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Viscous CFL: TreeMesh{1} #2035

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This adds a viscous CFL condition, see #1147 for the 1D TreeMesh.
In this draft, the user is expected to supply to CFL values for each contribution (convective & diffusive).

There are couple open points:

  • Do we want such an completely additional callback, or should we just dispatch based on the Semidiscretization used and store the diffusive cfl number also for the convection-dominated case (and never use it).
  • One could provide a constructor for only one CFL number, which is then used for both convective and diffusive cfl.
  • Currently the Navier-Stokes equations are implemented as having non-constant diffusivity (since the viscosity may be in principle a function of temperature). I believe that the current implementation is not too expensive, but could be cheaper for most cases.

By executing the convergence study, it is quite nicely shown that at some point of refinement the viscous CFL becomes active (note that for the last refinement the number of timesteps increases by a factor of 4, while before the number of timesteps only doubles):

julia> convergence_test("examples/tree_1d_dgsem/elixir_navierstokes_convergence_periodic_cfl.jl", 5)
Running convtest iteration 1/5

────────────────────────────────────────────────────────────────────────────────────────────────────
 Simulation running 'CompressibleEulerEquations1D' with DGSEM(polydeg=3)
────────────────────────────────────────────────────────────────────────────────────────────────────
 #timesteps:                  0                run time:       5.94000000e-07 s
 Δt:             1.00000000e+00                └── 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:            64                alloc'd memory:        221.779 MiB
 #elements:                  16

 Variable:       rho              rho_v1           rho_e         
 L2 error:       2.78684204e-06   2.48258995e-05   8.25131207e-05
 Linf error:     6.06474411e-06   6.97508753e-05   2.62188828e-04
 ∑∂S/∂U  Uₜ :  -9.39674968e-11
────────────────────────────────────────────────────────────────────────────────────────────────────

#timesteps:    100 │ Δt: 2.2333e-02 │ sim. time: 2.2737e+00 (22.737%)  │ run time: 4.9111e-03 s
#timesteps:    200 │ Δt: 2.6765e-02 │ sim. time: 4.6425e+00 (46.425%)  │ run time: 1.0349e-02 s
#timesteps:    300 │ Δt: 1.9879e-02 │ sim. time: 6.9357e+00 (69.357%)  │ run time: 1.5610e-02 s
#timesteps:    400 │ Δt: 2.0963e-02 │ sim. time: 9.2022e+00 (92.022%)  │ run time: 2.0918e-02 s

────────────────────────────────────────────────────────────────────────────────────────────────────
 Simulation running 'CompressibleEulerEquations1D' with DGSEM(polydeg=3)
────────────────────────────────────────────────────────────────────────────────────────────────────
 #timesteps:                434                run time:       2.29529780e-02 s
 Δt:             4.73551507e-03                └── GC time:    0.00000000e+00 s (0.000%)
 sim. time:      1.00000000e+01 (100.000%)     time/DOF/rhs!:  1.60360893e-07 s
                                               PID:            1.64177273e-07 s
 #DOFs per field:            64                alloc'd memory:        221.829 MiB
 #elements:                  16

 Variable:       rho              rho_v1           rho_e         
 L2 error:       1.13385608e-04   6.24015827e-05   2.84851021e-04
 Linf error:     6.23318952e-04   3.59294299e-04   1.61057645e-03
 ∑∂S/∂U  Uₜ :   1.03788253e-05
────────────────────────────────────────────────────────────────────────────────────────────────────





####################################################################################################
Running convtest iteration 2/5

────────────────────────────────────────────────────────────────────────────────────────────────────
 Simulation running 'CompressibleEulerEquations1D' with DGSEM(polydeg=3)
────────────────────────────────────────────────────────────────────────────────────────────────────
 #timesteps:                  0                run time:       4.25000000e-07 s
 Δt:             1.00000000e+00                └── 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:           128                alloc'd memory:        317.297 MiB
 #elements:                  32

 Variable:       rho              rho_v1           rho_e         
 L2 error:       1.74397553e-07   1.55828568e-06   5.18452192e-06
 Linf error:     3.85056627e-07   4.57259856e-06   1.75874988e-05
 ∑∂S/∂U  Uₜ :  -1.48622886e-12
────────────────────────────────────────────────────────────────────────────────────────────────────

#timesteps:    100 │ Δt: 1.0100e-02 │ sim. time: 1.1321e+00 (11.321%)  │ run time: 8.9110e-03 s
#timesteps:    200 │ Δt: 1.1308e-02 │ sim. time: 2.2743e+00 (22.743%)  │ run time: 1.7956e-02 s
#timesteps:    300 │ Δt: 1.4528e-02 │ sim. time: 3.4447e+00 (34.447%)  │ run time: 2.7720e-02 s
#timesteps:    400 │ Δt: 1.3057e-02 │ sim. time: 4.6438e+00 (46.438%)  │ run time: 3.7396e-02 s
#timesteps:    500 │ Δt: 1.0746e-02 │ sim. time: 5.7990e+00 (57.990%)  │ run time: 4.7400e-02 s
#timesteps:    600 │ Δt: 9.9088e-03 │ sim. time: 6.9353e+00 (69.353%)  │ run time: 5.7470e-02 s
#timesteps:    700 │ Δt: 9.8612e-03 │ sim. time: 8.0665e+00 (80.665%)  │ run time: 6.7767e-02 s
#timesteps:    800 │ Δt: 1.0566e-02 │ sim. time: 9.2022e+00 (92.022%)  │ run time: 7.8062e-02 s

────────────────────────────────────────────────────────────────────────────────────────────────────
 Simulation running 'CompressibleEulerEquations1D' with DGSEM(polydeg=3)
────────────────────────────────────────────────────────────────────────────────────────────────────
 #timesteps:                867                run time:       8.50463770e-02 s
 Δt:             5.28141472e-03                └── GC time:    0.00000000e+00 s (0.000%)
 sim. time:      1.00000000e+01 (100.000%)     time/DOF/rhs!:  1.49683604e-07 s
                                               PID:            1.52964204e-07 s
 #DOFs per field:           128                alloc'd memory:        317.357 MiB
 #elements:                  32

 Variable:       rho              rho_v1           rho_e         
 L2 error:       6.12662720e-06   3.50990633e-06   1.74534044e-05
 Linf error:     4.74767520e-05   2.36262690e-05   1.05334479e-04
 ∑∂S/∂U  Uₜ :   2.28683129e-08
────────────────────────────────────────────────────────────────────────────────────────────────────

────────────────────────────────────────────────────────────────────────────────────────────────────
Trixi.jl simulation finished.  Final time: 10.0  Time steps: 867 (accepted), 867 (total)
────────────────────────────────────────────────────────────────────────────────────────────────────

Running convtest iteration 3/5

────────────────────────────────────────────────────────────────────────────────────────────────────
 Simulation running 'CompressibleEulerEquations1D' with DGSEM(polydeg=3)
────────────────────────────────────────────────────────────────────────────────────────────────────
 #timesteps:                  0                run time:       5.98000000e-07 s
 Δt:             1.00000000e+00                └── 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:           256                alloc'd memory:        247.620 MiB
 #elements:                  64

 Variable:       rho              rho_v1           rho_e         
 L2 error:       1.09032859e-08   9.74973482e-08   3.24463465e-07
 Linf error:     2.41603408e-08   2.89169676e-07   1.11846141e-06
 ∑∂S/∂U  Uₜ :  -2.13746982e-14
────────────────────────────────────────────────────────────────────────────────────────────────────

#timesteps:    100 │ Δt: 6.9644e-03 │ sim. time: 5.9959e-01 (5.996%)   │ run time: 1.5432e-02 s
#timesteps:    200 │ Δt: 5.0634e-03 │ sim. time: 1.1322e+00 (11.322%)  │ run time: 3.1606e-02 s
#timesteps:    300 │ Δt: 5.5352e-03 │ sim. time: 1.7625e+00 (17.625%)  │ run time: 4.9084e-02 s
#timesteps:    400 │ Δt: 5.6924e-03 │ sim. time: 2.2747e+00 (22.747%)  │ run time: 6.6979e-02 s
#timesteps:    500 │ Δt: 5.0065e-03 │ sim. time: 2.9017e+00 (29.017%)  │ run time: 8.6109e-02 s
#timesteps:    600 │ Δt: 7.3861e-03 │ sim. time: 3.4462e+00 (34.462%)  │ run time: 1.0549e-01 s
#timesteps:    700 │ Δt: 4.9064e-03 │ sim. time: 4.0332e+00 (40.332%)  │ run time: 1.2377e-01 s
#timesteps:    800 │ Δt: 6.4517e-03 │ sim. time: 4.6446e+00 (46.446%)  │ run time: 1.4149e-01 s
#timesteps:    900 │ Δt: 5.1685e-03 │ sim. time: 5.1669e+00 (51.669%)  │ run time: 1.5955e-01 s

────────────────────────────────────────────────────────────────────────────────────────────────────
 Simulation running 'CompressibleEulerEquations1D' with DGSEM(polydeg=3)
────────────────────────────────────────────────────────────────────────────────────────────────────
 #timesteps:               1000                run time:       1.77567412e-01 s
 Δt:             5.34698902e-03                └── GC time:    0.00000000e+00 s (0.000%)
 sim. time:      5.79916140e+00 (57.992%)      time/DOF/rhs!:  1.35702104e-07 s
                                               PID:            1.38568028e-07 s
 #DOFs per field:           256                alloc'd memory:        247.682 MiB
 #elements:                  64

 Variable:       rho              rho_v1           rho_e         
 L2 error:       1.99742240e-07   1.45805874e-07   6.59358566e-07
 Linf error:     2.01195807e-06   1.01950938e-06   4.46561633e-06
 ∑∂S/∂U  Uₜ :  -1.41751579e-01
────────────────────────────────────────────────────────────────────────────────────────────────────

#timesteps:   1100 │ Δt: 5.9728e-03 │ sim. time: 6.3143e+00 (63.143%)  │ run time: 1.9552e-01 s
#timesteps:   1200 │ Δt: 4.9472e-03 │ sim. time: 6.9353e+00 (69.353%)  │ run time: 2.1308e-01 s
#timesteps:   1300 │ Δt: 8.2364e-03 │ sim. time: 7.4993e+00 (74.993%)  │ run time: 2.3118e-01 s
#timesteps:   1400 │ Δt: 4.9364e-03 │ sim. time: 8.0664e+00 (80.664%)  │ run time: 2.4920e-01 s
#timesteps:   1500 │ Δt: 6.0623e-03 │ sim. time: 8.6867e+00 (86.867%)  │ run time: 2.6701e-01 s
#timesteps:   1600 │ Δt: 5.3060e-03 │ sim. time: 9.2023e+00 (92.023%)  │ run time: 2.8504e-01 s
#timesteps:   1700 │ Δt: 5.1998e-03 │ sim. time: 9.8347e+00 (98.347%)  │ run time: 3.0399e-01 s

────────────────────────────────────────────────────────────────────────────────────────────────────
 Simulation running 'CompressibleEulerEquations1D' with DGSEM(polydeg=3)
────────────────────────────────────────────────────────────────────────────────────────────────────
 #timesteps:               1734                run time:       3.10515491e-01 s
 Δt:             4.52359594e-04                └── GC time:    0.00000000e+00 s (0.000%)
 sim. time:      1.00000000e+01 (100.000%)     time/DOF/rhs!:  1.38486418e-07 s
                                               PID:            1.41317169e-07 s
 #DOFs per field:           256                alloc'd memory:        247.715 MiB
 #elements:                  64

 Variable:       rho              rho_v1           rho_e         
 L2 error:       3.49096115e-07   2.18867078e-07   1.10217187e-06
 Linf error:     3.50486484e-06   1.49639857e-06   6.66292667e-06
 ∑∂S/∂U  Uₜ :  -2.08324524e-09
────────────────────────────────────────────────────────────────────────────────────────────────────

────────────────────────────────────────────────────────────────────────────────────────────────────
Trixi.jl simulation finished.  Final time: 10.0  Time steps: 1734 (accepted), 1734 (total)
────────────────────────────────────────────────────────────────────────────────────────────────────

Running convtest iteration 4/5

────────────────────────────────────────────────────────────────────────────────────────────────────
 Simulation running 'CompressibleEulerEquations1D' with DGSEM(polydeg=3)
────────────────────────────────────────────────────────────────────────────────────────────────────
 #timesteps:                  0                run time:       5.10000000e-07 s
 Δt:             1.00000000e+00                └── 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:           512                alloc'd memory:        253.330 MiB
 #elements:                 128

 Variable:       rho              rho_v1           rho_e         
 L2 error:       6.81509099e-10   6.09521822e-09   2.02857059e-08
 Linf error:     1.51149671e-09   1.81261561e-08   7.02064220e-08
 ∑∂S/∂U  Uₜ :  -9.08890265e-15
────────────────────────────────────────────────────────────────────────────────────────────────────

#timesteps:    100 │ Δt: 2.7965e-03 │ sim. time: 2.5579e-01 (2.558%)   │ run time: 2.7105e-02 s
#timesteps:    200 │ Δt: 3.0134e-03 │ sim. time: 5.5477e-01 (5.548%)   │ run time: 5.9316e-02 s
#timesteps:    300 │ Δt: 2.5825e-03 │ sim. time: 8.4189e-01 (8.419%)   │ run time: 9.0399e-02 s
#timesteps:    400 │ Δt: 2.4879e-03 │ sim. time: 1.0900e+00 (10.900%)  │ run time: 1.2205e-01 s
#timesteps:    500 │ Δt: 3.0134e-03 │ sim. time: 1.3636e+00 (13.636%)  │ run time: 1.5412e-01 s
#timesteps:    600 │ Δt: 3.0134e-03 │ sim. time: 1.6649e+00 (16.649%)  │ run time: 1.8716e-01 s
#timesteps:    700 │ Δt: 2.4728e-03 │ sim. time: 1.9339e+00 (19.339%)  │ run time: 2.3192e-01 s
#timesteps:    800 │ Δt: 2.6189e-03 │ sim. time: 2.1831e+00 (21.831%)  │ run time: 2.6210e-01 s
#timesteps:    900 │ Δt: 3.0134e-03 │ sim. time: 2.4737e+00 (24.737%)  │ run time: 2.9515e-01 s

────────────────────────────────────────────────────────────────────────────────────────────────────
 Simulation running 'CompressibleEulerEquations1D' with DGSEM(polydeg=3)
────────────────────────────────────────────────────────────────────────────────────────────────────
 #timesteps:               1000                run time:       3.28131345e-01 s
 Δt:             2.73769976e-03                └── GC time:    0.00000000e+00 s (0.000%)
 sim. time:      2.77061166e+00 (27.706%)      time/DOF/rhs!:  1.25242258e-07 s
                                               PID:            1.28074538e-07 s
 #DOFs per field:           512                alloc'd memory:        253.392 MiB
 #elements:                 128

 Variable:       rho              rho_v1           rho_e         
 L2 error:       1.09173993e-08   7.95287516e-09   3.60202037e-08
 Linf error:     1.24667378e-07   5.65820266e-08   2.49352672e-07
 ∑∂S/∂U  Uₜ :  -1.47340366e-01
────────────────────────────────────────────────────────────────────────────────────────────────────

#timesteps:   1100 │ Δt: 2.4515e-03 │ sim. time: 3.0237e+00 (30.237%)  │ run time: 3.6081e-01 s
#timesteps:   1200 │ Δt: 2.8840e-03 │ sim. time: 3.2833e+00 (32.833%)  │ run time: 3.9500e-01 s
#timesteps:   1300 │ Δt: 3.0134e-03 │ sim. time: 3.5839e+00 (35.839%)  │ run time: 4.2980e-01 s
#timesteps:   1400 │ Δt: 2.5437e-03 │ sim. time: 3.8666e+00 (38.666%)  │ run time: 4.6429e-01 s
#timesteps:   1500 │ Δt: 2.5125e-03 │ sim. time: 4.1142e+00 (41.142%)  │ run time: 5.0002e-01 s
#timesteps:   1600 │ Δt: 3.0134e-03 │ sim. time: 4.3927e+00 (43.927%)  │ run time: 5.3430e-01 s
#timesteps:   1700 │ Δt: 2.9891e-03 │ sim. time: 4.6940e+00 (46.940%)  │ run time: 5.6822e-01 s
#timesteps:   1800 │ Δt: 2.4592e-03 │ sim. time: 4.9578e+00 (49.578%)  │ run time: 6.0212e-01 s
#timesteps:   1900 │ Δt: 2.6731e-03 │ sim. time: 5.2087e+00 (52.087%)  │ run time: 6.3618e-01 s

────────────────────────────────────────────────────────────────────────────────────────────────────
 Simulation running 'CompressibleEulerEquations1D' with DGSEM(polydeg=3)
────────────────────────────────────────────────────────────────────────────────────────────────────
 #timesteps:               2000                run time:       6.70339007e-01 s
 Δt:             3.01339286e-03                └── GC time:    0.00000000e+00 s (0.000%)
 sim. time:      5.50286691e+00 (55.029%)      time/DOF/rhs!:  1.30840493e-07 s
                                               PID:            1.33589529e-07 s
 #DOFs per field:           512                alloc'd memory:        253.430 MiB
 #elements:                 128

 Variable:       rho              rho_v1           rho_e         
 L2 error:       6.48167855e-09   3.45616058e-10   1.28046369e-09
 Linf error:     6.77284393e-08   1.18161017e-09   4.53744775e-09
 ∑∂S/∂U  Uₜ :  -2.65254051e-03
────────────────────────────────────────────────────────────────────────────────────────────────────

#timesteps:   2100 │ Δt: 2.6730e-03 │ sim. time: 5.7967e+00 (57.967%)  │ run time: 7.0419e-01 s
#timesteps:   2200 │ Δt: 2.4593e-03 │ sim. time: 6.0474e+00 (60.474%)  │ run time: 7.3877e-01 s
#timesteps:   2300 │ Δt: 2.9881e-03 │ sim. time: 6.3117e+00 (63.117%)  │ run time: 7.7440e-01 s
#timesteps:   2400 │ Δt: 3.0134e-03 │ sim. time: 6.6130e+00 (66.130%)  │ run time: 8.1152e-01 s
#timesteps:   2500 │ Δt: 2.5123e-03 │ sim. time: 6.8911e+00 (68.911%)  │ run time: 8.4626e-01 s
#timesteps:   2600 │ Δt: 2.5440e-03 │ sim. time: 7.1386e+00 (71.386%)  │ run time: 8.7973e-01 s
#timesteps:   2700 │ Δt: 3.0134e-03 │ sim. time: 7.4218e+00 (74.218%)  │ run time: 9.1372e-01 s
#timesteps:   2800 │ Δt: 2.8846e-03 │ sim. time: 7.7223e+00 (77.223%)  │ run time: 9.4784e-01 s
#timesteps:   2900 │ Δt: 2.4514e-03 │ sim. time: 7.9815e+00 (79.815%)  │ run time: 9.8227e-01 s

────────────────────────────────────────────────────────────────────────────────────────────────────
 Simulation running 'CompressibleEulerEquations1D' with DGSEM(polydeg=3)
────────────────────────────────────────────────────────────────────────────────────────────────────
 #timesteps:               3000                run time:       1.01638069e+00 s
 Δt:             2.73768918e-03                └── GC time:    0.00000000e+00 s (0.000%)
 sim. time:      8.23485975e+00 (82.349%)      time/DOF/rhs!:  1.32267492e-07 s
                                               PID:            1.35079548e-07 s
 #DOFs per field:           512                alloc'd memory:        253.468 MiB
 #elements:                 128

 Variable:       rho              rho_v1           rho_e         
 L2 error:       1.64730366e-08   7.75686572e-09   3.57273237e-08
 Linf error:     2.08841422e-07   5.55077033e-08   2.44509636e-07
 ∑∂S/∂U  Uₜ :   1.47872327e-01
────────────────────────────────────────────────────────────────────────────────────────────────────

#timesteps:   3100 │ Δt: 3.0134e-03 │ sim. time: 8.5320e+00 (85.320%)  │ run time: 1.0504e+00 s
#timesteps:   3200 │ Δt: 2.6186e-03 │ sim. time: 8.8223e+00 (88.223%)  │ run time: 1.0848e+00 s
#timesteps:   3300 │ Δt: 2.4730e-03 │ sim. time: 9.0713e+00 (90.713%)  │ run time: 1.1191e+00 s
#timesteps:   3400 │ Δt: 3.0134e-03 │ sim. time: 9.3408e+00 (93.408%)  │ run time: 1.1547e+00 s
#timesteps:   3500 │ Δt: 3.0134e-03 │ sim. time: 9.6422e+00 (96.422%)  │ run time: 1.1897e+00 s
#timesteps:   3600 │ Δt: 2.4876e-03 │ sim. time: 9.9152e+00 (99.152%)  │ run time: 1.2239e+00 s

────────────────────────────────────────────────────────────────────────────────────────────────────
 Simulation running 'CompressibleEulerEquations1D' with DGSEM(polydeg=3)
────────────────────────────────────────────────────────────────────────────────────────────────────
 #timesteps:               3635                run time:       1.23615905e+00 s
 Δt:             1.09078283e-03                └── GC time:    0.00000000e+00 s (0.000%)
 sim. time:      1.00000000e+01 (100.000%)     time/DOF/rhs!:  1.32277574e-07 s
                                               PID:            1.35049996e-07 s
 #DOFs per field:           512                alloc'd memory:        253.498 MiB
 #elements:                 128

 Variable:       rho              rho_v1           rho_e         
 L2 error:       2.18223258e-08   1.36656588e-08   6.95936964e-08
 Linf error:     2.57629613e-07   9.39790414e-08   4.16853212e-07
 ∑∂S/∂U  Uₜ :  -5.86782117e-11
────────────────────────────────────────────────────────────────────────────────────────────────────

────────────────────────────────────────────────────────────────────────────────────────────────────
Trixi.jl simulation finished.  Final time: 10.0  Time steps: 3635 (accepted), 3635 (total)
────────────────────────────────────────────────────────────────────────────────────────────────────

Running convtest iteration 5/5

────────────────────────────────────────────────────────────────────────────────────────────────────
 Simulation running 'CompressibleEulerEquations1D' with DGSEM(polydeg=3)
────────────────────────────────────────────────────────────────────────────────────────────────────
 #timesteps:                  0                run time:       6.63000000e-07 s
 Δt:             1.00000000e+00                └── 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:          1024                alloc'd memory:        263.324 MiB
 #elements:                 256

 Variable:       rho              rho_v1           rho_e         
 L2 error:       4.25951487e-11   3.80976670e-10   1.26796191e-09
 Linf error:     9.44915257e-11   1.13371446e-09   4.39263559e-09
 ∑∂S/∂U  Uₜ :  -3.78976919e-15
────────────────────────────────────────────────────────────────────────────────────────────────────

#timesteps:    100 │ Δt: 7.5335e-04 │ sim. time: 7.5335e-02 (0.753%)   │ run time: 5.5452e-02 s
#timesteps:    200 │ Δt: 7.5335e-04 │ sim. time: 1.5067e-01 (1.507%)   │ run time: 1.1137e-01 s
#timesteps:    300 │ Δt: 7.5335e-04 │ sim. time: 2.2600e-01 (2.260%)   │ run time: 1.6666e-01 s
#timesteps:    400 │ Δt: 7.5335e-04 │ sim. time: 3.0134e-01 (3.013%)   │ run time: 2.2566e-01 s
#timesteps:    500 │ Δt: 7.5335e-04 │ sim. time: 3.7667e-01 (3.767%)   │ run time: 2.8697e-01 s
#timesteps:    600 │ Δt: 7.5335e-04 │ sim. time: 4.5201e-01 (4.520%)   │ run time: 3.4824e-01 s
#timesteps:    700 │ Δt: 7.5335e-04 │ sim. time: 5.2734e-01 (5.273%)   │ run time: 4.0940e-01 s
#timesteps:    800 │ Δt: 7.5335e-04 │ sim. time: 6.0268e-01 (6.027%)   │ run time: 4.6985e-01 s
#timesteps:    900 │ Δt: 7.5335e-04 │ sim. time: 6.7801e-01 (6.780%)   │ run time: 5.3209e-01 s

────────────────────────────────────────────────────────────────────────────────────────────────────
 Simulation running 'CompressibleEulerEquations1D' with DGSEM(polydeg=3)
────────────────────────────────────────────────────────────────────────────────────────────────────
 #timesteps:               1000                run time:       5.94904590e-01 s
 Δt:             7.53348214e-04                └── GC time:    0.00000000e+00 s (0.000%)
 sim. time:      7.53348214e-01 (7.533%)       time/DOF/rhs!:  1.13521595e-07 s
                                               PID:            1.16111738e-07 s
 #DOFs per field:          1024                alloc'd memory:        263.387 MiB
 #elements:                 256

 Variable:       rho              rho_v1           rho_e         
 L2 error:       6.96589003e-10   4.52931788e-10   2.08674910e-09
 Linf error:     9.10981424e-09   3.26686478e-09   1.43406282e-08
 ∑∂S/∂U  Uₜ :  -1.48423115e-01
────────────────────────────────────────────────────────────────────────────────────────────────────

#timesteps:   1100 │ Δt: 7.5335e-04 │ sim. time: 8.2868e-01 (8.287%)   │ run time: 6.5628e-01 s
#timesteps:   1200 │ Δt: 7.5335e-04 │ sim. time: 9.0402e-01 (9.040%)   │ run time: 7.1709e-01 s
#timesteps:   1300 │ Δt: 7.5335e-04 │ sim. time: 9.7935e-01 (9.794%)   │ run time: 7.7790e-01 s
#timesteps:   1400 │ Δt: 7.5335e-04 │ sim. time: 1.0547e+00 (10.547%)  │ run time: 8.3839e-01 s
#timesteps:   1500 │ Δt: 7.5335e-04 │ sim. time: 1.1300e+00 (11.300%)  │ run time: 9.0019e-01 s
#timesteps:   1600 │ Δt: 7.5335e-04 │ sim. time: 1.2054e+00 (12.054%)  │ run time: 9.6073e-01 s
#timesteps:   1700 │ Δt: 7.5335e-04 │ sim. time: 1.2807e+00 (12.807%)  │ run time: 1.0230e+00 s
#timesteps:   1800 │ Δt: 7.5335e-04 │ sim. time: 1.3560e+00 (13.560%)  │ run time: 1.0861e+00 s
#timesteps:   1900 │ Δt: 7.5335e-04 │ sim. time: 1.4314e+00 (14.314%)  │ run time: 1.1491e+00 s

────────────────────────────────────────────────────────────────────────────────────────────────────
 Simulation running 'CompressibleEulerEquations1D' with DGSEM(polydeg=3)
────────────────────────────────────────────────────────────────────────────────────────────────────
 #timesteps:               2000                run time:       1.21153316e+00 s
 Δt:             7.53348214e-04                └── GC time:    0.00000000e+00 s (0.000%)
 sim. time:      1.50669643e+00 (15.067%)      time/DOF/rhs!:  1.17843513e-07 s
                                               PID:            1.20371697e-07 s
 #DOFs per field:          1024                alloc'd memory:        263.425 MiB
 #elements:                 256

 Variable:       rho              rho_v1           rho_e         
 L2 error:       2.88399750e-10   5.68164663e-12   3.00608567e-11
 Linf error:     3.23670246e-09   3.70842107e-11   1.56722635e-10
 ∑∂S/∂U  Uₜ :  -6.19425556e-03
────────────────────────────────────────────────────────────────────────────────────────────────────

#timesteps:   2100 │ Δt: 7.5335e-04 │ sim. time: 1.5820e+00 (15.820%)  │ run time: 1.2739e+00 s
#timesteps:   2200 │ Δt: 7.5335e-04 │ sim. time: 1.6574e+00 (16.574%)  │ run time: 1.3367e+00 s
#timesteps:   2300 │ Δt: 7.5335e-04 │ sim. time: 1.7327e+00 (17.327%)  │ run time: 1.3983e+00 s
#timesteps:   2400 │ Δt: 7.5335e-04 │ sim. time: 1.8080e+00 (18.080%)  │ run time: 1.4587e+00 s
#timesteps:   2500 │ Δt: 7.5335e-04 │ sim. time: 1.8834e+00 (18.834%)  │ run time: 1.5299e+00 s
#timesteps:   2600 │ Δt: 7.5335e-04 │ sim. time: 1.9587e+00 (19.587%)  │ run time: 1.5889e+00 s
#timesteps:   2700 │ Δt: 7.5335e-04 │ sim. time: 2.0340e+00 (20.340%)  │ run time: 1.6502e+00 s
#timesteps:   2800 │ Δt: 7.5335e-04 │ sim. time: 2.1094e+00 (21.094%)  │ run time: 1.7126e+00 s
#timesteps:   2900 │ Δt: 7.5335e-04 │ sim. time: 2.1847e+00 (21.847%)  │ run time: 1.7741e+00 s

────────────────────────────────────────────────────────────────────────────────────────────────────
 Simulation running 'CompressibleEulerEquations1D' with DGSEM(polydeg=3)
────────────────────────────────────────────────────────────────────────────────────────────────────
 #timesteps:               3000                run time:       1.83814687e+00 s
 Δt:             7.53348214e-04                └── GC time:    0.00000000e+00 s (0.000%)
 sim. time:      2.26004464e+00 (22.600%)      time/DOF/rhs!:  1.19697584e-07 s
                                               PID:            1.22327772e-07 s
 #DOFs per field:          1024                alloc'd memory:        263.462 MiB
 #elements:                 256

 Variable:       rho              rho_v1           rho_e         
 L2 error:       8.94873761e-10   4.19308518e-10   1.94668396e-09
 Linf error:     1.27630972e-08   3.04126813e-09   1.34100393e-08
 ∑∂S/∂U  Uₜ :   1.48060789e-01
────────────────────────────────────────────────────────────────────────────────────────────────────

#timesteps:   3100 │ Δt: 7.5335e-04 │ sim. time: 2.3354e+00 (23.354%)  │ run time: 1.9018e+00 s
#timesteps:   3200 │ Δt: 7.5335e-04 │ sim. time: 2.4107e+00 (24.107%)  │ run time: 1.9672e+00 s
#timesteps:   3300 │ Δt: 7.5335e-04 │ sim. time: 2.4860e+00 (24.860%)  │ run time: 2.0320e+00 s
#timesteps:   3400 │ Δt: 7.5335e-04 │ sim. time: 2.5614e+00 (25.614%)  │ run time: 2.0968e+00 s
#timesteps:   3500 │ Δt: 7.5335e-04 │ sim. time: 2.6367e+00 (26.367%)  │ run time: 2.1628e+00 s
#timesteps:   3600 │ Δt: 7.5335e-04 │ sim. time: 2.7121e+00 (27.121%)  │ run time: 2.2279e+00 s
#timesteps:   3700 │ Δt: 7.5335e-04 │ sim. time: 2.7874e+00 (27.874%)  │ run time: 2.2929e+00 s
#timesteps:   3800 │ Δt: 7.5335e-04 │ sim. time: 2.8627e+00 (28.627%)  │ run time: 2.3585e+00 s
#timesteps:   3900 │ Δt: 7.5335e-04 │ sim. time: 2.9381e+00 (29.381%)  │ run time: 2.4233e+00 s

────────────────────────────────────────────────────────────────────────────────────────────────────
 Simulation running 'CompressibleEulerEquations1D' with DGSEM(polydeg=3)
────────────────────────────────────────────────────────────────────────────────────────────────────
 #timesteps:               4000                run time:       2.48771671e+00 s
 Δt:             7.53348214e-04                └── GC time:    0.00000000e+00 s (0.000%)
 sim. time:      3.01339286e+00 (30.134%)      time/DOF/rhs!:  1.24350048e-07 s
                                               PID:            1.26806491e-07 s
 #DOFs per field:          1024                alloc'd memory:        263.500 MiB
 #elements:                 256

 Variable:       rho              rho_v1           rho_e         
 L2 error:       1.41015037e-09   8.52488991e-10   4.41125993e-09
 Linf error:     1.88324965e-08   5.89579185e-09   2.60199080e-08
 ∑∂S/∂U  Uₜ :   1.25767851e-02
────────────────────────────────────────────────────────────────────────────────────────────────────

#timesteps:   4100 │ Δt: 7.5335e-04 │ sim. time: 3.0887e+00 (30.887%)  │ run time: 2.5528e+00 s
#timesteps:   4200 │ Δt: 7.5335e-04 │ sim. time: 3.1641e+00 (31.641%)  │ run time: 2.6193e+00 s
#timesteps:   4300 │ Δt: 7.5335e-04 │ sim. time: 3.2394e+00 (32.394%)  │ run time: 2.6852e+00 s
#timesteps:   4400 │ Δt: 7.5335e-04 │ sim. time: 3.3147e+00 (33.147%)  │ run time: 2.7496e+00 s
#timesteps:   4500 │ Δt: 7.5335e-04 │ sim. time: 3.3901e+00 (33.901%)  │ run time: 2.8154e+00 s
#timesteps:   4600 │ Δt: 7.5335e-04 │ sim. time: 3.4654e+00 (34.654%)  │ run time: 2.8801e+00 s
#timesteps:   4700 │ Δt: 7.5335e-04 │ sim. time: 3.5407e+00 (35.407%)  │ run time: 2.9443e+00 s
#timesteps:   4800 │ Δt: 7.5335e-04 │ sim. time: 3.6161e+00 (36.161%)  │ run time: 3.0099e+00 s
#timesteps:   4900 │ Δt: 7.5335e-04 │ sim. time: 3.6914e+00 (36.914%)  │ run time: 3.0744e+00 s

────────────────────────────────────────────────────────────────────────────────────────────────────
 Simulation running 'CompressibleEulerEquations1D' with DGSEM(polydeg=3)
────────────────────────────────────────────────────────────────────────────────────────────────────
 #timesteps:               5000                run time:       3.14002461e+00 s
 Δt:             7.53348214e-04                └── GC time:    0.00000000e+00 s (0.000%)
 sim. time:      3.76674107e+00 (37.667%)      time/DOF/rhs!:  1.24920727e-07 s
                                               PID:            1.27340911e-07 s
 #DOFs per field:          1024                alloc'd memory:        263.538 MiB
 #elements:                 256

 Variable:       rho              rho_v1           rho_e         
 L2 error:       7.49408356e-10   4.87177661e-10   2.25419491e-09
 Linf error:     9.87001725e-09   3.49580809e-09   1.53554645e-08
 ∑∂S/∂U  Uₜ :  -1.47734789e-01
────────────────────────────────────────────────────────────────────────────────────────────────────

#timesteps:   5100 │ Δt: 7.5335e-04 │ sim. time: 3.8421e+00 (38.421%)  │ run time: 3.2073e+00 s
#timesteps:   5200 │ Δt: 7.5335e-04 │ sim. time: 3.9174e+00 (39.174%)  │ run time: 3.2739e+00 s
#timesteps:   5300 │ Δt: 7.5335e-04 │ sim. time: 3.9927e+00 (39.927%)  │ run time: 3.3410e+00 s
#timesteps:   5400 │ Δt: 7.5335e-04 │ sim. time: 4.0681e+00 (40.681%)  │ run time: 3.4052e+00 s
#timesteps:   5500 │ Δt: 7.5335e-04 │ sim. time: 4.1434e+00 (41.434%)  │ run time: 3.4703e+00 s
#timesteps:   5600 │ Δt: 7.5335e-04 │ sim. time: 4.2188e+00 (42.188%)  │ run time: 3.5369e+00 s
#timesteps:   5700 │ Δt: 7.5335e-04 │ sim. time: 4.2941e+00 (42.941%)  │ run time: 3.6024e+00 s
#timesteps:   5800 │ Δt: 7.5335e-04 │ sim. time: 4.3694e+00 (43.694%)  │ run time: 3.6684e+00 s
#timesteps:   5900 │ Δt: 7.5335e-04 │ sim. time: 4.4448e+00 (44.448%)  │ run time: 3.7341e+00 s

────────────────────────────────────────────────────────────────────────────────────────────────────
 Simulation running 'CompressibleEulerEquations1D' with DGSEM(polydeg=3)
────────────────────────────────────────────────────────────────────────────────────────────────────
 #timesteps:               6000                run time:       3.79963240e+00 s
 Δt:             7.53348214e-04                └── GC time:    0.00000000e+00 s (0.000%)
 sim. time:      4.52008929e+00 (45.201%)      time/DOF/rhs!:  1.26256051e-07 s
                                               PID:            1.28776514e-07 s
 #DOFs per field:          1024                alloc'd memory:        263.576 MiB
 #elements:                 256

 Variable:       rho              rho_v1           rho_e         
 L2 error:       2.75905925e-10   1.62978396e-11   8.78954359e-11
 Linf error:     3.07883941e-09   1.10827070e-10   4.77026418e-10
 ∑∂S/∂U  Uₜ :  -1.85399541e-02
────────────────────────────────────────────────────────────────────────────────────────────────────

#timesteps:   6100 │ Δt: 7.5335e-04 │ sim. time: 4.5954e+00 (45.954%)  │ run time: 3.8649e+00 s
#timesteps:   6200 │ Δt: 7.5335e-04 │ sim. time: 4.6708e+00 (46.708%)  │ run time: 3.9303e+00 s
#timesteps:   6300 │ Δt: 7.5335e-04 │ sim. time: 4.7461e+00 (47.461%)  │ run time: 3.9965e+00 s
#timesteps:   6400 │ Δt: 7.5335e-04 │ sim. time: 4.8214e+00 (48.214%)  │ run time: 4.0622e+00 s
#timesteps:   6500 │ Δt: 7.5335e-04 │ sim. time: 4.8968e+00 (48.968%)  │ run time: 4.1288e+00 s
#timesteps:   6600 │ Δt: 7.5335e-04 │ sim. time: 4.9721e+00 (49.721%)  │ run time: 4.1947e+00 s
#timesteps:   6700 │ Δt: 7.5335e-04 │ sim. time: 5.0474e+00 (50.474%)  │ run time: 4.2607e+00 s
#timesteps:   6800 │ Δt: 7.5335e-04 │ sim. time: 5.1228e+00 (51.228%)  │ run time: 4.3277e+00 s
#timesteps:   6900 │ Δt: 7.5335e-04 │ sim. time: 5.1981e+00 (51.981%)  │ run time: 4.3948e+00 s

────────────────────────────────────────────────────────────────────────────────────────────────────
 Simulation running 'CompressibleEulerEquations1D' with DGSEM(polydeg=3)
────────────────────────────────────────────────────────────────────────────────────────────────────
 #timesteps:               7000                run time:       4.45746215e+00 s
 Δt:             7.53348214e-04                └── GC time:    0.00000000e+00 s (0.000%)
 sim. time:      5.27343750e+00 (52.734%)      time/DOF/rhs!:  1.25944446e-07 s
                                               PID:            1.28421354e-07 s
 #DOFs per field:          1024                alloc'd memory:        263.614 MiB
 #elements:                 256

 Variable:       rho              rho_v1           rho_e         
 L2 error:       8.53370760e-10   3.85186726e-10   1.78418153e-09
 Linf error:     1.21411525e-08   2.81123036e-09   1.23954571e-08
 ∑∂S/∂U  Uₜ :   1.46652481e-01
────────────────────────────────────────────────────────────────────────────────────────────────────

#timesteps:   7100 │ Δt: 7.5335e-04 │ sim. time: 5.3488e+00 (53.488%)  │ run time: 4.5215e+00 s
#timesteps:   7200 │ Δt: 7.5335e-04 │ sim. time: 5.4241e+00 (54.241%)  │ run time: 4.5865e+00 s
#timesteps:   7300 │ Δt: 7.5335e-04 │ sim. time: 5.4994e+00 (54.994%)  │ run time: 4.6516e+00 s
#timesteps:   7400 │ Δt: 7.5335e-04 │ sim. time: 5.5748e+00 (55.748%)  │ run time: 4.7177e+00 s
#timesteps:   7500 │ Δt: 7.5335e-04 │ sim. time: 5.6501e+00 (56.501%)  │ run time: 4.7840e+00 s
#timesteps:   7600 │ Δt: 7.5335e-04 │ sim. time: 5.7254e+00 (57.254%)  │ run time: 4.8489e+00 s
#timesteps:   7700 │ Δt: 7.5335e-04 │ sim. time: 5.8008e+00 (58.008%)  │ run time: 4.9147e+00 s
#timesteps:   7800 │ Δt: 7.5335e-04 │ sim. time: 5.8761e+00 (58.761%)  │ run time: 4.9801e+00 s
#timesteps:   7900 │ Δt: 7.5335e-04 │ sim. time: 5.9515e+00 (59.515%)  │ run time: 5.0454e+00 s

────────────────────────────────────────────────────────────────────────────────────────────────────
 Simulation running 'CompressibleEulerEquations1D' with DGSEM(polydeg=3)
────────────────────────────────────────────────────────────────────────────────────────────────────
 #timesteps:               8000                run time:       5.11204246e+00 s
 Δt:             7.53348214e-04                └── GC time:    0.00000000e+00 s (0.000%)
 sim. time:      6.02678571e+00 (60.268%)      time/DOF/rhs!:  1.25348366e-07 s
                                               PID:            1.27779228e-07 s
 #DOFs per field:          1024                alloc'd memory:        263.652 MiB
 #elements:                 256

 Variable:       rho              rho_v1           rho_e         
 L2 error:       1.40956776e-09   8.48200512e-10   4.38418432e-09
 Linf error:     1.88835028e-08   5.86802917e-09   2.59008850e-08
 ∑∂S/∂U  Uₜ :   2.50623883e-02
────────────────────────────────────────────────────────────────────────────────────────────────────

#timesteps:   8100 │ Δt: 7.5335e-04 │ sim. time: 6.1021e+00 (61.021%)  │ run time: 5.1778e+00 s
#timesteps:   8200 │ Δt: 7.5335e-04 │ sim. time: 6.1775e+00 (61.775%)  │ run time: 5.2437e+00 s
#timesteps:   8300 │ Δt: 7.5335e-04 │ sim. time: 6.2528e+00 (62.528%)  │ run time: 5.3094e+00 s
#timesteps:   8400 │ Δt: 7.5335e-04 │ sim. time: 6.3281e+00 (63.281%)  │ run time: 5.3749e+00 s
#timesteps:   8500 │ Δt: 7.5335e-04 │ sim. time: 6.4035e+00 (64.035%)  │ run time: 5.4403e+00 s
#timesteps:   8600 │ Δt: 7.5335e-04 │ sim. time: 6.4788e+00 (64.788%)  │ run time: 5.5063e+00 s
#timesteps:   8700 │ Δt: 7.5335e-04 │ sim. time: 6.5541e+00 (65.541%)  │ run time: 5.5725e+00 s
#timesteps:   8800 │ Δt: 7.5335e-04 │ sim. time: 6.6295e+00 (66.295%)  │ run time: 5.6375e+00 s
#timesteps:   8900 │ Δt: 7.5335e-04 │ sim. time: 6.7048e+00 (67.048%)  │ run time: 5.7023e+00 s

────────────────────────────────────────────────────────────────────────────────────────────────────
 Simulation running 'CompressibleEulerEquations1D' with DGSEM(polydeg=3)
────────────────────────────────────────────────────────────────────────────────────────────────────
 #timesteps:               9000                run time:       5.76830534e+00 s
 Δt:             7.53348214e-04                └── GC time:    0.00000000e+00 s (0.000%)
 sim. time:      6.78013393e+00 (67.801%)      time/DOF/rhs!:  1.25684422e-07 s
                                               PID:            1.28121813e-07 s
 #DOFs per field:          1024                alloc'd memory:        263.689 MiB
 #elements:                 256

 Variable:       rho              rho_v1           rho_e         
 L2 error:       8.02208651e-10   5.21132901e-10   2.42384926e-09
 Linf error:     1.06241655e-08   3.72223918e-09   1.63594418e-08
 ∑∂S/∂U  Uₜ :  -1.45998573e-01
────────────────────────────────────────────────────────────────────────────────────────────────────

#timesteps:   9100 │ Δt: 7.5335e-04 │ sim. time: 6.8555e+00 (68.555%)  │ run time: 5.8332e+00 s
#timesteps:   9200 │ Δt: 7.5335e-04 │ sim. time: 6.9308e+00 (69.308%)  │ run time: 5.8989e+00 s
#timesteps:   9300 │ Δt: 7.5335e-04 │ sim. time: 7.0061e+00 (70.061%)  │ run time: 5.9644e+00 s
#timesteps:   9400 │ Δt: 7.5335e-04 │ sim. time: 7.0815e+00 (70.815%)  │ run time: 6.0302e+00 s
#timesteps:   9500 │ Δt: 7.5335e-04 │ sim. time: 7.1568e+00 (71.568%)  │ run time: 6.0955e+00 s
#timesteps:   9600 │ Δt: 7.5335e-04 │ sim. time: 7.2321e+00 (72.321%)  │ run time: 6.1615e+00 s
#timesteps:   9700 │ Δt: 7.5335e-04 │ sim. time: 7.3075e+00 (73.075%)  │ run time: 6.2421e+00 s
#timesteps:   9800 │ Δt: 7.5335e-04 │ sim. time: 7.3828e+00 (73.828%)  │ run time: 6.3180e+00 s
#timesteps:   9900 │ Δt: 7.5335e-04 │ sim. time: 7.4581e+00 (74.581%)  │ run time: 6.3804e+00 s

────────────────────────────────────────────────────────────────────────────────────────────────────
 Simulation running 'CompressibleEulerEquations1D' with DGSEM(polydeg=3)
────────────────────────────────────────────────────────────────────────────────────────────────────
 #timesteps:              10000                run time:       6.44423282e+00 s
 Δt:             7.53348214e-04                └── GC time:    0.00000000e+00 s (0.000%)
 sim. time:      7.53348214e+00 (75.335%)      time/DOF/rhs!:  1.29290318e-07 s
                                               PID:            1.31961523e-07 s
 #DOFs per field:          1024                alloc'd memory:        263.727 MiB
 #elements:                 256

 Variable:       rho              rho_v1           rho_e         
 L2 error:       2.60444026e-10   2.84795280e-11   1.50333928e-10
 Linf error:     2.94285929e-09   2.09061490e-10   8.84620377e-10
 ∑∂S/∂U  Uₜ :  -3.07574900e-02
────────────────────────────────────────────────────────────────────────────────────────────────────

#timesteps:  10100 │ Δt: 7.5335e-04 │ sim. time: 7.6088e+00 (76.088%)  │ run time: 6.5082e+00 s
#timesteps:  10200 │ Δt: 7.5335e-04 │ sim. time: 7.6842e+00 (76.842%)  │ run time: 6.5742e+00 s
#timesteps:  10300 │ Δt: 7.5335e-04 │ sim. time: 7.7595e+00 (77.595%)  │ run time: 6.6402e+00 s
#timesteps:  10400 │ Δt: 7.5335e-04 │ sim. time: 7.8348e+00 (78.348%)  │ run time: 6.7049e+00 s
#timesteps:  10500 │ Δt: 7.5335e-04 │ sim. time: 7.9102e+00 (79.102%)  │ run time: 6.7714e+00 s
#timesteps:  10600 │ Δt: 7.5335e-04 │ sim. time: 7.9855e+00 (79.855%)  │ run time: 6.8379e+00 s
#timesteps:  10700 │ Δt: 7.5335e-04 │ sim. time: 8.0608e+00 (80.608%)  │ run time: 6.8972e+00 s
#timesteps:  10800 │ Δt: 7.5335e-04 │ sim. time: 8.1362e+00 (81.362%)  │ run time: 6.9601e+00 s
#timesteps:  10900 │ Δt: 7.5335e-04 │ sim. time: 8.2115e+00 (82.115%)  │ run time: 7.0253e+00 s

────────────────────────────────────────────────────────────────────────────────────────────────────
 Simulation running 'CompressibleEulerEquations1D' with DGSEM(polydeg=3)
────────────────────────────────────────────────────────────────────────────────────────────────────
 #timesteps:              11000                run time:       7.09149469e+00 s
 Δt:             7.53348214e-04                └── GC time:    0.00000000e+00 s (0.000%)
 sim. time:      8.28683036e+00 (82.868%)      time/DOF/rhs!:  1.23871564e-07 s
                                               PID:            1.26356386e-07 s
 #DOFs per field:          1024                alloc'd memory:        263.765 MiB
 #elements:                 256

 Variable:       rho              rho_v1           rho_e         
 L2 error:       8.11806704e-10   3.51480736e-10   1.62628064e-09
 Linf error:     1.15091754e-08   2.58241672e-09   1.13854135e-08
 ∑∂S/∂U  Uₜ :   1.44210202e-01
────────────────────────────────────────────────────────────────────────────────────────────────────

#timesteps:  11100 │ Δt: 7.5335e-04 │ sim. time: 8.3622e+00 (83.622%)  │ run time: 7.1571e+00 s
#timesteps:  11200 │ Δt: 7.5335e-04 │ sim. time: 8.4375e+00 (84.375%)  │ run time: 7.2221e+00 s
#timesteps:  11300 │ Δt: 7.5335e-04 │ sim. time: 8.5128e+00 (85.128%)  │ run time: 7.2882e+00 s
#timesteps:  11400 │ Δt: 7.5335e-04 │ sim. time: 8.5882e+00 (85.882%)  │ run time: 7.3534e+00 s
#timesteps:  11500 │ Δt: 7.5335e-04 │ sim. time: 8.6635e+00 (86.635%)  │ run time: 7.4196e+00 s
#timesteps:  11600 │ Δt: 7.5335e-04 │ sim. time: 8.7388e+00 (87.388%)  │ run time: 7.4845e+00 s
#timesteps:  11700 │ Δt: 7.5335e-04 │ sim. time: 8.8142e+00 (88.142%)  │ run time: 7.5500e+00 s
#timesteps:  11800 │ Δt: 7.5335e-04 │ sim. time: 8.8895e+00 (88.895%)  │ run time: 7.6157e+00 s
#timesteps:  11900 │ Δt: 7.5335e-04 │ sim. time: 8.9648e+00 (89.648%)  │ run time: 7.6814e+00 s

────────────────────────────────────────────────────────────────────────────────────────────────────
 Simulation running 'CompressibleEulerEquations1D' with DGSEM(polydeg=3)
────────────────────────────────────────────────────────────────────────────────────────────────────
 #timesteps:              12000                run time:       7.74849630e+00 s
 Δt:             7.53348214e-04                └── GC time:    0.00000000e+00 s (0.000%)
 sim. time:      9.04017857e+00 (90.402%)      time/DOF/rhs!:  1.25799454e-07 s
                                               PID:            1.28256309e-07 s
 #DOFs per field:          1024                alloc'd memory:        263.803 MiB
 #elements:                 256

 Variable:       rho              rho_v1           rho_e         
 L2 error:       1.40414562e-09   8.41040385e-10   4.33669186e-09
 Linf error:     1.88831222e-08   5.82085224e-09   2.56962771e-08
 ∑∂S/∂U  Uₜ :   3.73663371e-02
────────────────────────────────────────────────────────────────────────────────────────────────────

#timesteps:  12100 │ Δt: 7.5335e-04 │ sim. time: 9.1155e+00 (91.155%)  │ run time: 7.8181e+00 s
#timesteps:  12200 │ Δt: 7.5335e-04 │ sim. time: 9.1908e+00 (91.908%)  │ run time: 7.8845e+00 s
#timesteps:  12300 │ Δt: 7.5335e-04 │ sim. time: 9.2662e+00 (92.662%)  │ run time: 7.9497e+00 s
#timesteps:  12400 │ Δt: 7.5335e-04 │ sim. time: 9.3415e+00 (93.415%)  │ run time: 8.0159e+00 s
#timesteps:  12500 │ Δt: 7.5335e-04 │ sim. time: 9.4169e+00 (94.169%)  │ run time: 8.0808e+00 s
#timesteps:  12600 │ Δt: 7.5335e-04 │ sim. time: 9.4922e+00 (94.922%)  │ run time: 8.1457e+00 s
#timesteps:  12700 │ Δt: 7.5335e-04 │ sim. time: 9.5675e+00 (95.675%)  │ run time: 8.2112e+00 s
#timesteps:  12800 │ Δt: 7.5335e-04 │ sim. time: 9.6429e+00 (96.429%)  │ run time: 8.2769e+00 s
#timesteps:  12900 │ Δt: 7.5335e-04 │ sim. time: 9.7182e+00 (97.182%)  │ run time: 8.3440e+00 s

────────────────────────────────────────────────────────────────────────────────────────────────────
 Simulation running 'CompressibleEulerEquations1D' with DGSEM(polydeg=3)
────────────────────────────────────────────────────────────────────────────────────────────────────
 #timesteps:              13000                run time:       8.40997451e+00 s
 Δt:             7.53348214e-04                └── GC time:    0.00000000e+00 s (0.000%)
 sim. time:      9.79352679e+00 (97.935%)      time/DOF/rhs!:  1.26665898e-07 s
                                               PID:            1.29133338e-07 s
 #DOFs per field:          1024                alloc'd memory:        263.840 MiB
 #elements:                 256

 Variable:       rho              rho_v1           rho_e         
 L2 error:       8.54686351e-10   5.54555405e-10   2.59479092e-09
 Linf error:     1.13689698e-08   3.94378863e-09   1.73413657e-08
 ∑∂S/∂U  Uₜ :  -1.43224703e-01
────────────────────────────────────────────────────────────────────────────────────────────────────

#timesteps:  13100 │ Δt: 7.5335e-04 │ sim. time: 9.8689e+00 (98.689%)  │ run time: 8.4755e+00 s
#timesteps:  13200 │ Δt: 7.5335e-04 │ sim. time: 9.9442e+00 (99.442%)  │ run time: 8.5418e+00 s

────────────────────────────────────────────────────────────────────────────────────────────────────
 Simulation running 'CompressibleEulerEquations1D' with DGSEM(polydeg=3)
────────────────────────────────────────────────────────────────────────────────────────────────────
 #timesteps:              13275                run time:       8.59231152e+00 s
 Δt:             5.58035736e-05                └── GC time:    0.00000000e+00 s (0.000%)
 sim. time:      1.00000000e+01 (100.000%)     time/DOF/rhs!:  1.26831590e-07 s
                                               PID:            1.29301607e-07 s
 #DOFs per field:          1024                alloc'd memory:        263.860 MiB
 #elements:                 256

 Variable:       rho              rho_v1           rho_e         
 L2 error:       1.40578515e-09   8.53876245e-10   4.41750594e-09
 Linf error:     1.87284726e-08   5.90549476e-09   2.60598476e-08
 ∑∂S/∂U  Uₜ :   8.23934258e-14
────────────────────────────────────────────────────────────────────────────────────────────────────

────────────────────────────────────────────────────────────────────────────────────────────────────
Trixi.jl simulation finished.  Final time: 10.0  Time steps: 13275 (accepted), 13275 (total)
────────────────────────────────────────────────────────────────────────────────────────────────────


####################################################################################################
l2
rho                 rho_v1              rho_e               
error     EOC       error     EOC       error     EOC       
1.13e-04  -         6.24e-05  -         2.85e-04  -         
6.13e-06  4.21      3.51e-06  4.15      1.75e-05  4.03      
3.49e-07  4.13      2.19e-07  4.00      1.10e-06  3.99      
2.18e-08  4.00      1.37e-08  4.00      6.96e-08  3.99      
1.41e-09  3.96      8.54e-10  4.00      4.42e-09  3.98      

mean      4.07      mean      4.04      mean      3.99      
----------------------------------------------------------------------------------------------------
linf
rho                 rho_v1              rho_e               
error     EOC       error     EOC       error     EOC       
6.23e-04  -         3.59e-04  -         1.61e-03  -         
4.75e-05  3.71      2.36e-05  3.93      1.05e-04  3.93      
3.50e-06  3.76      1.50e-06  3.98      6.66e-06  3.98      
2.58e-07  3.77      9.40e-08  3.99      4.17e-07  4.00      
1.87e-08  3.78      5.91e-09  3.99      2.61e-08  4.00      

mean      3.76      mean      3.97      mean      3.98      
----------------------------------------------------------------------------------------------------
Dict{Symbol, Any} with 3 entries:
  :variables => ("rho", "rho_v1", "rho_e")
  :l2        => [4.07488, 4.0393, 3.99415]
  :linf      => [3.75561, 3.97319, 3.97885]

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Created with ❤️ by the Trixi.jl community.

@DanielDoehring DanielDoehring added the enhancement New feature or request label Aug 12, 2024
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codecov bot commented Aug 12, 2024

Codecov Report

Attention: Patch coverage is 97.45763% with 3 lines in your changes missing coverage. Please review.

Project coverage is 96.23%. Comparing base (e1aabb3) to head (4ac4970).
Report is 2 commits behind head on main.

Files Patch % Lines
src/callbacks_step/stepsize.jl 89.66% 3 Missing ⚠️
Additional details and impacted files
@@           Coverage Diff            @@
##             main    #2035    +/-   ##
========================================
  Coverage   96.23%   96.23%            
========================================
  Files         462      464     +2     
  Lines       37084    37184   +100     
========================================
+ Hits        35687    35784    +97     
- Misses       1397     1400     +3     
Flag Coverage Δ
unittests 96.23% <97.46%> (+<0.01%) ⬆️

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@DanielDoehring DanielDoehring marked this pull request as ready for review August 13, 2024 19:35
Comment on lines +158 to +160
# NOTE:
# For non-zero `cfl_diffusive`, `semi` is expected to be a `SemidiscretizationHyperbolicParabolic`.
if cfl_diffusive > 0.0
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This is a bit of a hack, as this would crash if someone supplies cfl_diffusive for a simulation without parabolic equations.

I first tried another if-clause if hasfield(semi, :equations_parabolic) which unfortunately gave errors in some particular cases.

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