This project studies robust and efficient methods for the numerical solution of ideal and resistive magnetohydrodynamics (MHD), with applications to a variety of space physics applications. This will allow users to routinely perform simulations of such phenomena as cometary x-ray emission, the Earth's magnetosphere, and coronal mass ejections on current and future generations of massively parallel computer architectures. These MHD simulations are performed by block-based hierarchical adaptive mesh refinement (AMR) techniques for which the investigators have developed a highly efficient parallel implementation. Future applications to resistive MHD, however, require a more sophisticated time integration procedure to effectively deal with the large disparities of time scale associated with convection, magnetosonic and Alfven waves, and thermal transport. The researchers will investigate parallel implementations of both implicit Newton-Krylov-Schwarz (NKS) and full approximate storage (FAS) multigrid strategies in this context. In summary, the combination of robust finite-volume discretization of the governing equations, block-based AMR, domain decomposition, and parallel implementation of implicit NKS and/or multigrid strategies should yield an efficient, reliable, and powerful numerical method for large-scale simulation of MHD flows on high-performance parallel machines. Moreover, the resulting method should represent a significant improvement over the current generation of space plasma simulation tools and permit the study of a wider class of problems.
