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Added Shu-Osher initialization for 1D compressible Euler with Gauss n…
…odes (#1943) * Added 1D Shu-Osher initialization for compressible Euler 1D * Fix: Addresses comments from PR 1943 * Added test for Euler 1D Shu Osher with Gauss nodes * Remove useless comment in test * Formate files with JuliaFormatter 1.0.45 * Fixed error in test for Shu Osher Gauss node problem * Fix issue in initial condition for Shu Osher --------- Co-authored-by: Hendrik Ranocha <[email protected]>
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examples/dgmulti_1d/elixir_euler_shu_osher_gauss_shock_capturing.jl
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using Trixi | ||
using OrdinaryDiffEq | ||
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gamma_gas = 1.4 | ||
equations = CompressibleEulerEquations1D(gamma_gas) | ||
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############################################################################### | ||
# setup the GSBP DG discretization that uses the Gauss operators from | ||
# Chan, Del Rey Fernandez, Carpenter (2019). | ||
# [https://doi.org/10.1137/18M1209234](https://doi.org/10.1137/18M1209234) | ||
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# Shu-Osher initial condition for 1D compressible Euler equations | ||
# Example 8 from Shu, Osher (1989). | ||
# [https://doi.org/10.1016/0021-9991(89)90222-2](https://doi.org/10.1016/0021-9991(89)90222-2) | ||
function initial_condition_shu_osher(x, t, equations::CompressibleEulerEquations1D) | ||
x0 = -4 | ||
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rho_left = 27 / 7 | ||
v_left = 4 * sqrt(35) / 9 | ||
p_left = 31 / 3 | ||
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# Replaced v_right = 0 to v_right = 0.1 to avoid positivity issues. | ||
v_right = 0.1 | ||
p_right = 1.0 | ||
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rho = ifelse(x[1] > x0, 1 + 1 / 5 * sin(5 * x[1]), rho_left) | ||
v = ifelse(x[1] > x0, v_right, v_left) | ||
p = ifelse(x[1] > x0, p_right, p_left) | ||
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return prim2cons(SVector(rho, v, p), | ||
equations) | ||
end | ||
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initial_condition = initial_condition_shu_osher | ||
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surface_flux = flux_lax_friedrichs | ||
volume_flux = flux_ranocha | ||
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polydeg = 3 | ||
basis = DGMultiBasis(Line(), polydeg, approximation_type = GaussSBP()) | ||
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indicator_sc = IndicatorHennemannGassner(equations, basis, | ||
alpha_max = 0.5, | ||
alpha_min = 0.001, | ||
alpha_smooth = true, | ||
variable = density_pressure) | ||
volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; | ||
volume_flux_dg = volume_flux, | ||
volume_flux_fv = surface_flux) | ||
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dg = DGMulti(basis, | ||
surface_integral = SurfaceIntegralWeakForm(surface_flux), | ||
volume_integral = volume_integral) | ||
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boundary_condition = BoundaryConditionDirichlet(initial_condition) | ||
boundary_conditions = (; :entire_boundary => boundary_condition) | ||
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############################################################################### | ||
# setup the 1D mesh | ||
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cells_per_dimension = (64,) | ||
mesh = DGMultiMesh(dg, cells_per_dimension, | ||
coordinates_min = (-5.0,), coordinates_max = (5.0,), | ||
periodicity = false) | ||
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############################################################################### | ||
# setup the semidiscretization and ODE problem | ||
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semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, | ||
dg, boundary_conditions = boundary_conditions) | ||
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tspan = (0.0, 1.0) | ||
ode = semidiscretize(semi, tspan) | ||
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############################################################################### | ||
# setup the callbacks | ||
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# prints a summary of the simulation setup and resets the timers | ||
summary_callback = SummaryCallback() | ||
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# analyse the solution in regular intervals and prints the results | ||
analysis_callback = AnalysisCallback(semi, interval = 100, uEltype = real(dg)) | ||
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# handles the re-calculation of the maximum Δt after each time step | ||
stepsize_callback = StepsizeCallback(cfl = 0.1) | ||
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# collect all callbacks such that they can be passed to the ODE solver | ||
callbacks = CallbackSet(summary_callback, analysis_callback, stepsize_callback) | ||
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# ############################################################################### | ||
# # run the simulation | ||
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sol = solve(ode, SSPRK43(), adaptive = true, callback = callbacks, save_everystep = false) |
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