Adaptive Mesh Refinement MHD for Global Simulations

Techniques that have become common in aerodynamics codes have recently begun to be implemented in space-physic codes, which solve the governing equations for a compressible plasma. These techniques include high-resolution upwind schemes, block-based solution-adaptive grids and domain decomposition for parallelization. While some of these techniques carry over relatively straightforwardly from aerodynamics to space physics, space physics simulations pose some new challenges. This paper gives a brief review of the state-of-the-art in modern space-physics codes, including a validation study of several of the techniques in common use. A remaining challenge is that of flows that include regions in which relativistic effects are important; some background and preliminary results for these problems are given. 1 Governing Equations The governing equations for an ideal, non-relativistic, compressible plasma may be written in a number of different forms. In primitive variables, the governing equations, which represent a combination of the Euler equations of gasdynamics and the Maxwell equations of electromagnetics, may be written as: