geodynamics · gassmoeller · Jul 25, 2025 · Jul 25, 2025
diff --git a/source/simulator/parameters.cc b/source/simulator/parameters.cc
@@ -1154,25 +1154,28 @@ namespace aspect
                            "This parameter corresponds "
                            "to the factor $\\alpha_E$ in the formulas following equation (15) of "
                            "the paper.) Units: None.");
-        prm.declare_entry ("beta", "0.052",
+        prm.declare_entry ("beta", "0.0",
                            Patterns::List(Patterns::Double (0.)),
-                           "The $\\beta$ factor in the artificial viscosity "
+                           "This parameter is deprecated and has been replaced by 'alpha_max' and is "
+                           "only kept for backward compatibility. If this parameter is set to a value "
+                           "different from 0 it will overwrite the usual maximum entropy viscosity "
+                           "stabilization constant of $\\alpha_{\\text{max}} d$, with $\\beta$."
+                           "Units: None.");
+        prm.declare_entry ("alpha max", "0.026",
+                           Patterns::List(Patterns::Double (0.)),
+                           "The $\\alpha_{\\text{max}}$ factor in the artificial viscosity "
                            "stabilization. This parameter controls the maximum dissipation of the "
                            "entropy viscosity, which is the part that only scales with the cell diameter "
                            "and the maximum velocity in the cell, but does not depend on the solution "
-                           "field itself or its residual. An appropriate value for 2d is 0.052 and "
-                           "0.078 for 3d. (For historical reasons, the name used here is different "
-                           "from the one used in the 2012 paper by Kronbichler, "
-                           "Heister and Bangerth that describes ASPECT, see \\cite{kronbichler:etal:2012}. "
+                           "field itself or its residual. An appropriate value is 0.026, which was "
+                           "experimentally determined in \\cite{kronbicher:etal:2012}."
                            "This parameter can be given as a single value or as a list with as "
                            "many entries as one plus the number of compositional fields. In the "
                            "former case all advection fields use the same stabilization parameters, "
                            "in the latter case each field (temperature first, then all compositions) "
                            "use individual parameters. This can be useful to reduce the stabilization "
                            "for the temperature, which already has some physical diffusion. "
-                           "This parameter corresponds "
-                           "to the factor $\\alpha_{\\text{max}}$ in the formulas following equation (15) of "
-                           "the paper.) Units: None.");
+                           "Units: None.");
         prm.declare_entry ("gamma", "0.0",
                            Patterns::Double (0.),
                            "The strain rate scaling factor in the artificial viscosity "
@@ -1931,9 +1934,19 @@ namespace aspect
         stabilization_c_R                   = Utilities::possibly_extend_from_1_to_N (Utilities::string_to_double(Utilities::split_string_list(prm.get("cR"))),
                                                                                       n_compositional_fields+1,
                                                                                       "cR");
-        stabilization_beta                  = Utilities::possibly_extend_from_1_to_N (Utilities::string_to_double(Utilities::split_string_list(prm.get("beta"))),
-                                                                                      n_compositional_fields+1,
-                                                                                      "beta");
+        stabilization_beta         = Utilities::possibly_extend_from_1_to_N (Utilities::string_to_double(Utilities::split_string_list(prm.get("alpha max"))),
+                                                                             n_compositional_fields+1,
+                                                                             "alpha max");
+
+        const std::vector<double> stabilization_constant_beta                  = Utilities::possibly_extend_from_1_to_N (Utilities::string_to_double(Utilities::split_string_list(prm.get("beta"))),
+                                                                                 n_compositional_fields+1,
+                                                                                 "beta");
+
+        for (unsigned int i=0; i<stabilization_beta.size(); ++i)
+          if (stabilization_constant_beta[i] != 0.0)
+            stabilization_beta[i] = stabilization_constant_beta[i];
+          else
+            stabilization_beta[i] *= dim;
 
         stabilization_gamma                 = prm.get_double ("gamma");
         discontinuous_penalty               = prm.get_double ("Discontinuous penalty");

diff --git a/tests/advection_reaction/screen-output b/tests/advection_reaction/screen-output
@@ -16,14 +16,14 @@ Number of degrees of freedom: 17,989 (8,450+1,089+4,225+4,225)
 
 *** Timestep 1:  t=1 seconds, dt=1 seconds
    Solving composition reactions... in 1 substep(s).
-   Solving temperature system... 22 iterations.
-   Solving C_1 system ... 22 iterations.
+   Solving temperature system... 13 iterations.
+   Solving C_1 system ... 13 iterations.
    Solving Stokes system (GMG)... 0+0 iterations.
 
    Postprocessing:
-     Compositions min/max/mass: -0.9974/0.9974/-3.301e-08
+     Compositions min/max/mass: -0.9962/0.9962/-3.206e-05
      Writing graphical output:  output-advection_reaction/solution/solution-00001
-     Errors                     time=1.000000e+00 ndofs= 17989 C_L2_current= 1.348377e-03 C_L2_max= 1.348377e-03 T_L2_current= 1.348377e-03 T_L2_max= 1.348377e-03
+     Errors                     time=1.000000e+00 ndofs= 17989 C_L2_current= 2.078899e-03 C_L2_max= 2.078899e-03 T_L2_current= 2.078899e-03 T_L2_max= 2.078899e-03
 
 Termination requested by criterion: end time
 

diff --git a/tests/ascii_data_boundary_composition_3d_box/screen-output b/tests/ascii_data_boundary_composition_3d_box/screen-output
@@ -37,7 +37,7 @@ Number of degrees of freedom: 652 (375+27+125+125)
      RMS, max velocity:                  1 m/year, 1 m/year
      Temperature min/avg/max:            0 K, 1369 K, 1920 K
      Heat fluxes through boundary parts: -7.468e+13 W, 7.442e+13 W, 0 W, 0 W, 1.18e+11 W, -4.623e+10 W
-     Compositions min/max/mass:          -0.04592/1/6.606e+16
+     Compositions min/max/mass:          -0.05244/1/6.723e+16
 
 Termination requested by criterion: end time
 

diff --git a/tests/ascii_data_boundary_composition_3d_box/statistics b/tests/ascii_data_boundary_composition_3d_box/statistics
@@ -25,4 +25,4 @@
 # 25: Maximal value for composition C_1
 # 26: Global mass for composition C_1
 0 0.000000000000e+00 0.000000000000e+00 8 402 125 125 0 10 13 14 14 1.00002477e+00 1.00284019e+00 0.00000000e+00 1.36916667e+03 1.91300000e+03 -7.45161591e+13 7.45161591e+13 0.00000000e+00 0.00000000e+00 1.41357410e+11 -9.49349646e+10 -3.30009387e-16 1.00000000e+00 6.18915000e+16 
-1 1.000000000000e+04 1.000000000000e+04 8 402 125 125 9  8 12 13 13 1.00002476e+00 1.00251269e+00 0.00000000e+00 1.36923327e+03 1.91969963e+03 -7.46760976e+13 7.44218584e+13 0.00000000e+00 0.00000000e+00 1.18017003e+11 -4.62250808e+10 -4.59158525e-02 1.00000000e+00 6.60580322e+16 
+1 1.000000000000e+04 1.000000000000e+04 8 402 125 125 9  8 12 13 13 1.00002476e+00 1.00251269e+00 0.00000000e+00 1.36923327e+03 1.91969963e+03 -7.46760976e+13 7.44218584e+13 0.00000000e+00 0.00000000e+00 1.18017003e+11 -4.62250808e+10 -5.24396545e-02 1.00000000e+00 6.72326380e+16 
diff --git a/tests/ascii_data_boundary_temperature_3d_box/screen-output b/tests/ascii_data_boundary_temperature_3d_box/screen-output
@@ -30,67 +30,67 @@ Number of degrees of freedom: 527 (375+27+125)
      Heat fluxes through boundary parts: -2.669e+12 W, 2.667e+12 W, -5.387e+08 W, -5.387e+08 W, -4.371e+08 W, -6.403e+08 W
 
 *** Timestep 1:  t=164901 years, dt=164901 years
-   Solving temperature system... 10 iterations.
+   Solving temperature system... 9 iterations.
    Solving Stokes system (GMG)... 11+0 iterations.
 
    Postprocessing:
      RMS, max velocity:                  1 m/year, 1 m/year
-     Temperature min/avg/max:            -12.24 K, 40.92 K, 100 K
-     Heat fluxes through boundary parts: -4.002e+12 W, 1.926e+12 W, -3.131e+11 W, -3.131e+11 W, -3.132e+11 W, -3.131e+11 W
+     Temperature min/avg/max:            -1.435 K, 43.67 K, 100 K
+     Heat fluxes through boundary parts: -4.26e+12 W, 1.89e+12 W, -3.971e+11 W, -3.971e+11 W, -3.972e+11 W, -3.97e+11 W
 
-*** Timestep 2:  t=329583 years, dt=164681 years
-   Solving temperature system... 9 iterations.
+*** Timestep 2:  t=329626 years, dt=164725 years
+   Solving temperature system... 8 iterations.
    Solving Stokes system (GMG)... 11+0 iterations.
 
    Postprocessing:
      RMS, max velocity:                  1 m/year, 1 m/year
-     Temperature min/avg/max:            0 K, 52.89 K, 100 K
-     Heat fluxes through boundary parts: -4.075e+12 W, 2.09e+12 W, -1.175e+11 W, -1.175e+11 W, -1.175e+11 W, -1.174e+11 W
+     Temperature min/avg/max:            0 K, 56.26 K, 100 K
+     Heat fluxes through boundary parts: -4.258e+12 W, 2.296e+12 W, -9.827e+10 W, -9.827e+10 W, -9.845e+10 W, -9.809e+10 W
 
-*** Timestep 3:  t=494191 years, dt=164608 years
-   Solving temperature system... 9 iterations.
+*** Timestep 3:  t=494302 years, dt=164676 years
+   Solving temperature system... 8 iterations.
    Solving Stokes system (GMG)... 11+0 iterations.
 
    Postprocessing:
      RMS, max velocity:                  1 m/year, 1 m/year
-     Temperature min/avg/max:            0 K, 61.34 K, 100.3 K
-     Heat fluxes through boundary parts: -4.115e+12 W, 2.565e+12 W, 3.468e+09 W, 3.468e+09 W, 3.109e+09 W, 3.826e+09 W
+     Temperature min/avg/max:            0 K, 63.96 K, 100 K
+     Heat fluxes through boundary parts: -4.268e+12 W, 2.829e+12 W, 5.886e+10 W, 5.886e+10 W, 5.846e+10 W, 5.927e+10 W
 
-*** Timestep 4:  t=658889 years, dt=164698 years
+*** Timestep 4:  t=659057 years, dt=164755 years
    Solving temperature system... 8 iterations.
    Solving Stokes system (GMG)... 10+0 iterations.
 
    Postprocessing:
      RMS, max velocity:                  1 m/year, 1 m/year
-     Temperature min/avg/max:            0 K, 66.38 K, 108.4 K
-     Heat fluxes through boundary parts: -4.156e+12 W, 3.118e+12 W, 6.907e+10 W, 6.907e+10 W, 6.867e+10 W, 6.947e+10 W
+     Temperature min/avg/max:            0 K, 67.85 K, 100 K
+     Heat fluxes through boundary parts: -4.281e+12 W, 3.302e+12 W, 1.311e+11 W, 1.311e+11 W, 1.307e+11 W, 1.315e+11 W
 
-*** Timestep 5:  t=823709 years, dt=164820 years
-   Solving temperature system... 9 iterations.
+*** Timestep 5:  t=823905 years, dt=164848 years
+   Solving temperature system... 8 iterations.
    Solving Stokes system (GMG)... 10+0 iterations.
 
    Postprocessing:
      RMS, max velocity:                  1 m/year, 1 m/year
-     Temperature min/avg/max:            0 K, 68.83 K, 105.6 K
-     Heat fluxes through boundary parts: -4.197e+12 W, 3.534e+12 W, 9.896e+10 W, 9.896e+10 W, 9.871e+10 W, 9.92e+10 W
+     Temperature min/avg/max:            0 K, 69.34 K, 100 K
+     Heat fluxes through boundary parts: -4.291e+12 W, 3.593e+12 W, 1.574e+11 W, 1.574e+11 W, 1.572e+11 W, 1.576e+11 W
 
-*** Timestep 6:  t=988611 years, dt=164902 years
+*** Timestep 6:  t=988810 years, dt=164905 years
    Solving temperature system... 8 iterations.
    Solving Stokes system (GMG)... 10+0 iterations.
 
    Postprocessing:
      RMS, max velocity:                  1 m/year, 1 m/year
-     Temperature min/avg/max:            0 K, 69.76 K, 100.8 K
-     Heat fluxes through boundary parts: -4.226e+12 W, 3.752e+12 W, 1.095e+11 W, 1.095e+11 W, 1.094e+11 W, 1.096e+11 W
+     Temperature min/avg/max:            0 K, 69.65 K, 100 K
+     Heat fluxes through boundary parts: -4.295e+12 W, 3.712e+12 W, 1.623e+11 W, 1.623e+11 W, 1.622e+11 W, 1.623e+11 W
 
-*** Timestep 7:  t=1e+06 years, dt=11389.3 years
+*** Timestep 7:  t=1e+06 years, dt=11189.6 years
    Solving temperature system... 6 iterations.
-   Solving Stokes system (GMG)... 7+0 iterations.
+   Solving Stokes system (GMG)... 6+0 iterations.
 
    Postprocessing:
      RMS, max velocity:                  1 m/year, 1 m/year
-     Temperature min/avg/max:            0 K, 69.77 K, 100.5 K
-     Heat fluxes through boundary parts: -4.227e+12 W, 3.76e+12 W, 1.096e+11 W, 1.096e+11 W, 1.095e+11 W, 1.096e+11 W
+     Temperature min/avg/max:            0 K, 69.63 K, 100 K
+     Heat fluxes through boundary parts: -4.295e+12 W, 3.714e+12 W, 1.619e+11 W, 1.619e+11 W, 1.619e+11 W, 1.62e+11 W
 
 Termination requested by criterion: end time
 

diff --git a/tests/ascii_data_boundary_temperature_3d_box/statistics b/tests/ascii_data_boundary_temperature_3d_box/statistics
@@ -19,11 +19,11 @@
 # 19: Outward heat flux through boundary with indicator 3 ("back") (W)
 # 20: Outward heat flux through boundary with indicator 4 ("bottom") (W)
 # 21: Outward heat flux through boundary with indicator 5 ("top") (W)
-0 0.000000000000e+00 0.000000000000e+00 8 402 125  8  9 10 10 1.00000029e+00 1.00038980e+00 -1.50961805e-14 2.63888889e+01 1.00000000e+02 -2.66852239e+12 2.66686247e+12 -5.38714000e+08 -5.38714000e+08 -4.37148083e+08 -6.40279917e+08 
-1 1.649013081817e+05 1.649013081817e+05 8 402 125 10 11 12 12 1.00000078e+00 1.00157236e+00 -1.22385465e+01 4.09150275e+01 1.00000000e+02 -4.00172867e+12 1.92626209e+12 -3.13133616e+11 -3.13133616e+11 -3.13174249e+11 -3.13092967e+11 
-2 3.295826360698e+05 1.646813278881e+05 8 402 125  9 11 12 12 1.00000106e+00 1.00190513e+00  0.00000000e+00 5.28872944e+01 1.00000000e+02 -4.07512505e+12 2.08979330e+12 -1.17454786e+11 -1.17454786e+11 -1.17535597e+11 -1.17374243e+11 
-3 4.941907342554e+05 1.646080981856e+05 8 402 125  9 11 12 12 1.00000067e+00 1.00147886e+00  0.00000000e+00 6.13403471e+01 1.00317788e+02 -4.11482980e+12 2.56465471e+12  3.46763583e+09  3.46763583e+09  3.10875868e+09  3.82598345e+09 
-4 6.588885837223e+05 1.646978494668e+05 8 402 125  8 10 11 11 1.00000028e+00 1.00093295e+00  0.00000000e+00 6.63768859e+01 1.08389470e+02 -4.15629358e+12 3.11757654e+12  6.90673395e+10  6.90673395e+10  6.86668828e+10  6.94667849e+10 
-5 8.237085032306e+05 1.648199195084e+05 8 402 125  9 10 11 11 1.00000013e+00 1.00051757e+00  0.00000000e+00 6.88333135e+01 1.05627670e+02 -4.19684449e+12 3.53436810e+12  9.89552408e+10  9.89552408e+10  9.87086981e+10  9.92010451e+10 
-6 9.886107186708e+05 1.649022154402e+05 8 402 125  8 10 11 11 1.00000009e+00 1.00032577e+00  0.00000000e+00 6.97569743e+01 1.00823145e+02 -4.22577187e+12 3.75194316e+12  1.09500068e+11  1.09500068e+11  1.09405969e+11  1.09593940e+11 
-7 1.000000000000e+06 1.138928132919e+04 8 402 125  6  7  8  8 1.00000009e+00 1.00032074e+00  0.00000000e+00 6.97691752e+01 1.00455173e+02 -4.22726285e+12 3.75960046e+12  1.09567590e+11  1.09567590e+11  1.09503545e+11  1.09631434e+11 
+0 0.000000000000e+00 0.000000000000e+00 8 402 125 8  9 10 10 1.00000029e+00 1.00038980e+00 -1.50961805e-14 2.63888889e+01 1.00000000e+02 -2.66852239e+12 2.66686247e+12 -5.38714000e+08 -5.38714000e+08 -4.37148083e+08 -6.40279917e+08 
+1 1.649013081817e+05 1.649013081817e+05 8 402 125 9 11 12 12 1.00000061e+00 1.00143047e+00 -1.43524035e+00 4.36652596e+01 1.00000000e+02 -4.25953562e+12 1.88962449e+12 -3.97115027e+11 -3.97115027e+11 -3.97186561e+11 -3.97043495e+11 
+2 3.296264961035e+05 1.647251879218e+05 8 402 125 8 11 12 12 1.00000073e+00 1.00157546e+00  0.00000000e+00 5.62642270e+01 1.00000000e+02 -4.25765014e+12 2.29613590e+12 -9.82689854e+10 -9.82689854e+10 -9.84497950e+10 -9.80882871e+10 
+3 4.943022574520e+05 1.646757613486e+05 8 402 125 8 11 12 12 1.00000043e+00 1.00119026e+00  0.00000000e+00 6.39598928e+01 1.00000000e+02 -4.26769186e+12 2.82924391e+12  5.88628592e+10  5.88628592e+10  5.84573904e+10  5.92681557e+10 
+4 6.590572061668e+05 1.647549487148e+05 8 402 125 8 10 11 11 1.00000020e+00 1.00073802e+00  0.00000000e+00 6.78483422e+01 1.00000000e+02 -4.28091234e+12 3.30211469e+12  1.31108449e+11  1.31108449e+11  1.30744964e+11  1.31471562e+11 
+5 8.239052221059e+05 1.648480159391e+05 8 402 125 8 10 11 11 1.00000012e+00 1.00046010e+00  0.00000000e+00 6.93435974e+01 1.00000000e+02 -4.29052547e+12 3.59294773e+12  1.57368940e+11  1.57368940e+11  1.57180569e+11  1.57557081e+11 
+6 9.888104436698e+05 1.649052215639e+05 8 402 125 8 10 11 11 1.00000009e+00 1.00035683e+00  0.00000000e+00 6.96504933e+01 1.00000000e+02 -4.29501577e+12 3.71168587e+12  1.62289815e+11  1.62289815e+11  1.62229997e+11  1.62349601e+11 
+7 1.000000000000e+06 1.118955633016e+04 8 402 125 6  6  7  7 1.00000009e+00 1.00035594e+00  0.00000000e+00 6.96332410e+01 1.00000000e+02 -4.29511889e+12 3.71377111e+12  1.61925319e+11  1.61925319e+11  1.61891918e+11  1.61958692e+11 
diff --git a/tests/ascii_data_boundary_velocity_3d_shell/screen-output b/tests/ascii_data_boundary_velocity_3d_shell/screen-output
@@ -33,7 +33,7 @@ Number of degrees of freedom: 1,277 (915+57+305)
    Postprocessing:
      RMS, max velocity:                  3.75 m/year, 12.4 m/year
      Temperature min/avg/max:            273 K, 1487 K, 3000 K
-     Heat fluxes through boundary parts: -6.403e+15 W, 2.326e+16 W, -1.125e+16 W, 1.134e+16 W, 0.07825 W
+     Heat fluxes through boundary parts: -9.583e+15 W, 3.482e+16 W, -1.124e+16 W, 1.134e+16 W, 0.0782 W
 
 Termination requested by criterion: end time
 

diff --git a/tests/ascii_data_boundary_velocity_3d_shell/statistics b/tests/ascii_data_boundary_velocity_3d_shell/statistics
@@ -20,4 +20,4 @@
 # 20: Outward heat flux through boundary with indicator 3 ("west") (W)
 # 21: Outward heat flux through boundary with indicator 4 ("south") (W)
 0 0.000000000000e+00 0.000000000000e+00 24 972 305 0 51 52 52 3.75481711e+00 1.24071278e+01 2.73000000e+02 1.48854480e+03 3.00000000e+03 4.45744333e-01 -3.64068403e+13 -6.38515043e+13 -1.12506468e+16 1.13429758e+16 7.83775571e-02 
-1 1.000000000000e+03 1.000000000000e+03 24 972 305 9 16 17 17 3.75481850e+00 1.24071278e+01 2.73000000e+02 1.48732708e+03 3.00000000e+03 4.45297791e-01 -6.40310574e+15  2.32603003e+16 -1.12459563e+16 1.13382299e+16 7.82540264e-02 
+1 1.000000000000e+03 1.000000000000e+03 24 972 305 9 16 17 17 3.75482092e+00 1.24071278e+01 2.73000000e+02 1.48673852e+03 3.00000000e+03 4.45081966e-01 -9.58308618e+15  3.48201132e+16 -1.12436392e+16 1.13358104e+16 7.81951788e-02 
diff --git a/tests/ascii_data_boundary_velocity_3d_shell_spherical/screen-output b/tests/ascii_data_boundary_velocity_3d_shell_spherical/screen-output
@@ -28,12 +28,12 @@ Number of degrees of freedom: 1,277 (915+57+305)
 
 *** Timestep 1:  t=1000 years, dt=1000 years
    Solving temperature system... 9 iterations.
-   Solving Stokes system (GMG)... 15+0 iterations.
+   Solving Stokes system (GMG)... 16+0 iterations.
 
    Postprocessing:
      RMS, max velocity:                  3.44 m/year, 12.4 m/year
-     Temperature min/avg/max:            273 K, 1488 K, 3000 K
-     Heat fluxes through boundary parts: -4.882e+15 W, 1.754e+16 W, -1.125e+16 W, 1.134e+16 W, 0.0716 W
+     Temperature min/avg/max:            273 K, 1487 K, 3000 K
+     Heat fluxes through boundary parts: -7.306e+15 W, 2.627e+16 W, -1.124e+16 W, 1.134e+16 W, 0.07154 W
 
 Termination requested by criterion: end time
 

diff --git a/tests/ascii_data_boundary_velocity_3d_shell_spherical/statistics b/tests/ascii_data_boundary_velocity_3d_shell_spherical/statistics
@@ -20,4 +20,4 @@
 # 20: Outward heat flux through boundary with indicator 3 ("west") (W)
 # 21: Outward heat flux through boundary with indicator 4 ("south") (W)
 0 0.000000000000e+00 0.000000000000e+00 24 972 305 0 51 52 52 3.43969200e+00 1.23592847e+01 2.73000000e+02 1.48854480e+03 3.00000000e+03 4.45744333e-01 -3.21993345e+13 -7.17165646e+13 -1.12506522e+16 1.13429758e+16 7.16989457e-02 
-1 1.000000000000e+03 1.000000000000e+03 24 972 305 9 15 16 16 3.43974062e+00 1.23592847e+01 2.73000000e+02 1.48762300e+03 3.00000000e+03 4.45406308e-01 -4.88190885e+15  1.75409333e+16 -1.12468187e+16 1.13391502e+16 7.15952510e-02 
+1 1.000000000000e+03 1.000000000000e+03 24 972 305 9 16 17 17 3.43974266e+00 1.23592847e+01 2.73000000e+02 1.48717990e+03 3.00000000e+03 4.45243822e-01 -7.30639113e+15  2.62745075e+16 -1.12449365e+16 1.13371804e+16 7.15435797e-02 
diff --git a/tests/ascii_data_boundary_velocity_3d_sphere/screen-output b/tests/ascii_data_boundary_velocity_3d_sphere/screen-output
@@ -20,8 +20,8 @@ Number of degrees of freedom: 2,147 (1,551+79+517)
 
    Postprocessing:
      RMS, max velocity:                  4.93 m/year, 27.3 m/year
-     Temperature min/avg/max:            -1.117 K, 54.94 K, 273 K
-     Heat fluxes through boundary parts: -6.12e+15 W
+     Temperature min/avg/max:            -1.595 K, 54.96 K, 273 K
+     Heat fluxes through boundary parts: -8.953e+15 W
 
 Termination requested by criterion: end time