High Resolution and High Order Schemes for Two-Fluid Plasma Equation

Summary form only given. Two algorithms for the simulation of an ideal two-fluid plasma are presented. The two-fluid model is more general than the often used magnetohydrodynamic (MHD) model. The model takes into account electron inertia effects, charge separation and the full electromagnetic field equations and allows for electron and ion demagnetization. The algorithms used are the wave propagation method and the weighted essentially non oscillatory (WENO) method. The wave propagation method is based on solutions to the Riemann problem at cell interfaces. A semi-implicit method is used to incorporate the Lorentz and electromagnetic source terms. The WENO method is based on a high order (up to 13th order) reconstruction of solution variables at cell interfaces. The solution is then advanced using a 3rd order Runge-Kutta time stepping scheme. To preserve the divergence constraints on the electric and magnetic fields the so called perfectly-hyperbolic form of Maxwell´s equations are used which explicitly incorporate the divergence equations into the time stepping scheme. The algorithm is validated with the one dimensional MHD shock problem and a Z-pinch and theta-pinch equilibrium. It is shown that complex flows exhibiting turbulence and instabilities, not hitherto observed using MHD, can be simulated. A two dimensional shock problem is simulated which shows a Weibel instability leading to turbulence. Results of a magnetic reconnection problem and theta-pinch instabilities are presented