Viscous CFL: `TreeMesh{1}` #2035

DanielDoehring · 2024-08-12T14:39:56Z

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]

github-actions · 2024-08-12T14:40:12Z

Review checklist

This checklist is meant to assist creators of PRs (to let them know what reviewers will typically look for) and reviewers (to guide them in a structured review process). Items do not need to be checked explicitly for a PR to be eligible for merging.

Purpose and scope

The PR has a single goal that is clear from the PR title and/or description.
All code changes represent a single set of modifications that logically belong together.
No more than 500 lines of code are changed or there is no obvious way to split the PR into multiple PRs.

Code quality

The code can be understood easily.
Newly introduced names for variables etc. are self-descriptive and consistent with existing naming conventions.
There are no redundancies that can be removed by simple modularization/refactoring.
There are no leftover debug statements or commented code sections.
The code adheres to our conventions and style guide, and to the Julia guidelines.

Documentation

New functions and types are documented with a docstring or top-level comment.
Relevant publications are referenced in docstrings (see example for formatting).
Inline comments are used to document longer or unusual code sections.
Comments describe intent ("why?") and not just functionality ("what?").
If the PR introduces a significant change or new feature, it is documented in NEWS.md with its PR number.

Testing

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New or modified lines of code are covered by tests.
New or modified tests run in less then 10 seconds.

Performance

There are no type instabilities or memory allocations in performance-critical parts.
If the PR intent is to improve performance, before/after time measurements are posted in the PR.

Verification

The correctness of the code was verified using appropriate tests.
If new equations/methods are added, a convergence test has been run and the results
are posted in the PR.

Created with ❤️ by the Trixi.jl community.

codecov · 2024-08-12T15:23:15Z

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 · 2024-08-14T06:53:36Z

src/callbacks_step/stepsize.jl

+    # NOTE: 
+    # For non-zero `cfl_diffusive`, `semi` is expected to be a `SemidiscretizationHyperbolicParabolic`.
+    if cfl_diffusive > 0.0


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.

DanielDoehring added 7 commits August 12, 2024 15:19

1st version viscous cfl

3e7cb8e

non-constant diffusivities

e8f6651

Comment

0ce6f12

tests

131b5ab

fmt

8b538fb

Comment

55b52b1

Bring back adv diff since this has const diff

5c00816

fmt

b67b7c6

DanielDoehring added the enhancement New feature or request label Aug 12, 2024

DanielDoehring added 9 commits August 13, 2024 09:12

test values for t = 0.4

4fb09f0

use only one stepsize method

dd78bc7

fmt

bd76a7e

else case

a677363

fmt

acdbd20

remove hasfield query

a3bd884

try kw

8a8e6d6

no kw

9bd9a70

cfl for coupled systems

4ac4970

DanielDoehring marked this pull request as ready for review August 13, 2024 19:35

DanielDoehring requested a review from andrewwinters5000 August 13, 2024 19:35

DanielDoehring commented Aug 14, 2024

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Viscous CFL: `TreeMesh{1}` #2035

Viscous CFL: `TreeMesh{1}` #2035

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DanielDoehring Aug 14, 2024

Viscous CFL: TreeMesh{1} #2035

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Viscous CFL: TreeMesh{1} #2035

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Viscous CFL: `TreeMesh{1}` #2035

Viscous CFL: `TreeMesh{1}` #2035

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