A Higher-Order Godunov Method for Multidimensional Ideal Magnetohydrodynamics

Abstract

The authors present a higher-order Godunov method for the solution of the two- and three-dimensional equations of ideal magnetohydrodynamics (MHD). This work is based both on a suitable operator-split approximation to the full multidimensional equations, and on a one-dimensional Riemann solver. This Riemann solver is sufficiently robust to handle the nonstrictly hyperbolic nature of the MHD equations and the presence of local linear degeneracies. Results from a set of test problems show that this operator-split methodology has no problems handling any of the three MHD waves, yet resolves shocks to three or four computational zones. The advantages and limitations of this method are discussed.