Numerical scheme for three-dimensional supersonic magnetohydrodynamical flows and implementation in a massively parallel multiprocessor environment

We have proposed an approach to exactly maintain the eight conservation laws and the divergence-free condition in numerical simulations for supersonic magnetohydrodynamical flows. In this paper, we extend our algorithm from the two-dimensional to the three-dimensional situation. The algorithm is second order accurate in space and time, and no Poisson solver is involved to maintain the divergence-free condition. The algorithm has been implemented in a massively parallel multiprocessor environment.