A staggered grid, Lagrangian-Eulerian remap code for 3-D MHD simulations

In this paper an approach to multidimensional magnetohydrodynamics (MI-ID) which correctly handles shocks but does not use an approximate Riemann solv er is proposed. This approach is simple and is based on control volume aver aging with a staggered grid. The method builds on the older and often overl ooked technique of on each step taking a fully 3-D Lagrangian step and then conservatively remapping onto the original grid. At the remap step gradien t limiters are applied so that the scheme is monotonicity-preserving. For E uler's equations this technique, combined with an appropriately staggered g rid and Wilkins artificial viscosity, can give results comparable to those from approximate Riemann solvers. We show how this can be extended to inclu de a magnetic field, maintaining the divergence-free condition and pressure positivity and then present numerical test results. Where possible a compa rison with other shock capturing techniques is presented and the advantages and disadvantages of the proposed scheme are clearly explained. (C) 2001 A cademic Press.