Fluid equation of state with density floor

[bendudson]

A relatively simple fix that seems to greatly help reduce unphysical behavior near density floors.

Defines the internal energy E as E = Cv * Nlim * T rather than the usual Cv * N * T. This effectively puts a floor on the heat capacity of the fluid. Then solve the pressure equation consistent with this equation of state.

Changes made to pressure equations in evolve_pressure, neutral_mixed and neutral_full_velocity. Unfortunately I ran clang-format on the files so the changes seem numerous. The actual change is quite small: In the pressure advection replace (5/3)P with Nlim * T + (2/3) * P.

This is an example from the midplane of a DIII-D simulation using neutral_full_velocity. The density floor is 1e-5, and previously produced quite unphysical behavior.

[mikekryjak]

@bendudson this is awesome. Looking at evolve_pressure only for now: am I understanding correctly that this in effect makes the density floor in use everywhere consistently, whereas before it was only used where we divided by zero? And P_solver is the pressure without floors that the solver sees, while P is the pressure calculated using floored density?

What about flooring pressure itself? I see that now it's only flooring the density.

I raised an issue to put clang-format in the CI: #360

[bendudson]

Hey @mikekryjak . Thanks! The solver now evolves a modified internal energy P_solver = N_lim T, which is divided by N_lim to get temperature, and then the pressure is P = N T. This is why neutral pressure can continue to fall into the core, even when temperature is increasing and the density has hit the floor: the internal energy P_solver is going up into the core, while pressure P is going down.