21639639306

Committed 03 Feb 2026 05:01PM UTC coverage: 14.281% (-82.8%) from 97.034%

Build # 21639639306

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Pull #2601

github

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web-flow

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Merge fd2e0cdf8 into ead0db32a

Pull Request Pull Request #2601: Adaptive Volume Integral

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0.0

/examples/tree_2d_dgsem/elixir_euler_vortex_mortar_split.jl

using OrdinaryDiffEqLowStorageRK
using Trixi

###############################################################################
# semidiscretization of the compressible Euler equations

equations = CompressibleEulerEquations2D(1.4)

"""
    initial_condition_isentropic_vortex(x, t, equations::CompressibleEulerEquations2D)

The classical isentropic vortex test case of
- Chi-Wang Shu (1997)
  Essentially Non-Oscillatory and Weighted Essentially Non-Oscillatory
  Schemes for Hyperbolic Conservation Laws
  [NASA/CR-97-206253](https://ntrs.nasa.gov/citations/19980007543)
"""
function initial_condition_isentropic_vortex(x, t, equations::CompressibleEulerEquations2D)
    # needs appropriate mesh size, e.g. [-10,-10]x[10,10]
    # for error convergence: make sure that the end time is such that the vortex is back at the initial state!!
    # for the current velocity and domain size: t_end should be a multiple of 20s
    # initial center of the vortex
    RealT = eltype(x)
    inicenter = SVector(0, 0)
    # size and strength of the vortex
    iniamplitude = 5
    # base flow
    rho = 1
    v1 = 1
    v2 = 1
    vel = SVector(v1, v2)
    p = convert(RealT, 25)
    rt = p / rho                  # ideal gas equation
    t_loc = 0
    cent = inicenter + vel * t_loc      # advection of center
    # ATTENTION: handle periodic BC, but only for v1 = v2 = 1.0 (!!!!)
    cent = x - cent # distance to center point
    # cent = cross(iniaxis, cent) # distance to axis, tangent vector, length r
    # cross product with iniaxis = [0, 0, 1]
    cent = SVector(-cent[2], cent[1])
    r2 = cent[1]^2 + cent[2]^2
    du = iniamplitude / (2 * convert(RealT, pi)) * exp(0.5f0 * (1 - r2)) # vel. perturbation
    dtemp = -(equations.gamma - 1) / (2 * equations.gamma * rt) * du^2 # isentropic
    rho = rho * (1 + dtemp)^(1 / (equations.gamma - 1))
    vel = vel + du * cent
    v1, v2 = vel
    p = p * (1 + dtemp)^(equations.gamma / (equations.gamma - 1))
    prim = SVector(rho, v1, v2, p)
    return prim2cons(prim, equations)
end
initial_condition = initial_condition_isentropic_vortex

# Up to version 0.13.0, `max_abs_speed_naive` was used as the default wave speed estimate of
# `const flux_lax_friedrichs = FluxLaxFriedrichs(), i.e., `FluxLaxFriedrichs(max_abs_speed = max_abs_speed_naive)`.
# In the `StepsizeCallback`, though, the less diffusive `max_abs_speeds` is employed which is consistent with `max_abs_speed`.
# Thus, we exchanged in PR#2458 the default wave speed used in the LLF flux to `max_abs_speed`.
# To ensure that every example still runs we specify explicitly `FluxLaxFriedrichs(max_abs_speed_naive)`.
# We remark, however, that the now default `max_abs_speed` is in general recommended due to compliance with the 
# `StepsizeCallback` (CFL-Condition) and less diffusion.
surface_flux = FluxLaxFriedrichs(max_abs_speed_naive)
volume_flux = flux_shima_etal

polydeg = 3
basis = LobattoLegendreBasis(polydeg)
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)
solver = DGSEM(basis, surface_flux, volume_integral)

coordinates_min = (-10.0, -10.0)
coordinates_max = (10.0, 10.0)
mesh = TreeMesh(coordinates_min, coordinates_max,
                initial_refinement_level = 4,
                n_cells_max = 10_000)

semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver)

###############################################################################
# ODE solvers, callbacks etc.

tspan = (0.0, 1.0)
ode = semidiscretize(semi, tspan)

summary_callback = SummaryCallback()

analysis_interval = 100
analysis_callback = AnalysisCallback(semi, interval = analysis_interval,
                                     save_analysis = true,
                                     extra_analysis_errors = (:conservation_error,),
                                     extra_analysis_integrals = (entropy, energy_total,
                                                                 energy_kinetic,
                                                                 energy_internal))

alive_callback = AliveCallback(analysis_interval = analysis_interval)

save_restart = SaveRestartCallback(interval = 100,
                                   save_final_restart = true)

save_solution = SaveSolutionCallback(interval = 100,
                                     save_initial_solution = true,
                                     save_final_solution = true,
                                     solution_variables = cons2prim)

stepsize_callback = StepsizeCallback(cfl = 0.7)

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

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

sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false);
            dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback
            ode_default_options()..., callback = callbacks);

1	using OrdinaryDiffEqLowStorageRK
2	using Trixi
3
4	###############################################################################
5	# semidiscretization of the compressible Euler equations
6
7	equations = CompressibleEulerEquations2D(1.4)
8
9	"""
10	initial_condition_isentropic_vortex(x, t, equations::CompressibleEulerEquations2D)
11
12	The classical isentropic vortex test case of
13	- Chi-Wang Shu (1997)
14	Essentially Non-Oscillatory and Weighted Essentially Non-Oscillatory
15	Schemes for Hyperbolic Conservation Laws
16	[NASA/CR-97-206253](https://ntrs.nasa.gov/citations/19980007543)
17	"""
UNCOV 18	function initial_condition_isentropic_vortex(x, t, equations::CompressibleEulerEquations2D)	×
19	# needs appropriate mesh size, e.g. [-10,-10]x[10,10]
20	# for error convergence: make sure that the end time is such that the vortex is back at the initial state!!
21	# for the current velocity and domain size: t_end should be a multiple of 20s
22	# initial center of the vortex
UNCOV 23	RealT = eltype(x)	×
UNCOV 24	inicenter = SVector(0, 0)	×
25	# size and strength of the vortex
UNCOV 26	iniamplitude = 5	×
27	# base flow
UNCOV 28	rho = 1	×
UNCOV 29	v1 = 1	×
UNCOV 30	v2 = 1	×
UNCOV 31	vel = SVector(v1, v2)	×
UNCOV 32	p = convert(RealT, 25)	×
UNCOV 33	rt = p / rho # ideal gas equation	×
UNCOV 34	t_loc = 0	×
UNCOV 35	cent = inicenter + vel * t_loc # advection of center	×
36	# ATTENTION: handle periodic BC, but only for v1 = v2 = 1.0 (!!!!)
UNCOV 37	cent = x - cent # distance to center point	×
38	# cent = cross(iniaxis, cent) # distance to axis, tangent vector, length r
39	# cross product with iniaxis = [0, 0, 1]
UNCOV 40	cent = SVector(-cent[2], cent[1])	×
UNCOV 41	r2 = cent[1]^2 + cent[2]^2	×
UNCOV 42	du = iniamplitude / (2 * convert(RealT, pi)) * exp(0.5f0 * (1 - r2)) # vel. perturbation	×
UNCOV 43	dtemp = -(equations.gamma - 1) / (2 * equations.gamma * rt) * du^2 # isentropic	×
UNCOV 44	rho = rho * (1 + dtemp)^(1 / (equations.gamma - 1))	×
UNCOV 45	vel = vel + du * cent	×
UNCOV 46	v1, v2 = vel	×
UNCOV 47	p = p * (1 + dtemp)^(equations.gamma / (equations.gamma - 1))	×
UNCOV 48	prim = SVector(rho, v1, v2, p)	×
UNCOV 49	return prim2cons(prim, equations)	×
50	end
51	initial_condition = initial_condition_isentropic_vortex
52
53	# Up to version 0.13.0, `max_abs_speed_naive` was used as the default wave speed estimate of
54	# `const flux_lax_friedrichs = FluxLaxFriedrichs(), i.e., `FluxLaxFriedrichs(max_abs_speed = max_abs_speed_naive)`.
55	# In the `StepsizeCallback`, though, the less diffusive `max_abs_speeds` is employed which is consistent with `max_abs_speed`.
56	# Thus, we exchanged in PR#2458 the default wave speed used in the LLF flux to `max_abs_speed`.
57	# To ensure that every example still runs we specify explicitly `FluxLaxFriedrichs(max_abs_speed_naive)`.
58	# We remark, however, that the now default `max_abs_speed` is in general recommended due to compliance with the
59	# `StepsizeCallback` (CFL-Condition) and less diffusion.
60	surface_flux = FluxLaxFriedrichs(max_abs_speed_naive)
61	volume_flux = flux_shima_etal
62
63	polydeg = 3
64	basis = LobattoLegendreBasis(polydeg)
65	indicator_sc = IndicatorHennemannGassner(equations, basis,
66	alpha_max = 0.5,
67	alpha_min = 0.001,
68	alpha_smooth = true,
69	variable = density_pressure)
70	volume_integral = VolumeIntegralShockCapturingHG(indicator_sc;
71	volume_flux_dg = volume_flux,
72	volume_flux_fv = surface_flux)
73	solver = DGSEM(basis, surface_flux, volume_integral)
74
75	coordinates_min = (-10.0, -10.0)
76	coordinates_max = (10.0, 10.0)
77	mesh = TreeMesh(coordinates_min, coordinates_max,
78	initial_refinement_level = 4,
79	n_cells_max = 10_000)
80
81	semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver)
82
83	###############################################################################
84	# ODE solvers, callbacks etc.
85
86	tspan = (0.0, 1.0)
87	ode = semidiscretize(semi, tspan)
88
89	summary_callback = SummaryCallback()
90
91	analysis_interval = 100
92	analysis_callback = AnalysisCallback(semi, interval = analysis_interval,
93	save_analysis = true,
94	extra_analysis_errors = (:conservation_error,),
95	extra_analysis_integrals = (entropy, energy_total,
96	energy_kinetic,
97	energy_internal))
98
99	alive_callback = AliveCallback(analysis_interval = analysis_interval)
100
101	save_restart = SaveRestartCallback(interval = 100,
102	save_final_restart = true)
103
104	save_solution = SaveSolutionCallback(interval = 100,
105	save_initial_solution = true,
106	save_final_solution = true,
107	solution_variables = cons2prim)
108
109	stepsize_callback = StepsizeCallback(cfl = 0.7)
110
111	callbacks = CallbackSet(summary_callback,
112	analysis_callback, alive_callback,
113	save_restart, save_solution,
114	stepsize_callback)
115
116	###############################################################################
117	# run the simulation
118
119	sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false);
120	dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback
121	ode_default_options()..., callback = callbacks);

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