Inverting speed with Godunov solver
 

Hi all,

I have written a simple Godunov upwind scheme and a HLLC solver to study an astrophysical problem. I tested it with the Sod test and it works smoothly.
Then, I change the initial conditions to the astrophysical ones of my interest and still works fine, until something happens. The problem has spherical symmetry and the gas initially moves with increasing radial distance from the star. As a consequence of gravity, the gas slows down and eventually inverts the motion. That is, the velocity is positive at the beginning and negative after some time. At the inverting point, the program crashes. I suppose that I failed to implement correctly the Godunov flux, writing it only in the positive velocity case. Could you give me a reference where I can find a clear description of this issue?

Thank you very much

Marco