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Use total pressure for 1D HLLC MHD #1756

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merged 4 commits into from
Dec 1, 2023
Merged

Use total pressure for 1D HLLC MHD #1756

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cb3060c
Use total pressure
DanielDoehring Nov 22, 2023
300c9b3
Merge branch 'main' into HLLC_MHD_1D_TotalPressure
DanielDoehring Nov 24, 2023
26503ab
Update src/equations/ideal_glm_mhd_1d.jl
DanielDoehring Nov 24, 2023
eb006ff
Merge branch 'main' into HLLC_MHD_1D_TotalPressure
DanielDoehring Nov 28, 2023
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20 changes: 12 additions & 8 deletions src/equations/ideal_glm_mhd_1d.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -272,6 +272,10 @@ function flux_hllc(u_ll, u_rr, orientation::Integer,
rho_ll, v1_ll, v2_ll, v3_ll, p_ll, B1_ll, B2_ll, B3_ll = cons2prim(u_ll, equations)
rho_rr, v1_rr, v2_rr, v3_rr, p_rr, B1_rr, B2_rr, B3_rr = cons2prim(u_rr, equations)

# Total pressure, i.e., thermal + magnetic pressures (eq. (12))
p_tot_ll = p_ll + 0.5 * (B1_ll^2 + B2_ll^2 + B3_ll^2)
p_tot_rr = p_rr + 0.5 * (B1_rr^2 + B2_rr^2 + B3_rr^2)

# Conserved variables
rho_v1_ll = u_ll[2]
rho_v2_ll = u_ll[3]
Expand Down Expand Up @@ -309,11 +313,11 @@ function flux_hllc(u_ll, u_rr, orientation::Integer,
else
# Compute the "HLLC-speed", eq. (14) from paper mentioned above
#=
SStar = (rho_rr * v1_rr * sMu_R - rho_ll * v1_ll * sMu_L + p_ll - p_rr - B1_ll^2 + B1_rr^2 ) /
SStar = (rho_rr * v1_rr * sMu_R - rho_ll * v1_ll * sMu_L + p_tot_ll - p_tot_rr - B1_ll^2 + B1_rr^2 ) /
(rho_rr * sMu_R - rho_ll * sMu_L)
=#
# Simplification for 1D: B1 is constant
SStar = (rho_rr * v1_rr * sMu_R - rho_ll * v1_ll * sMu_L + p_ll - p_rr) /
SStar = (rho_rr * v1_rr * sMu_R - rho_ll * v1_ll * sMu_L + p_tot_ll - p_tot_rr) /
(rho_rr * sMu_R - rho_ll * sMu_L)

Sdiff = SsR - SsL
Expand Down Expand Up @@ -347,12 +351,12 @@ function flux_hllc(u_ll, u_rr, orientation::Integer,
mom_3_Star = densStar * v3_ll -
(B1Star * B3Star - B1_ll * B3_ll) / SdiffStar # (22)

#pstar = rho_ll * sMu_L * (SStar - v1_ll) + p_ll - B1_ll^2 + B1Star^2 # (17)
#p_tot_Star = rho_ll * sMu_L * (SStar - v1_ll) + p_tot_ll - B1_ll^2 + B1Star^2 # (17)
# 1D B1 = constant => B1_ll = B1_rr = B1Star
pstar = rho_ll * sMu_L * (SStar - v1_ll) + p_ll # (17)
p_tot_Star = rho_ll * sMu_L * (SStar - v1_ll) + p_tot_ll # (17)

enerStar = u_ll[5] * sMu_L / SdiffStar +
(pstar * SStar - p_ll * v1_ll - (B1Star *
(p_tot_Star * SStar - p_tot_ll * v1_ll - (B1Star *
(B1Star * v1Star + B2Star * v2Star + B3Star * v3Star) -
B1_ll * (B1_ll * v1_ll + B2_ll * v2_ll + B3_ll * v3_ll))) /
SdiffStar # (23)
Expand All @@ -377,12 +381,12 @@ function flux_hllc(u_ll, u_rr, orientation::Integer,
mom_3_Star = densStar * v3_rr -
(B1Star * B3Star - B1_rr * B3_rr) / SdiffStar # (22)

#pstar = rho_rr * sMu_R * (SStar - v1_rr) + p_rr - B1_rr^2 + B1Star^2 # (17)
#p_tot_Star = rho_rr * sMu_R * (SStar - v1_rr) + p_tot_rr - B1_rr^2 + B1Star^2 # (17)
# 1D B1 = constant => B1_ll = B1_rr = B1Star
pstar = rho_rr * sMu_R * (SStar - v1_rr) + p_rr # (17)
p_tot_Star = rho_rr * sMu_R * (SStar - v1_rr) + p_tot_rr # (17)

enerStar = u_rr[5] * sMu_R / SdiffStar +
(pstar * SStar - p_rr * v1_rr - (B1Star *
(p_tot_Star * SStar - p_tot_rr * v1_rr - (B1Star *
(B1Star * v1Star + B2Star * v2Star + B3Star * v3Star) -
B1_rr * (B1_rr * v1_rr + B2_rr * v2_rr + B3_rr * v3_rr))) /
SdiffStar # (23)
Expand Down
41 changes: 33 additions & 8 deletions test/test_tree_1d_mhd.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -109,6 +109,31 @@ end
end
end

@trixi_testset "elixir_mhd_alfven_wave.jl with flux_hllc" begin
@test_trixi_include(joinpath(EXAMPLES_DIR, "elixir_mhd_alfven_wave.jl"),
l2=[
1.036850596986597e-5, 1.965192583650368e-6,
3.5882124656715505e-5, 3.5882124656638764e-5,
5.270975504780837e-6, 1.1963224165731992e-16,
3.595811808912869e-5, 3.5958118089159453e-5,
],
linf=[
2.887280521446378e-5, 7.310580790352001e-6,
0.00012390046377899755, 0.00012390046377787345,
1.5102711136583125e-5, 2.220446049250313e-16,
0.0001261935452181312, 0.0001261935452182006,
],
surface_flux=flux_hllc)
# 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

@trixi_testset "elixir_mhd_ec.jl" begin
@test_trixi_include(joinpath(EXAMPLES_DIR, "elixir_mhd_ec.jl"),
l2=[
Expand Down Expand Up @@ -210,16 +235,16 @@ end
@test_trixi_include(joinpath(EXAMPLES_DIR, "elixir_mhd_torrilhon_shock_tube.jl"),
surface_flux=flux_hllc,
l2=[
0.45738965718253993, 0.479402222862685, 0.34069729746967664,
0.44795514335568865, 0.9206813325913135,
1.3216517820475193e-16, 0.2889672868491632,
0.2552794220777942,
0.4573799618744708, 0.4792633358230866, 0.34064852506872795,
0.4479668434955162, 0.9203891782415092,
1.3216517820475193e-16, 0.28887826520860815,
0.255281629265771,
],
linf=[
1.2181099854251536, 0.8869319941747589, 0.8763562906332134,
0.9712221036087284, 1.6734231113527818,
2.220446049250313e-16, 0.7035011427822779,
0.6562884129650286,
1.2382842201671505, 0.8929169308132259, 0.871298623806198,
0.9822415614542821, 1.6726170732132717,
2.220446049250313e-16, 0.7016155888023747,
0.6556091522071984,
])
# Ensure that we do not have excessive memory allocations
# (e.g., from type instabilities)
Expand Down
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