Using an implicit-explicit (IMEX) Runge-Kutta solver based on Ariadne with Trixi.jl

using Trixi
using Theseus
using CairoMakie

Notes: You must disable both Polyester and LoopVectorization for Enzyme to be able to differentiate Trixi.jl.

LocalPreferences.jl

[Trixi]
loop_vectorization = false
backend = "static"
@assert Trixi._PREFERENCE_THREADING !== :polyester
@assert !Trixi._PREFERENCE_LOOPVECTORIZATION

First call to load callbacks

trixi_include(@__MODULE__, joinpath(examples_dir(), "p4est_2d_dgsem", "elixir_navierstokes_vortex_street.jl"), sol = nothing, analysis_interval = 10);

stepsize_callback = StepsizeCallback(cfl = 1.0)

callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, stepsize_callback)
tspan = (0.0, 0.5)
trixi_include(@__MODULE__, joinpath(examples_dir(), "p4est_2d_dgsem", "elixir_navierstokes_vortex_street.jl"), sol = nothing, callbacks = callbacks, tspan = tspan);
###############################################################################
[ Info: You just called `trixi_include`. Julia may now compile the code, please be patient.
[ Info: You just called `trixi_include`. Julia may now compile the code, please be patient.

run the simulation

sol = solve(
    ode,
    Theseus.ARS443(); # ARS111, ARS222, ARS443
    dt = 0.001, # solve needs some value here but it will be overwritten by the stepsize_callback
    ode_default_options()..., callback = callbacks,
    krylov_algo = :gmres,
);

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┌──────────────────────────────────────────────────────────────────────────────────────────────────┐
│ SemidiscretizationHyperbolicParabolic                                                            │
│ ═════════════════════════════════════                                                            │
│ #spatial dimensions: ………………………… 2                                                                │
│ mesh: ………………………………………………………………… P4estMesh{2, 2, Float64}                                         │
│ hyperbolic equations: ……………………… CompressibleEulerEquations2D                                     │
│ parabolic equations: ………………………… CompressibleNavierStokesDiffusion2D                              │
│ initial condition: ……………………………… initial_condition                                                │
│ source terms: …………………………………………… nothing                                                          │
│ source terms parabolic: ………………… nothing                                                          │
│ solver: …………………………………………………………… DG                                                               │
│ parabolic solver: ………………………………… ViscousFormulationBassiRebay1                                    │
│ total #DOFs per field: …………………… 36128                                                            │
└──────────────────────────────────────────────────────────────────────────────────────────────────┘

┌──────────────────────────────────────────────────────────────────────────────────────────────────┐
│ P4estMesh{2, 2, Float64}                                                                         │
│ ════════════════════════                                                                         │
│ #trees: …………………………………………………………… 2258                                                             │
│ current #cells: ……………………………………… 2258                                                             │
│ polydeg: ………………………………………………………… 3                                                                │
└──────────────────────────────────────────────────────────────────────────────────────────────────┘

┌──────────────────────────────────────────────────────────────────────────────────────────────────┐
│ CompressibleEulerEquations2D                                                                     │
│ ════════════════════════════                                                                     │
│ #variables: ………………………………………………… 4                                                                │
│ │ variable 1: …………………………………………… rho                                                              │
│ │ variable 2: …………………………………………… rho_v1                                                           │
│ │ variable 3: …………………………………………… rho_v2                                                           │
│ │ variable 4: …………………………………………… rho_e                                                            │
└──────────────────────────────────────────────────────────────────────────────────────────────────┘

┌──────────────────────────────────────────────────────────────────────────────────────────────────┐
│ DG{Float64}                                                                                      │
│ ═══════════                                                                                      │
│ basis: ……………………………………………………………… LobattoLegendreBasis{Float64}(polydeg=3)                         │
│ mortar: …………………………………………………………… LobattoLegendreMortarL2{Float64}(polydeg=3)                      │
│ surface integral: ………………………………… SurfaceIntegralWeakForm                                          │
│ │ surface flux: ……………………………………… FluxHLL(min_max_speed_davis)                                     │
│ volume integral: …………………………………… VolumeIntegralWeakForm                                           │
└──────────────────────────────────────────────────────────────────────────────────────────────────┘

┌──────────────────────────────────────────────────────────────────────────────────────────────────┐
│ AnalysisCallback                                                                                 │
│ ════════════════                                                                                 │
│ interval: ……………………………………………………… 10                                                               │
│ analyzer: ……………………………………………………… LobattoLegendreAnalyzer{Float64}(polydeg=6)                      │
│ │ error 1: …………………………………………………… l2_error                                                         │
│ │ error 2: …………………………………………………… linf_error                                                       │
│ │ integral 1: …………………………………………… entropy_timederivative                                           │
│ save analysis to file: …………………… no                                                               │
└──────────────────────────────────────────────────────────────────────────────────────────────────┘

┌──────────────────────────────────────────────────────────────────────────────────────────────────┐
│ AliveCallback                                                                                    │
│ ═════════════                                                                                    │
│ interval: ……………………………………………………… 1                                                                │
└──────────────────────────────────────────────────────────────────────────────────────────────────┘

┌──────────────────────────────────────────────────────────────────────────────────────────────────┐
│ StepsizeCallback                                                                                 │
│ ════════════════                                                                                 │
│ CFL Advective: ………………………………………… Returns{Float64}(1.0)                                            │
│ CFL Diffusive: ………………………………………… Returns{Float64}(0.0)                                            │
│ Interval: ……………………………………………………… 1                                                                │
└──────────────────────────────────────────────────────────────────────────────────────────────────┘

┌──────────────────────────────────────────────────────────────────────────────────────────────────┐
│ Time integration                                                                                 │
│ ════════════════                                                                                 │
│ Start time: ………………………………………………… 0.0                                                              │
│ Final time: ………………………………………………… 0.5                                                              │
│ time integrator: …………………………………… ARS443                                                           │
│ adaptive: ……………………………………………………… false                                                            │
└──────────────────────────────────────────────────────────────────────────────────────────────────┘
┌──────────────────────────────────────────────────────────────────────────────────────────────────┐
│ Environment information                                                                          │
│ ═══════════════════════                                                                          │
│ #threads: ……………………………………………………… 1                                                                │
│ threading backend: ……………………………… static                                                           │
│ LoopVectorization: ……………………………… disabled                                                         │
└──────────────────────────────────────────────────────────────────────────────────────────────────┘

────────────────────────────────────────────────────────────────────────────────────────────────────
 Simulation running 'CompressibleEulerEquations2D' with DGSEM(polydeg=3)
────────────────────────────────────────────────────────────────────────────────────────────────────
 #timesteps:                  0                run time:       1.22275338e+00 s
 Δt:             1.00000000e-03                └── GC time:    0.00000000e+00 s (0.000%)
 sim. time:      0.00000000e+00 (0.000%)       time/DOF/rhs!:         NaN s
                                               PID:                   Inf s
 #DOFs per field:         36128                alloc'd memory:        990.217 MiB
 #elements:                2258

 Variable:       rho              rho_v1           rho_v2           rho_e
 L2 error:       8.96518598e-17   8.96518598e-17   0.00000000e+00   1.27756504e-15
 Linf error:     4.44089210e-16   4.44089210e-16   0.00000000e+00   2.66453526e-15
 ∑∂S/∂U ⋅ Uₜ :  -1.20647355e-03
────────────────────────────────────────────────────────────────────────────────────────────────────

┌ Warning: TODO forward zero-set of memorycopy used memset rather than runtime type
│ Caused by:
│ Stacktrace:
│   [1] copy
│     @ ./array.jl:350
│   [2] unaliascopy
│     @ ./abstractarray.jl:1516
│   [3] unalias
│     @ ./abstractarray.jl:1500
│   [4] broadcast_unalias
│     @ ./broadcast.jl:946
│   [5] preprocess
│     @ ./broadcast.jl:953
│   [6] preprocess_args
│     @ ./broadcast.jl:956
│   [7] preprocess_args
│     @ ./broadcast.jl:955
│   [8] preprocess
│     @ ./broadcast.jl:952
│   [9] preprocess_args
│     @ ./broadcast.jl:956
│  [10] preprocess_args
│     @ ./broadcast.jl:955
│  [11] preprocess
│     @ ./broadcast.jl:952
│  [12] preprocess_args
│     @ ./broadcast.jl:955
│  [13] preprocess
│     @ ./broadcast.jl:952
│  [14] override_bc_copyto!
│     @ ~/.julia/packages/Enzyme/C5rSn/src/compiler/interpreter.jl:818
│  [15] copyto!
│     @ ./broadcast.jl:925
│  [16] materialize!
│     @ ./broadcast.jl:883
│  [17] materialize!
│     @ ./broadcast.jl:880
│  [18] RKIMEX
│     @ ~/work/Ariadne.jl/Ariadne.jl/libs/Theseus/src/imex/imex.jl:33
└ @ Enzyme.Compiler ~/.julia/packages/Enzyme/C5rSn/src/rules/llvmrules.jl:812
┌ Warning: TODO forward zero-set of memorycopy used memset rather than runtime type
│ Caused by:
│ Stacktrace:
│   [1] copy
│     @ ./array.jl:350
│   [2] unaliascopy
│     @ ./abstractarray.jl:1516
│   [3] unalias
│     @ ./abstractarray.jl:1500
│   [4] broadcast_unalias
│     @ ./broadcast.jl:946
│   [5] preprocess
│     @ ./broadcast.jl:953
│   [6] preprocess_args
│     @ ./broadcast.jl:956
│   [7] preprocess_args
│     @ ./broadcast.jl:955
│   [8] preprocess
│     @ ./broadcast.jl:952
│   [9] preprocess_args
│     @ ./broadcast.jl:956
│  [10] preprocess_args
│     @ ./broadcast.jl:955
│  [11] preprocess
│     @ ./broadcast.jl:952
│  [12] override_bc_copyto!
│     @ ~/.julia/packages/Enzyme/C5rSn/src/compiler/interpreter.jl:818
│  [13] copyto!
│     @ ./broadcast.jl:925
│  [14] materialize!
│     @ ./broadcast.jl:883
│  [15] materialize!
│     @ ./broadcast.jl:880
│  [16] RKIMEX
│     @ ~/work/Ariadne.jl/Ariadne.jl/libs/Theseus/src/imex/imex.jl:33
└ @ Enzyme.Compiler ~/.julia/packages/Enzyme/C5rSn/src/rules/llvmrules.jl:812
#timesteps:      1 │ Δt: 4.6182e-03 │ sim. time: 4.6182e-03 (0.924%)   │ run time: 9.5024e+01 s
#timesteps:      2 │ Δt: 4.4948e-03 │ sim. time: 9.1130e-03 (1.823%)   │ run time: 1.0654e+02 s
#timesteps:      3 │ Δt: 4.4714e-03 │ sim. time: 1.3584e-02 (2.717%)   │ run time: 1.1787e+02 s
#timesteps:      4 │ Δt: 4.4766e-03 │ sim. time: 1.8061e-02 (3.612%)   │ run time: 1.2888e+02 s
#timesteps:      5 │ Δt: 4.4931e-03 │ sim. time: 2.2554e-02 (4.511%)   │ run time: 1.4113e+02 s
#timesteps:      6 │ Δt: 4.5254e-03 │ sim. time: 2.7079e-02 (5.416%)   │ run time: 1.5259e+02 s
#timesteps:      7 │ Δt: 4.5643e-03 │ sim. time: 3.1644e-02 (6.329%)   │ run time: 1.6385e+02 s
#timesteps:      8 │ Δt: 4.5740e-03 │ sim. time: 3.6218e-02 (7.244%)   │ run time: 1.7552e+02 s
#timesteps:      9 │ Δt: 4.5552e-03 │ sim. time: 4.0773e-02 (8.155%)   │ run time: 1.8697e+02 s

────────────────────────────────────────────────────────────────────────────────────────────────────
 Simulation running 'CompressibleEulerEquations2D' with DGSEM(polydeg=3)
────────────────────────────────────────────────────────────────────────────────────────────────────
 #timesteps:                 10                run time:       1.99087831e+02 s
 Δt:             4.55501201e-03                └── GC time:    9.62775701e+00 s (4.836%)
 sim. time:      4.53278729e-02 (9.066%)       time/DOF/rhs!:  5.86617174e-06 s
                                               PID:            1.09439460e-04 s
 #DOFs per field:         36128                alloc'd memory:        932.421 MiB
 #elements:                2258

 Variable:       rho              rho_v1           rho_v2           rho_e
 L2 error:       4.64923431e-03   8.85283724e-03   4.72300190e-03   4.80992841e-02
 Linf error:     7.16158036e-01   1.42833015e+00   6.28720604e-01   7.47949255e+00
 ∑∂S/∂U ⋅ Uₜ :  -1.98606192e-04
────────────────────────────────────────────────────────────────────────────────────────────────────

#timesteps:     11 │ Δt: 4.5783e-03 │ sim. time: 4.9906e-02 (9.981%)   │ run time: 2.0812e+02 s
#timesteps:     12 │ Δt: 4.6280e-03 │ sim. time: 5.4534e-02 (10.907%)  │ run time: 2.1894e+02 s
#timesteps:     13 │ Δt: 4.6537e-03 │ sim. time: 5.9188e-02 (11.838%)  │ run time: 2.2786e+02 s
#timesteps:     14 │ Δt: 4.6430e-03 │ sim. time: 6.3831e-02 (12.766%)  │ run time: 2.3779e+02 s
#timesteps:     15 │ Δt: 4.6370e-03 │ sim. time: 6.8468e-02 (13.694%)  │ run time: 2.4669e+02 s
#timesteps:     16 │ Δt: 4.5785e-03 │ sim. time: 7.3046e-02 (14.609%)  │ run time: 2.5655e+02 s
#timesteps:     17 │ Δt: 4.5293e-03 │ sim. time: 7.7576e-02 (15.515%)  │ run time: 2.6564e+02 s
#timesteps:     18 │ Δt: 4.4909e-03 │ sim. time: 8.2067e-02 (16.413%)  │ run time: 2.7459e+02 s
#timesteps:     19 │ Δt: 4.4629e-03 │ sim. time: 8.6529e-02 (17.306%)  │ run time: 2.8453e+02 s

────────────────────────────────────────────────────────────────────────────────────────────────────
 Simulation running 'CompressibleEulerEquations2D' with DGSEM(polydeg=3)
────────────────────────────────────────────────────────────────────────────────────────────────────
 #timesteps:                 20                run time:       2.94913433e+02 s
 Δt:             4.44400238e-03                └── GC time:    1.51240010e+01 s (5.128%)
 sim. time:      9.09734380e-02 (18.195%)      time/DOF/rhs!:  5.69905727e-06 s
                                               PID:            5.29640863e-05 s
 #DOFs per field:         36128                alloc'd memory:       1013.879 MiB
 #elements:                2258

 Variable:       rho              rho_v1           rho_v2           rho_e
 L2 error:       6.53365544e-03   1.26659983e-02   7.73995358e-03   6.75443615e-02
 Linf error:     5.43630658e-01   1.03003896e+00   7.51581870e-01   5.56166488e+00
 ∑∂S/∂U ⋅ Uₜ :  -1.20583267e-04
────────────────────────────────────────────────────────────────────────────────────────────────────

#timesteps:     21 │ Δt: 4.4324e-03 │ sim. time: 9.5406e-02 (19.081%)  │ run time: 3.0359e+02 s
#timesteps:     22 │ Δt: 4.4259e-03 │ sim. time: 9.9832e-02 (19.966%)  │ run time: 3.1265e+02 s
#timesteps:     23 │ Δt: 4.4223e-03 │ sim. time: 1.0425e-01 (20.851%)  │ run time: 3.2165e+02 s
#timesteps:     24 │ Δt: 4.4198e-03 │ sim. time: 1.0867e-01 (21.735%)  │ run time: 3.3161e+02 s
#timesteps:     25 │ Δt: 4.4168e-03 │ sim. time: 1.1309e-01 (22.618%)  │ run time: 3.4061e+02 s
#timesteps:     26 │ Δt: 4.4126e-03 │ sim. time: 1.1750e-01 (23.501%)  │ run time: 3.5047e+02 s
#timesteps:     27 │ Δt: 4.4068e-03 │ sim. time: 1.2191e-01 (24.382%)  │ run time: 3.5947e+02 s
#timesteps:     28 │ Δt: 4.3996e-03 │ sim. time: 1.2631e-01 (25.262%)  │ run time: 3.6935e+02 s
#timesteps:     29 │ Δt: 4.3915e-03 │ sim. time: 1.3070e-01 (26.140%)  │ run time: 3.7836e+02 s

────────────────────────────────────────────────────────────────────────────────────────────────────
 Simulation running 'CompressibleEulerEquations2D' with DGSEM(polydeg=3)
────────────────────────────────────────────────────────────────────────────────────────────────────
 #timesteps:                 30                run time:       3.89602390e+02 s
 Δt:             4.38295054e-03                └── GC time:    2.14049870e+01 s (5.494%)
 sim. time:      1.35083929e-01 (27.017%)      time/DOF/rhs!:  5.74979737e-06 s
                                               PID:            5.23351276e-05 s
 #DOFs per field:         36128                alloc'd memory:       1032.300 MiB
 #elements:                2258

 Variable:       rho              rho_v1           rho_v2           rho_e
 L2 error:       7.67756568e-03   1.52760645e-02   9.94581650e-03   7.93270443e-02
 Linf error:     5.02625662e-01   1.03367280e+00   8.28764923e-01   5.09487231e+00
 ∑∂S/∂U ⋅ Uₜ :  -1.30655214e-04
────────────────────────────────────────────────────────────────────────────────────────────────────

#timesteps:     31 │ Δt: 4.3747e-03 │ sim. time: 1.3946e-01 (27.892%)  │ run time: 3.9736e+02 s
#timesteps:     32 │ Δt: 4.3672e-03 │ sim. time: 1.4383e-01 (28.765%)  │ run time: 4.0718e+02 s
#timesteps:     33 │ Δt: 4.3608e-03 │ sim. time: 1.4819e-01 (29.637%)  │ run time: 4.1619e+02 s
#timesteps:     34 │ Δt: 4.3558e-03 │ sim. time: 1.5254e-01 (30.508%)  │ run time: 4.2501e+02 s
#timesteps:     35 │ Δt: 4.3521e-03 │ sim. time: 1.5689e-01 (31.379%)  │ run time: 4.3484e+02 s
#timesteps:     36 │ Δt: 4.3499e-03 │ sim. time: 1.6124e-01 (32.249%)  │ run time: 4.4370e+02 s
#timesteps:     37 │ Δt: 4.3487e-03 │ sim. time: 1.6559e-01 (33.119%)  │ run time: 4.5357e+02 s
#timesteps:     38 │ Δt: 4.3484e-03 │ sim. time: 1.6994e-01 (33.988%)  │ run time: 4.6249e+02 s
#timesteps:     39 │ Δt: 4.3485e-03 │ sim. time: 1.7429e-01 (34.858%)  │ run time: 4.7227e+02 s

────────────────────────────────────────────────────────────────────────────────────────────────────
 Simulation running 'CompressibleEulerEquations2D' with DGSEM(polydeg=3)
────────────────────────────────────────────────────────────────────────────────────────────────────
 #timesteps:                 40                run time:       4.82212056e+02 s
 Δt:             4.34863116e-03                └── GC time:    2.68446193e+01 s (5.567%)
 sim. time:      1.78638705e-01 (35.728%)      time/DOF/rhs!:  5.61584981e-06 s
                                               PID:            5.11807392e-05 s
 #DOFs per field:         36128                alloc'd memory:        893.347 MiB
 #elements:                2258

 Variable:       rho              rho_v1           rho_v2           rho_e
 L2 error:       8.47801438e-03   1.71648658e-02   1.18338209e-02   8.74177339e-02
 Linf error:     4.82193165e-01   1.10797823e+00   7.28017033e-01   4.84304661e+00
 ∑∂S/∂U ⋅ Uₜ :  -1.19358050e-04
────────────────────────────────────────────────────────────────────────────────────────────────────

#timesteps:     41 │ Δt: 4.3484e-03 │ sim. time: 1.8299e-01 (36.597%)  │ run time: 4.9072e+02 s
#timesteps:     42 │ Δt: 4.3474e-03 │ sim. time: 1.8733e-01 (37.467%)  │ run time: 4.9981e+02 s
#timesteps:     43 │ Δt: 4.3456e-03 │ sim. time: 1.9168e-01 (38.336%)  │ run time: 5.0882e+02 s
#timesteps:     44 │ Δt: 4.3428e-03 │ sim. time: 1.9602e-01 (39.205%)  │ run time: 5.1863e+02 s
#timesteps:     45 │ Δt: 4.3392e-03 │ sim. time: 2.0036e-01 (40.072%)  │ run time: 5.2752e+02 s
#timesteps:     46 │ Δt: 4.3349e-03 │ sim. time: 2.0470e-01 (40.939%)  │ run time: 5.3739e+02 s
#timesteps:     47 │ Δt: 4.3302e-03 │ sim. time: 2.0903e-01 (41.805%)  │ run time: 5.4628e+02 s
#timesteps:     48 │ Δt: 4.3252e-03 │ sim. time: 2.1335e-01 (42.670%)  │ run time: 5.5621e+02 s
#timesteps:     49 │ Δt: 4.3203e-03 │ sim. time: 2.1767e-01 (43.535%)  │ run time: 5.6511e+02 s

────────────────────────────────────────────────────────────────────────────────────────────────────
 Simulation running 'CompressibleEulerEquations2D' with DGSEM(polydeg=3)
────────────────────────────────────────────────────────────────────────────────────────────────────
 #timesteps:                 50                run time:       5.76322278e+02 s
 Δt:             4.31568887e-03                └── GC time:    3.30440104e+01 s (5.734%)
 sim. time:      2.21988498e-01 (44.398%)      time/DOF/rhs!:  5.72503102e-06 s
                                               PID:            5.20145785e-05 s
 #DOFs per field:         36128                alloc'd memory:       1335.334 MiB
 #elements:                2258

 Variable:       rho              rho_v1           rho_v2           rho_e
 L2 error:       9.06400123e-03   1.86724634e-02   1.35000328e-02   9.31248152e-02
 Linf error:     5.03004190e-01   1.10957733e+00   7.17579661e-01   5.07149968e+00
 ∑∂S/∂U ⋅ Uₜ :  -1.22996211e-04
────────────────────────────────────────────────────────────────────────────────────────────────────

#timesteps:     51 │ Δt: 4.3115e-03 │ sim. time: 2.2630e-01 (45.260%)  │ run time: 5.8410e+02 s
#timesteps:     52 │ Δt: 4.3079e-03 │ sim. time: 2.3061e-01 (46.122%)  │ run time: 5.9387e+02 s
#timesteps:     53 │ Δt: 4.3049e-03 │ sim. time: 2.3491e-01 (46.983%)  │ run time: 6.0303e+02 s
#timesteps:     54 │ Δt: 4.3027e-03 │ sim. time: 2.3922e-01 (47.843%)  │ run time: 6.1192e+02 s
#timesteps:     55 │ Δt: 4.3010e-03 │ sim. time: 2.4352e-01 (48.703%)  │ run time: 6.2139e+02 s
#timesteps:     56 │ Δt: 4.3000e-03 │ sim. time: 2.4782e-01 (49.563%)  │ run time: 6.2947e+02 s
#timesteps:     57 │ Δt: 4.2994e-03 │ sim. time: 2.5212e-01 (50.423%)  │ run time: 6.3796e+02 s
#timesteps:     58 │ Δt: 4.2992e-03 │ sim. time: 2.5642e-01 (51.283%)  │ run time: 6.4535e+02 s
#timesteps:     59 │ Δt: 4.2992e-03 │ sim. time: 2.6071e-01 (52.143%)  │ run time: 6.5263e+02 s

────────────────────────────────────────────────────────────────────────────────────────────────────
 Simulation running 'CompressibleEulerEquations2D' with DGSEM(polydeg=3)
────────────────────────────────────────────────────────────────────────────────────────────────────
 #timesteps:                 60                run time:       6.62181834e+02 s
 Δt:             4.29925400e-03                └── GC time:    3.82989854e+01 s (5.784%)
 sim. time:      2.65013456e-01 (53.003%)      time/DOF/rhs!:  5.63292975e-06 s
                                               PID:            4.74068646e-05 s
 #DOFs per field:         36128                alloc'd memory:       1135.525 MiB
 #elements:                2258

 Variable:       rho              rho_v1           rho_v2           rho_e
 L2 error:       9.53070797e-03   1.98856287e-02   1.49628554e-02   9.73582091e-02
 Linf error:     4.32755742e-01   1.04262767e+00   7.27908089e-01   4.26683140e+00
 ∑∂S/∂U ⋅ Uₜ :  -1.11519114e-04
────────────────────────────────────────────────────────────────────────────────────────────────────

#timesteps:     61 │ Δt: 4.2993e-03 │ sim. time: 2.6931e-01 (53.863%)  │ run time: 6.6876e+02 s
#timesteps:     62 │ Δt: 4.2993e-03 │ sim. time: 2.7361e-01 (54.722%)  │ run time: 6.7645e+02 s
#timesteps:     63 │ Δt: 4.2990e-03 │ sim. time: 2.7791e-01 (55.582%)  │ run time: 6.8505e+02 s
#timesteps:     64 │ Δt: 4.2985e-03 │ sim. time: 2.8221e-01 (56.442%)  │ run time: 6.9273e+02 s
#timesteps:     65 │ Δt: 4.2979e-03 │ sim. time: 2.8651e-01 (57.301%)  │ run time: 7.0095e+02 s
#timesteps:     66 │ Δt: 4.2970e-03 │ sim. time: 2.9080e-01 (58.161%)  │ run time: 7.0838e+02 s
#timesteps:     67 │ Δt: 4.2959e-03 │ sim. time: 2.9510e-01 (59.020%)  │ run time: 7.1576e+02 s
#timesteps:     68 │ Δt: 4.2948e-03 │ sim. time: 2.9940e-01 (59.879%)  │ run time: 7.2312e+02 s
#timesteps:     69 │ Δt: 4.2936e-03 │ sim. time: 3.0369e-01 (60.738%)  │ run time: 7.3045e+02 s

────────────────────────────────────────────────────────────────────────────────────────────────────
 Simulation running 'CompressibleEulerEquations2D' with DGSEM(polydeg=3)
────────────────────────────────────────────────────────────────────────────────────────────────────
 #timesteps:                 70                run time:       7.39198251e+02 s
 Δt:             4.29240354e-03                └── GC time:    4.17766341e+01 s (5.652%)
 sim. time:      3.07981065e-01 (61.596%)      time/DOF/rhs!:  5.57726449e-06 s
                                               PID:            4.25482974e-05 s
 #DOFs per field:         36128                alloc'd memory:       1102.562 MiB
 #elements:                2258

 Variable:       rho              rho_v1           rho_v2           rho_e
 L2 error:       9.90399293e-03   2.08711478e-02   1.62492564e-02   1.00514287e-01
 Linf error:     3.98488709e-01   1.04898027e+00   7.35060870e-01   3.89853935e+00
 ∑∂S/∂U ⋅ Uₜ :  -1.17807394e-04
────────────────────────────────────────────────────────────────────────────────────────────────────

#timesteps:     71 │ Δt: 4.2913e-03 │ sim. time: 3.1227e-01 (62.454%)  │ run time: 7.4665e+02 s
#timesteps:     72 │ Δt: 4.2902e-03 │ sim. time: 3.1656e-01 (63.313%)  │ run time: 7.5439e+02 s
#timesteps:     73 │ Δt: 4.2892e-03 │ sim. time: 3.2085e-01 (64.170%)  │ run time: 7.6221e+02 s
#timesteps:     74 │ Δt: 4.2882e-03 │ sim. time: 3.2514e-01 (65.028%)  │ run time: 7.7086e+02 s
#timesteps:     75 │ Δt: 4.2873e-03 │ sim. time: 3.2943e-01 (65.885%)  │ run time: 7.7827e+02 s
#timesteps:     76 │ Δt: 4.2864e-03 │ sim. time: 3.3371e-01 (66.743%)  │ run time: 7.8646e+02 s
#timesteps:     77 │ Δt: 4.2854e-03 │ sim. time: 3.3800e-01 (67.600%)  │ run time: 7.9395e+02 s
#timesteps:     78 │ Δt: 4.2844e-03 │ sim. time: 3.4228e-01 (68.457%)  │ run time: 8.0132e+02 s
#timesteps:     79 │ Δt: 4.2833e-03 │ sim. time: 3.4657e-01 (69.313%)  │ run time: 8.0866e+02 s

────────────────────────────────────────────────────────────────────────────────────────────────────
 Simulation running 'CompressibleEulerEquations2D' with DGSEM(polydeg=3)
────────────────────────────────────────────────────────────────────────────────────────────────────
 #timesteps:                 80                run time:       8.18231660e+02 s
 Δt:             4.28121331e-03                └── GC time:    4.68221572e+01 s (5.722%)
 sim. time:      3.50847983e-01 (70.170%)      time/DOF/rhs!:  5.71169387e-06 s
                                               PID:            4.36681550e-05 s
 #DOFs per field:         36128                alloc'd memory:       1277.992 MiB
 #elements:                2258

 Variable:       rho              rho_v1           rho_v2           rho_e
 L2 error:       1.02147848e-02   2.16637967e-02   1.73659533e-02   1.02893942e-01
 Linf error:     3.71854479e-01   1.05297438e+00   7.20233874e-01   3.56770023e+00
 ∑∂S/∂U ⋅ Uₜ :  -1.14063852e-04
────────────────────────────────────────────────────────────────────────────────────────────────────

#timesteps:     81 │ Δt: 4.2790e-03 │ sim. time: 3.5513e-01 (71.025%)  │ run time: 8.2446e+02 s
#timesteps:     82 │ Δt: 4.2769e-03 │ sim. time: 3.5940e-01 (71.881%)  │ run time: 8.3191e+02 s
#timesteps:     83 │ Δt: 4.2748e-03 │ sim. time: 3.6368e-01 (72.736%)  │ run time: 8.4011e+02 s
#timesteps:     84 │ Δt: 4.2729e-03 │ sim. time: 3.6795e-01 (73.590%)  │ run time: 8.4753e+02 s
#timesteps:     85 │ Δt: 4.2709e-03 │ sim. time: 3.7222e-01 (74.445%)  │ run time: 8.5487e+02 s
#timesteps:     86 │ Δt: 4.2691e-03 │ sim. time: 3.7649e-01 (75.298%)  │ run time: 8.6308e+02 s
#timesteps:     87 │ Δt: 4.2674e-03 │ sim. time: 3.8076e-01 (76.152%)  │ run time: 8.7054e+02 s
#timesteps:     88 │ Δt: 4.2657e-03 │ sim. time: 3.8502e-01 (77.005%)  │ run time: 8.7784e+02 s
#timesteps:     89 │ Δt: 4.2641e-03 │ sim. time: 3.8929e-01 (77.858%)  │ run time: 8.8519e+02 s

────────────────────────────────────────────────────────────────────────────────────────────────────
 Simulation running 'CompressibleEulerEquations2D' with DGSEM(polydeg=3)
────────────────────────────────────────────────────────────────────────────────────────────────────
 #timesteps:                 90                run time:       8.94849011e+02 s
 Δt:             4.26264722e-03                └── GC time:    5.10779916e+01 s (5.708%)
 sim. time:      3.93551528e-01 (78.710%)      time/DOF/rhs!:  5.54759108e-06 s
                                               PID:            4.23228615e-05 s
 #DOFs per field:         36128                alloc'd memory:       1080.485 MiB
 #elements:                2258

 Variable:       rho              rho_v1           rho_v2           rho_e
 L2 error:       1.04832924e-02   2.23447434e-02   1.83272747e-02   1.04748173e-01
 Linf error:     4.04043565e-01   1.06669114e+00   7.11255592e-01   3.91773525e+00
 ∑∂S/∂U ⋅ Uₜ :  -1.14330464e-04
────────────────────────────────────────────────────────────────────────────────────────────────────

#timesteps:     91 │ Δt: 4.2612e-03 │ sim. time: 3.9781e-01 (79.563%)  │ run time: 9.0101e+02 s
#timesteps:     92 │ Δt: 4.2599e-03 │ sim. time: 4.0207e-01 (80.415%)  │ run time: 9.0837e+02 s
#timesteps:     93 │ Δt: 4.2587e-03 │ sim. time: 4.0633e-01 (81.266%)  │ run time: 9.1572e+02 s
#timesteps:     94 │ Δt: 4.2575e-03 │ sim. time: 4.1059e-01 (82.118%)  │ run time: 9.2400e+02 s
#timesteps:     95 │ Δt: 4.2564e-03 │ sim. time: 4.1485e-01 (82.969%)  │ run time: 9.3137e+02 s
#timesteps:     96 │ Δt: 4.2554e-03 │ sim. time: 4.1910e-01 (83.820%)  │ run time: 9.3872e+02 s
#timesteps:     97 │ Δt: 4.2544e-03 │ sim. time: 4.2336e-01 (84.671%)  │ run time: 9.4604e+02 s
#timesteps:     98 │ Δt: 4.2535e-03 │ sim. time: 4.2761e-01 (85.522%)  │ run time: 9.5337e+02 s
#timesteps:     99 │ Δt: 4.2526e-03 │ sim. time: 4.3186e-01 (86.372%)  │ run time: 9.6068e+02 s

────────────────────────────────────────────────────────────────────────────────────────────────────
 Simulation running 'CompressibleEulerEquations2D' with DGSEM(polydeg=3)
────────────────────────────────────────────────────────────────────────────────────────────────────
 #timesteps:                100                run time:       9.70299430e+02 s
 Δt:             4.25181873e-03                └── GC time:    5.44351961e+01 s (5.610%)
 sim. time:      4.36113158e-01 (87.223%)      time/DOF/rhs!:  5.57268161e-06 s
                                               PID:            4.16812710e-05 s
 #DOFs per field:         36128                alloc'd memory:       1149.955 MiB
 #elements:                2258

 Variable:       rho              rho_v1           rho_v2           rho_e
 L2 error:       1.07266368e-02   2.29091724e-02   1.91465963e-02   1.06238167e-01
 Linf error:     3.67962100e-01   1.07731365e+00   7.12625840e-01   3.57594740e+00
 ∑∂S/∂U ⋅ Uₜ :  -1.13540624e-04
────────────────────────────────────────────────────────────────────────────────────────────────────

#timesteps:    101 │ Δt: 4.2510e-03 │ sim. time: 4.4036e-01 (88.073%)  │ run time: 9.7644e+02 s
#timesteps:    102 │ Δt: 4.2503e-03 │ sim. time: 4.4461e-01 (88.923%)  │ run time: 9.8385e+02 s
#timesteps:    103 │ Δt: 4.2496e-03 │ sim. time: 4.4886e-01 (89.773%)  │ run time: 9.9122e+02 s
#timesteps:    104 │ Δt: 4.2490e-03 │ sim. time: 4.5311e-01 (90.623%)  │ run time: 9.9858e+02 s
#timesteps:    105 │ Δt: 4.2484e-03 │ sim. time: 4.5736e-01 (91.472%)  │ run time: 1.0059e+03 s
#timesteps:    106 │ Δt: 4.2478e-03 │ sim. time: 4.6161e-01 (92.322%)  │ run time: 1.0132e+03 s
#timesteps:    107 │ Δt: 4.2473e-03 │ sim. time: 4.6586e-01 (93.171%)  │ run time: 1.0215e+03 s
#timesteps:    108 │ Δt: 4.2468e-03 │ sim. time: 4.7010e-01 (94.021%)  │ run time: 1.0289e+03 s
#timesteps:    109 │ Δt: 4.2463e-03 │ sim. time: 4.7435e-01 (94.870%)  │ run time: 1.0371e+03 s

────────────────────────────────────────────────────────────────────────────────────────────────────
 Simulation running 'CompressibleEulerEquations2D' with DGSEM(polydeg=3)
────────────────────────────────────────────────────────────────────────────────────────────────────
 #timesteps:                110                run time:       1.04595877e+03 s
 Δt:             4.24591874e-03                └── GC time:    5.78337988e+01 s (5.529%)
 sim. time:      4.78595613e-01 (95.719%)      time/DOF/rhs!:  5.60551313e-06 s
                                               PID:            4.17969955e-05 s
 #DOFs per field:         36128                alloc'd memory:       1036.963 MiB
 #elements:                2258

 Variable:       rho              rho_v1           rho_v2           rho_e
 L2 error:       1.09501166e-02   2.34077070e-02   1.98398506e-02   1.07485665e-01
 Linf error:     3.73765631e-01   1.08279798e+00   7.10650160e-01   3.31172185e+00
 ∑∂S/∂U ⋅ Uₜ :  -1.15721767e-04
────────────────────────────────────────────────────────────────────────────────────────────────────

#timesteps:    111 │ Δt: 4.2456e-03 │ sim. time: 4.8284e-01 (96.568%)  │ run time: 1.0521e+03 s
#timesteps:    112 │ Δt: 4.2453e-03 │ sim. time: 4.8709e-01 (97.417%)  │ run time: 1.0595e+03 s
#timesteps:    113 │ Δt: 4.2450e-03 │ sim. time: 4.9133e-01 (98.266%)  │ run time: 1.0678e+03 s
#timesteps:    114 │ Δt: 4.2448e-03 │ sim. time: 4.9558e-01 (99.115%)  │ run time: 1.0751e+03 s
#timesteps:    115 │ Δt: 4.2447e-03 │ sim. time: 4.9982e-01 (99.964%)  │ run time: 1.0824e+03 s

────────────────────────────────────────────────────────────────────────────────────────────────────
 Simulation running 'CompressibleEulerEquations2D' with DGSEM(polydeg=3)
────────────────────────────────────────────────────────────────────────────────────────────────────
 #timesteps:                116                run time:       1.08784672e+03 s
 Δt:             1.79026594e-04                └── GC time:    5.96078815e+01 s (5.479%)
 sim. time:      5.00000000e-01 (100.000%)     time/DOF/rhs!:  5.45212639e-06 s
                                               PID:            3.85035900e-05 s
 #DOFs per field:         36128                alloc'd memory:       1128.941 MiB
 #elements:                2258

 Variable:       rho              rho_v1           rho_v2           rho_e
 L2 error:       1.10537553e-02   2.36419928e-02   2.01463055e-02   1.08021750e-01
 Linf error:     3.79655915e-01   1.08633228e+00   7.08879871e-01   3.29414734e+00
 ∑∂S/∂U ⋅ Uₜ :  -1.16165019e-04
────────────────────────────────────────────────────────────────────────────────────────────────────

────────────────────────────────────────────────────────────────────────────────────────────────────
Trixi.jl simulation finished.  Final time: 0.5  Time steps: 116 (accepted), 116 (total)
────────────────────────────────────────────────────────────────────────────────────────────────────

───────────────────────────────────────────────────────────────────────────────────────
              Trixi.jl                        Time                    Allocations
                                     ───────────────────────   ────────────────────────
          Tot / % measured:               1088s /  89.7%            231GiB /  83.8%

Section                      ncalls     time    %tot     avg     alloc    %tot      avg
───────────────────────────────────────────────────────────────────────────────────────
parabolic rhs!                4.83k     972s   99.6%   201ms    193GiB   99.8%  40.9MiB
  prolong2interfaces          4.83k     918s   94.1%   190ms    190GiB   98.3%  40.3MiB
  calculate gradient          4.83k    20.0s    2.1%  4.15ms   3.33KiB    0.0%    0.71B
    volume integral           4.83k    10.1s    1.0%  2.09ms     0.00B    0.0%    0.00B
    surface integral          4.83k    4.68s    0.5%   969μs     0.00B    0.0%    0.00B
    Jacobian                  4.83k    1.64s    0.2%   340μs     0.00B    0.0%    0.00B
    interface flux            4.83k    1.52s    0.2%   315μs     0.00B    0.0%    0.00B
    prolong2interfaces        4.83k    1.39s    0.1%   287μs     0.00B    0.0%    0.00B
    reset gradients           4.83k    629ms    0.1%   130μs     0.00B    0.0%    0.00B
    boundary flux             4.83k   37.7ms    0.0%  7.81μs     0.00B    0.0%    0.00B
    prolong2boundaries        4.83k   27.9ms    0.0%  5.76μs     0.00B    0.0%    0.00B
    ~calculate gradient~      4.83k   16.3ms    0.0%  3.37μs   3.33KiB    0.0%    0.71B
    prolong2mortars           4.83k   2.64ms    0.0%   546ns     0.00B    0.0%    0.00B
    mortar flux               4.83k   2.15ms    0.0%   445ns     0.00B    0.0%    0.00B
  prolong2boundaries          4.83k    13.6s    1.4%  2.82ms   2.84GiB    1.5%   616KiB
  volume integral             4.83k    7.91s    0.8%  1.64ms     0.00B    0.0%    0.00B
  calculate viscous fluxes    4.83k    7.13s    0.7%  1.48ms     0.00B    0.0%    0.00B
  interface flux              4.83k    1.48s    0.2%   306μs     0.00B    0.0%    0.00B
  transform variables         4.83k    1.39s    0.1%   287μs     0.00B    0.0%    0.00B
  surface integral            4.83k    1.05s    0.1%   218μs     0.00B    0.0%    0.00B
  Jacobian                    4.83k    818ms    0.1%   169μs     0.00B    0.0%    0.00B
  reset ∂u/∂t                 4.83k    250ms    0.0%  51.7μs     0.00B    0.0%    0.00B
  ~parabolic rhs!~            4.83k   40.9ms    0.0%  8.46μs   5.38KiB    0.0%    1.14B
  boundary flux               4.83k   38.7ms    0.0%  8.01μs     0.00B    0.0%    0.00B
  prolong2mortars             4.83k   11.1ms    0.0%  2.29μs    894KiB    0.0%     190B
  mortar flux                 4.83k   1.68ms    0.0%   347ns     0.00B    0.0%    0.00B
analyze solution                 13    2.10s    0.2%   162ms    420MiB    0.2%  32.3MiB
rhs!                            580    2.03s    0.2%  3.50ms   4.78KiB    0.0%    8.44B
  volume integral               580    1.07s    0.1%  1.84ms     0.00B    0.0%    0.00B
  interface flux                580    461ms    0.0%   795μs     0.00B    0.0%    0.00B
  prolong2interfaces            580    178ms    0.0%   307μs     0.00B    0.0%    0.00B
  Jacobian                      580    139ms    0.0%   239μs     0.00B    0.0%    0.00B
  surface integral              580    133ms    0.0%   229μs     0.00B    0.0%    0.00B
  reset ∂u/∂t                   580   32.1ms    0.0%  55.3μs     0.00B    0.0%    0.00B
  boundary flux                 580   13.0ms    0.0%  22.4μs     0.00B    0.0%    0.00B
  prolong2boundaries            580   3.33ms    0.0%  5.74μs     0.00B    0.0%    0.00B
  ~rhs!~                        580   2.12ms    0.0%  3.66μs   4.78KiB    0.0%    8.44B
  prolong2mortars               580    221μs    0.0%   381ns     0.00B    0.0%    0.00B
  mortar flux                   580    205μs    0.0%   353ns     0.00B    0.0%    0.00B
  source terms                  580   62.3μs    0.0%   107ns     0.00B    0.0%    0.00B
calculate dt                    117   53.0ms    0.0%   453μs   16.5KiB    0.0%     144B
───────────────────────────────────────────────────────────────────────────────────────

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