Modification of the MHD equations to reduce numerical instability in the simulation of slow plasma motions

Abstract

The stability of explicit finite difference numerical schemes for the solution of equations admitting wave solutions is always limited by a stability condition of the type $$\frac{{\Delta t}}{{\Delta x}}< \frac{{constant}}{v}$$ where δt and δx are the time- and space steps of the scheme, respectively, andv is the phase velocity of the wave. In certain cases we are interested in slow, non-ondulatory motions described by the equations, while the fast waves superposed on this motion play no essential role and do not influence the slow phenomenon at all, but make the numerical simulation of it quite impossible.