A Parallel Unsplit Staggered Mesh Algorithm for Magnetohydrodynamics

Abstract

The chapter discusses a parallel unsplit staggered mesh algorithm for magnetohydrodynamics. It describes the results of several test problems and discusses related performances for parallel computation. A dimensional splitting scheme has been used widely in most of multidimensional Godunov type finite-volume schemes because of its simplicity and relatively less expensive computational efforts for implementing multidimensional problems. The dimensional splitting scheme basically generalizes one-dimensional algorithms to higher dimensional cases by taking one-dimensional sweep in each direction. During each sweep, one generally introduces splitting errors because of the noncommutativity of the linearized Jacobian flux matrices in most of the nonlinear multidimensional problems. To avoid these unphysical errors in computation, it is desirable to use an unsplit approach. Compared to a dimensional splitting algorithm, an unsplit scheme usually requires more storage for cell face and cell edge values, and it limits the implementation of solving MHD problems.