try QSS for primordial chem

[BenWibking]

We can try this integrator: https://github.com/AMReX-Astro/Microphysics/tree/main/integration/QSS

[BenWibking]

I think Rosenbrock is the right choice for now.

[BenWibking]

For QSS to work correctly, the generator needs to emit more than the net RHS:

ydot(i) = production_i - destruction_i

It needs to expose the split:

f_plus(i) = sum of all positive contributions to species i
f_minus(i) = sum of all negative contributions to species i
dedt_plus = positive energy contribution
dedt_minus = negative energy contribution

The QSS integrator then forms:

dX_i/dt = f_plus(i) - f_minus(i)
k_i = f_minus(i) / X_i

and uses k_i in the semi-implicit denominator. Without a real f_minus, QSS cannot identify stiff depletion.

We need the code generator to separately compute production and destruction terms for the QSS integrator to work:

  AMREX_GPU_HOST_DEVICE AMREX_INLINE
  void actual_rhs_split(
      const burn_t& state,
      amrex::Array1D<amrex::Real, 1, NumSpec>& f_plus,
      amrex::Array1D<amrex::Real, 1, NumSpec>& f_minus,
      amrex::Real& dedt_plus,
      amrex::Real& dedt_minus);

[BenWibking]

@psharda Can your code do this?