Pressureless Euler-Poisson Equations
 

Hi, CFD People!

I'm solving 1D pressureless Euler-Poisson equations for the cold electron plasma, i.e. continuity equation, pressureless Euler equation with electrostatic force and Poisson equation for electrons and immobile ions.

Can you recommend me a numerical method for the treating the problem?

Also I have some more specific questions:

Question 1. Is it possible to implement the Riemann solver in the case of pressureless equations and, if yes, how ?

Question 2. Should I use the splitting procedure for the separate treating of homogeneous part of hydrodynamical equations and inhomogeneous part with Poisson equation?