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.

[codecov]

Codecov Report

❌ Patch coverage is 65.85366% with 14 lines in your changes missing coverage. Please review.
✅ Project coverage is 48.59%. Comparing base (8220ead) to head (440d98f).

Files with missing lines	Patch %	Lines
src/evolve_pressure.cxx	45.00%	11 Missing ⚠️
src/evolve_momentum.cxx	0.00%	3 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #359      +/-   ##
==========================================
+ Coverage   48.54%   48.59%   +0.04%     
==========================================
  Files          96       96              
  Lines        9842     9836       -6     
  Branches     1435     1431       -4     
==========================================
+ Hits         4778     4780       +2     
+ Misses       4574     4566       -8     
  Partials      490      490              

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[mikekryjak]

@bendudson am I right in thinking that this PR will have no effect if no floor is crossed?

[bendudson]

Hey @mikekryjak ! I think that's right, though the softFloor function does change the input above the floor: It's an exponential decay so above 5 or 10 times the floor it will have negligible effect.

[totork]

Hi @bendudson
Maybe I am misunderstanding something, but isn't the 5/3 already included in basically e_plus_p? That was my understanding why it is not present in the parallel advection anymore.

[bendudson]

Thanks, @totork ! Yes I think you are right: e_plus_p is (5/3) * P so the leading factor should be removed