_integrals = (energy_total,
energy_kinetic,
energy_internal))

alive_callback = AliveCallback(analysis_interval = analysis_interval)

save_solution = SaveSolutionCallback(interval = 100,
save_initial_solution = true,
save_final_solution = true)

stepsize_callback = StepsizeCallback(cfl = 0.5)

callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution,
stepsize_callback)

stage_limiter! = PositivityPreservingLimiterShallowWater(variables = (Trixi.waterheight,))

###############################################################################
# run the simulation

sol = solve(ode, SSPRK43(stage_limiter!);
ode_default_options()..., callback = callbacks, adaptive = false, dt = 1.0);
summary_callback() # print the timer summary
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