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von-Karman Vortex Street #2246

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von-Karman Vortex Street
DanielDoehring Jan 22, 2025
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DanielDoehring Jan 22, 2025
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DanielDoehring Jan 22, 2025
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115 changes: 115 additions & 0 deletions examples/p4est_2d_dgsem/elixir_navierstokes_vortex_street.jl
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using OrdinaryDiffEq
using Trixi

###############################################################################
# Semidiscretization of the compressible Euler equations

# Fluid parameters
gamma() = 5 / 3
prandtl_number() = 0.72

# Parameters for compressible von-Karman vortex street
Re() = 500
Ma() = 0.5f0
D() = 1 # Diameter of the cylinder as in the mesh file

# Parameters that can be freely chosen
v_in() = 1
p_in() = 1

# Parameters that follow from Reynolds and Mach number + adiabatic index gamma
mu() = v_in() * D() / Re()

c() = v_in() / Ma()
p_over_rho() = c()^2 / gamma()
rho_in() = p_in() / p_over_rho()

# Equations for this configuration
equations = CompressibleEulerEquations2D(gamma())
equations_parabolic = CompressibleNavierStokesDiffusion2D(equations, mu = mu(),
Prandtl = prandtl_number(),
gradient_variables = GradientVariablesPrimitive())

# Freestream configuration
@inline function initial_condition(x, t, equations::CompressibleEulerEquations2D)
rho = rho_in()
v1 = v_in()
v2 = 0.0
p = p_in()

prim = SVector(rho, v1, v2, p)
return prim2cons(prim, equations)
end

# Mesh which is refined around the cylinder and the wake region
mesh_file = Trixi.download("https://gist.githubusercontent.com/DanielDoehring/7312faba9a50ef506b13f01716b4ec26/raw/8e68f9006e634905544207ca322bc0a03a9313ad/cylinder_vortex_street.inp",
joinpath(@__DIR__, "cylinder_vortex_street.inp"))
mesh = P4estMesh{2}(mesh_file)

bc_freestream = BoundaryConditionDirichlet(initial_condition)

# Boundary names follow from the mesh file
boundary_conditions = Dict(:Bottom => bc_freestream,
:Circle => boundary_condition_slip_wall,
:Top => bc_freestream,
:Right => bc_freestream,
:Left => bc_freestream)

# Parabolic boundary conditions
velocity_bc_free = NoSlip((x, t, equations) -> SVector(v_in(), 0))
# Use adiabatic also on the boundaries to "copy" temperature from the domain
heat_bc_free = Adiabatic((x, t, equations) -> 0)
boundary_condition_free = BoundaryConditionNavierStokesWall(velocity_bc_free, heat_bc_free)

velocity_bc_cylinder = NoSlip((x, t, equations) -> SVector(0, 0))
heat_bc_cylinder = Adiabatic((x, t, equations) -> 0)
boundary_condition_cylinder = BoundaryConditionNavierStokesWall(velocity_bc_cylinder,
heat_bc_cylinder)

boundary_conditions_para = Dict(:Bottom => boundary_condition_free,
:Circle => boundary_condition_cylinder,
:Top => boundary_condition_free,
:Right => boundary_condition_free,
:Left => boundary_condition_free)
# Standard DGSEM sufficient here
solver = DGSEM(polydeg = 3, surface_flux = flux_hll)

semi = SemidiscretizationHyperbolicParabolic(mesh, (equations, equations_parabolic),
initial_condition, solver,
boundary_conditions = (boundary_conditions,
boundary_conditions_para))

###############################################################################
# Setup an ODE problem
tspan = (0, 100)
ode = semidiscretize(semi, tspan)

# Callbacks
summary_callback = SummaryCallback()

analysis_interval = 1000
analysis_callback = AnalysisCallback(semi, interval = analysis_interval)

alive_callback = AliveCallback(analysis_interval = analysis_interval)

save_solution = SaveSolutionCallback(interval = analysis_interval,
save_initial_solution = true,
save_final_solution = true,
solution_variables = cons2prim)

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

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

time_int_tol = 1e-6
sol = solve(ode,
# Moderate number of threads (e.g. 4) advisable to speed things up
RDPK3SpFSAL49(thread = OrdinaryDiffEq.True());
dt = 1e-3, abstol = time_int_tol, reltol = time_int_tol,
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Is setting dt required here?

ode_default_options()..., callback = callbacks)

summary_callback() # print the timer summary
1 change: 0 additions & 1 deletion src/equations/compressible_navier_stokes_1d.jl
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Expand Up @@ -286,7 +286,6 @@ end
t,
operator_type::Divergence,
equations::CompressibleNavierStokesDiffusion1D{GradientVariablesPrimitive})
# rho, v1, v2, _ = u_inner
normal_heat_flux = boundary_condition.boundary_condition_heat_flux.boundary_value_normal_flux_function(x,
t,
equations)
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1 change: 0 additions & 1 deletion src/equations/compressible_navier_stokes_2d.jl
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Expand Up @@ -325,7 +325,6 @@ end
t,
operator_type::Divergence,
equations::CompressibleNavierStokesDiffusion2D{GradientVariablesPrimitive})
# rho, v1, v2, _ = u_inner
normal_heat_flux = boundary_condition.boundary_condition_heat_flux.boundary_value_normal_flux_function(x,
t,
equations)
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1 change: 0 additions & 1 deletion src/equations/compressible_navier_stokes_3d.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -358,7 +358,6 @@ end
t,
operator_type::Divergence,
equations::CompressibleNavierStokesDiffusion3D{GradientVariablesPrimitive})
# rho, v1, v2, v3, _ = u_inner
normal_heat_flux = boundary_condition.boundary_condition_heat_flux.boundary_value_normal_flux_function(x,
t,
equations)
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26 changes: 26 additions & 0 deletions test/test_parabolic_2d.jl
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Expand Up @@ -811,6 +811,32 @@ end
@test (@allocated Trixi.rhs!(du_ode, u_ode, semi, t)) < 1000
end
end

@trixi_testset "elixir_navierstokes_vortex_street.jl" begin
@test_trixi_include(joinpath(examples_dir(), "p4est_2d_dgsem",
"elixir_navierstokes_vortex_street.jl"),
l2=[
0.005069706928574108,
0.011627798047777405,
0.009242702790766983,
0.02646416294015243
],
linf=[
0.21307118247870704,
0.5365731661670426,
0.29315320855786453,
0.9453411793625751
],
tspan=(0.0, 1.0))
# Ensure that we do not have excessive memory allocations
# (e.g., from type instabilities)
let
t = sol.t[end]
u_ode = sol.u[end]
du_ode = similar(u_ode)
@test (@allocated Trixi.rhs!(du_ode, u_ode, semi, t)) < 1000
end
end
end

# Clean up afterwards: delete Trixi.jl output directory
Expand Down
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