A finite volume scheme for the two fluid plasma system

Summary form only given. We present our work on a numerical one-dimensional two fluid plasma solver. We take the collisionless, nonrelativistic system of equations consisting of ion continuity, ion momentum, ion energy, combined with electron continuity, electron momentum and electron energy, coupled with the full electrodynamic Maxwell´s equations. The algorithm is a first-order time, second-order space finite volume formulation of a Roe-type approximate Riemann solver and uses flux limiters for good shock resolution without spurious oscillations. We address the issue of stiffness introduced by the speed of light and the stiffness associated with the strong coupling of the source terms in the hyperbolic system. Both explicit and implicit schemes are developed and the advantages of the implicit scheme are discussed. It is shown how the algorithm may be extended to multiple dimensions. The algorithm is tested on various numerical and physical problems including electrostatic and electromagnetic two fluid plasma waves and shock problems comparing the two fluid results to the MHD results.