A Comparative Study of Some Spatial-Temporal Discretization Schemes for Nonlinear Magnetohydrodynamic Simulation of Plasmas

摘要

Three widely used discretization schemes for the numerical solution of a hyperbolic system of equations are applied to are presentative nonlinear problem arising in the MHD simulation of plasmas. Two schemes based on simultaneous discretization of space and time Lax-Wendroff-Ritchmyer scheme and the MacCormack scheme. One scheme centered-space differencing to convert the original system of PDEs to a larger system of ODEs which are then integrated in time by the fourth order Runge-Kutta method. The linear stability conditions are necessary but not sufficient to guarantee the numerical stability of these algorithms when applied to a nonlinear hyperbolic problem.