SPIDER fails to find a solution for permanently-molten cases

[nichollsh]

I have already been investigating this, but will make an issue here in case this continues to be a problem or re-emerges after being 'fixed'.

In some cases, SPIDER will fail to obtain a solution. Either of the two errors are possible in this case:

• [CVODE ERROR] CVode At t = 4.95363e+07 and h = 0.000184003, the error test failed repeatedly or with |h| = hmin
• PETSC ERROR: Nonlinear solver didn't converge: DIVERGED_FNORM_NAN

These occur under the following conditions:

• When the flux boundary condition provided to SPIDER (from F_atm) is small (i.e. less than ~5 W m-2)
• When the time-step is too large.

Therefore, this issue most often occurs in the case of Type II planets, where the planet should stay molten and the net outgoing flux rapidly tends to zero within ~100 kyr. One way to mitigate this is to include a "steady-state break condition", which I've already done in a development branch. However, the model still fails in some cases.

This is still being investigated, but I expect that it should be resolved soon.

[nichollsh]

Some example plots taken from two cases, just to demonstrate this. The x-axes here are both Time, but I've not included the numbers because these are not from the same simulation setups.

What we want:

What we get:

[nichollsh]

This has been resolved, and the fix will be merged into master in the next PR. The solution is to introduce a form of 'step rejection', where the model can handle cases where SPIDER fails to find a solution. If this happens, the model will re-attempt the SPIDER step but with adjusted step sizes and tolerances. This can be done up to 7 times before giving up entirely. This approach has resolved the issue in all cases that have been tested.