(optionally) add T/e correction term to Strang Jacobians

[zingale]

this is the dT/dX |_e term that appears in all species
it is now controlled by integrator.correct_jacobian_for_const_e

[zingale]

closes #729

[zingale]

some Strang data using burn_cell. Build as:

make NETWORK_DIR=subch_simple

then run the old way:

./main3d.gnu.ex inputs_subch_simple integrator.jacobian=1 unit_test.nsteps=1 integrator.correct_jacobian_for_const_e=0

and it take 8084 steps.

Running with the new correction, integrator.correct_jacobian_for_const_e=1 and it takes

6788 steps

[zingale]

curiously, with aprox21, it goes the other way, and we are slower

[zingale]

for He-C-Fe-group, using the correction terms speeds things up by 4x

./main3d.gnu.ex inputs_subch_simple integrator.jacobian=1 unit_test.nsteps=1 integrator.correct_jacobian_for_const_e=1 unit_test.tmax=1.e-2

104499 without the corrections
24735 with the corrections

[zingale]

Here's some test_react runs:

• aprox13

  with new terms:

  Run time = 2.016436636
  min number of rhs calls: 6
  avg number of rhs calls: 96
  max number of rhs calls: 1171
  min number of steps: 3
  avg number of steps: 75
  max number of steps: 878
  

  without new terms:

  Run time = 2.397303023
  min number of rhs calls: 6
  avg number of rhs calls: 116
  max number of rhs calls: 3932
  min number of steps: 3
  avg number of steps: 94
  max number of steps: 3767
  

• subch_simple (using inputs_aprox13):

  with new terms:

  Run time = 101.0353978
  min number of rhs calls: 6
  avg number of rhs calls: 3962
  max number of rhs calls: 147079
  min number of steps: 3
  avg number of steps: 2219
  max number of steps: 79369
  

  without new terms:

  Run time = 100.0271792
  min number of rhs calls: 6
  avg number of rhs calls: 3975
  max number of rhs calls: 157375
  min number of steps: 3
  avg number of steps: 2284
  max number of steps: 86380
  

[zingale]

here's a Castro run with these changes:
http://groot.astro.sunysb.edu/Castro/test-suite/gfortran/2024-07-12-002/index.html

[zingale]

@BenWibking can you make sure that this works for you?

[BenWibking]

@BenWibking can you make sure that this works for you?

It works.

[zingale]

can you review it?

[BenWibking]

reviewing now

[BenWibking]

I think this is only mathematically valid for networks that use mass densities.

[BenWibking]

This may need to be disabled for number densities, since it assumes the species variables are mass fractions.

[zingale]

then I'm confused -- that means that this PR will do nothing for the number density case. Is that your intent?

[BenWibking]

I think it needs to be rederived for number densities. I can probably do that later this week if it can wait, or it can go in a separate PR.

[zingale]

let's do that in a separate PR. I'll wrap this in an if-test for now

[BenWibking]

It doesn't crash our network, and it still seems to get the right answer, so the correction must be small or zero in our network.