Solidification tests has poor tolerance choices

[GiudGiud]

Bug Description

The choice of 1e-2 for the relative tolerance on the nonlinear solver is leading every run of this input file to generate different results. By several percent in parallel!

Steps to Reproduce

Add basic postprocessing Run the input multiple times

Impact

I was debugging my physics all afternoon to try to match the results of the kernel-based formulation. Total waste of time, the kernel-based formulation does not have consistent results

[GiudGiud]

The 'as-is' input currently outputs >0.3 (it varies fluid fraction) after 180s trying to converge I now get this, so closer to 0.22. It takes me 400 time steps to get there though

+----------------+----------------+----------------+----------------+
| time           | ave_T          | ave_fl         | ave_p          |
+----------------+----------------+----------------+----------------+
:                :                :                :                :
|   1.814190e+02 |   3.031513e+02 |   2.149414e-01 |   4.056287e-13 |
|   1.817256e+02 |   3.031519e+02 |   2.150918e-01 |   4.941295e-13 |
|   1.820322e+02 |   3.031523e+02 |   2.152520e-01 |  -1.290637e-13 |
|   1.822622e+02 |   3.031529e+02 |   2.153878e-01 |   4.793794e-14 |
|   1.824922e+02 |   3.031536e+02 |   2.155225e-01 |   5.531301e-14 |
|   1.828372e+02 |   3.031551e+02 |   2.157504e-01 |  -9.181959e-13 |
|   1.833546e+02 |   3.031564e+02 |   2.160082e-01 |  -1.266053e-13 |
|   1.837427e+02 |   3.031570e+02 |   2.162083e-01 |  -1.180011e-13 |
|   1.841308e+02 |   3.031586e+02 |   2.164848e-01 |  -1.585640e-13 |
|   1.843249e+02 |   3.031592e+02 |   2.165837e-01 |   4.830669e-13 |
|   1.846160e+02 |   3.031601e+02 |   2.167610e-01 |  -4.732335e-13 |
|   1.847615e+02 |   3.031605e+02 |   2.168341e-01 |   2.003560e-13 |
|   1.849798e+02 |   3.031611e+02 |   2.169544e-01 |  -1.180011e-13 |
|   1.851981e+02 |   3.031618e+02 |   2.170782e-01 |   4.584834e-13 |
|   1.855255e+02 |   3.031625e+02 |   2.172440e-01 |   9.833424e-14 |
+----------------+----------------+----------------+----------------+