Update on Poisson solver/operator splitting

The code runs and takes the 1st time step (hydro+source step), after which it chokes during the next hydro step. I checked the initial data for scaling (see ​https://astrobear.pas.rochester.edu/trac/astrobear/wiki/u/erica/TestingOpSplitting - note at this small of a perturbation (delta = 1e-6), the pressure is a constant because of rounding error), and output from poisson solver during that first step. Here is the poisson output-

phi -

discrete 2nd derivative of phi -

forcing function -

The convergence requirement, (max(abs(u(n+1)-u(n))) < 10e-5, is reached, although the convergence between the actual solution and the numerical solution seems spotty in areas (as seen when comparing the discrete 2nd derivative to the forcing function),

The code goes through the first time step and produces this behavior,

density -

velocity -

pressure -

It seems to be qualitatively correct in density and velocity. Gamma = 1.4, and so am not immediately sure if the pressure behavior is as expected..

Potential bugs are,

  1. gamma=1.001 (for which my formulas for jeans mode are derived) diverges before can complete the first time step, but using gamma=1.4 gets through the first step
  2. not sure on u in energy source term update formula (see wiki page on that - ​https://astrobear.pas.rochester.edu/trac/astrobear/wiki/u/erica/PoissonPlusHydro)
  3. Scaling, either in the code or scaling the constants such as scalegrav (also here- ​https://astrobear.pas.rochester.edu/trac/astrobear/wiki/u/erica/TestingOpSplitting)
  1. making some modifications to the routine where I am getting divergence, such as increasing the number of iterations, or how it is calculating an initial guess at pstar
  1. The convergence of poisson solver is not good enough

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