MHD-A: A fluctuation splitting wave model for planar magnetohydrodynamics

This paper describes a two-dimensional (2D) upwind residual distribution or fluctuation splitting (FS) scheme (MHD-A) for the numerical solutions of p lanar magnetohydrodynamics (MHD) equations on structured or unstructured tr iangular meshes. The scheme is second order in space and time, and utilizes a consistent 2D wave model originating from the eigensystem of a 2D jacobi an matrix of the MHD flux vector. The possible waves existing in this wave model are entropy, magnetoacoustic, and (numerical) magnetic monopole waves ; however, Alfven waves do not exist since the problem is planar. One of the important features of the method is that the mesh structure has no influence on propagation directions of the waves. These directions are d ependent only on flow properties and field gradients (for example, it is sh own that the magnetoacoustic waves propagate in the directions of maximum a nd minimum magnetic strain rates). The other feature is that no flux evalua tions and no information from the neighboring cells are needed to obtain a second order, positive, and linearity preserving scheme. A variety of numerical tests carried out by the model on structured and uns tructured triangular meshes show that MHD-A produces rather encouraging num erical results even though it is the first FS wave model ever developed for multidimensional MHD. (C) 1999 Academic Press.