I am studying self-gravitating gas spheres in vacuum (not real stars as I am just using an ideal gas equation of state).

The classical CFL approach has some difficulties dealing with the gas-vacuum boundary mainly because approximated numerical solvers for this problem, like “vacuum Riemann solvers”, are not gravity aware and thus produce unphysical rarefaction waves in vacuum.

I am interested in the LBM as it seems easy to include self-gravitation in the Boltzmann equation.

So my question is, considering that the density drops in a very steep manner at the surface of the “star”, would the LBM method be able to handle this problem?

Thanks in advance.