A parallel solution-adaptive scheme for ideal magnetohydrodynamics

Abstract

A parallel adaptive mesh refinement (AMR) scheme is described for solving the hyperbolic system of partial-differential equations governing ideal magnetohydrodynamic (MHD) flows in three space dimensions. This highly parallelized algorithm adopts a cell-centered upwind finite-volume discretization procedure and uses limited solution reconstruction, approximate Riemann solvers, and explicit multistage time stepping to solve the MHD equations in divergence form, providing a combination of high solution accuracy and computational robustness across a large range in the plasma P (/3 is the ratio of thermal and magnetic pressures). A flexible block-based hierarchical data structure is used to facilitate automatic solution adaption on Cartesian mesh using physics-based refinement criteria. In addition, the data structure naturally lends itself to domain decomposition, thereby enabling efficient and scalable implementations of the method on MIMD (multiple-instruction multipledata) distributed-memory multi-processor architectures. The model has been developed on several massively parallel computer platforms and high parallel performance has been achieved (342 GFlops has been attained on a 1,490-processor Cray T3E 1200 with near-perfect scalability). Numerical results for MHD simulations of magnetospheric and heliospheric plasma flows are described to demonstrate the validity and capabilities of the approach for space physics applications. *Assistant Research Scientist, Atmospheric, Oceanic and Space Sciences, Senior Member AIAA t Assistant Research Scientist, Atmospheric, Oceanic and Space Sciences, Member AIAA XAssociate Professor, Aerospace Engineering, Senior Member AIAA §Professor, Atmospheric, Oceanic and Space Sciences ‘Professor, Electrical Engineering and Computer Science Copyright @I999 by the American Institute of Aeronautics and .4stronautics, Inc. All rights reserved.