Numerical robustness of the convective flux implementation

[lsoucasse]

When comparing coupled time evolution simulation in PROTEUS between Spider and Aragog, we notice significant differences in the results. Especially, the melt fraction profile features a ‘bump’ showing solidification from above. See here the comparison work performed by @planetmariana.

We suspect this behaviour results from the implementation of the convective flux in Aragog that is more sensitive to numerical precision. It is indeed proportional to the difference between the temperature gradient and the adiabatic temperature gradient while it is directly proportional to the entropy gradient in Spider.

We could consider the following

• The adiabatic temperature gradient is evaluated from thermophysics properties. We could instead directly use a look up table for this quantity, resulting (hopefully?) in a smoother behaviour. We can also consider the correction suggested in Adiabatic temperature gradient #66.
• A smoothing is applied to all thermophysics quantities during phase evaluation: when you evaluate a property close to the liquidus or the solidus, it will combine the single phase property and the mixed phase property using a hyperbolic tangent weighing. On top of that, we can consider applying a spatial smoothing (spatial filter) to the convective flux to ensure a continuous profile and avoid oscillations.
• The eddy diffusivity is also a sensitive quantity as it features different scalings depending on the flow regime. We can consider applying the spatial smoothing on this quantity instead of (or in addition to) the convective flux.

Note that some other terms might benefit from spatial smoothing, especially the dilatation source term that features stiff/sharp behaviour, see here.

[timlichtenberg]

Thanks a lot Laurent, this is very useful! We will see how we can implement these issues in the upcoming time.
Point 2 from above is related to #3.