(c)2001 American Institute of Aeronautics & Astronautics or Published with 15th AIAA Computational Fluid Dynamics Conference 11-14 June 2001 Anaheim, CA Permission of Author(s) and/or Author(s) 1 Sponsoring Organization. A01-31041 AIAA-2001-2525 DEVELOPMENT AND VALIDATION OF SOLUTION-ADAPTIVE, PARALLEL SCHEMES FOR COMPRESSIBLE PLASMAS K. G. Poweli: G. Tothf D. L. De ZeeuwJ P. L. Roe§ T. L GombosiWl Q. F. Stout 11 University of Michigan, Ann Arbor, Michigan 48109, U.S.A. Abstract 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 com- pressible plasma. These techniques include high-resolution upwind schemes, block-based solution-adaptive grids and domain decompo- sition for parallelization. While some of these techniques carry over relatively straightfor- wardly from aerodynamics to space physics, space physics simulations pose some new chal- lenges. 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 remain- ing challenge is that of flows that include re- gions in which relativistic effects are impor- tant; some background and preliminary re- * Professor, Aerospace Engineering, AIAA Senior Member ^Visiting Research Scientist II, Atmospheric, Oceanic and Space Sciences •'•Associate Research Scientist, Atmospheric, Oceanic and Space Sciences, AIAA Member § Professor, Aerospace Engineering, AIAA Fellow ^Professor, Atmospheric, Oceanic and Space Sci- ences, AIAA Fellow "Professor, Electrical Engineering and Computer Science Copyright ©2001 by the American Institute of Aero- nautics and Astronautics, Inc. All rights reserved. suits for these problems are given. Governing Equations The governing equations for an ideal, non- relativistic, compressible plasma may be writ- ten in a number of different forms. In primi- tive variables, the governing equations, which represent a combination of the Euler equations of gasdynamics and the Maxwell equations of electromagnetics, may be written as: -T at pV-u = 0 r\ p— + pu - Vu + Vp - j x B at = 0 OB dt + V x E = 0 dp ~dt u = 0 (1) where the current density j and the electric field vector E are related to the magnetic field B by Ampere's law and Ohm's law, respec- tively: j = -VxB (2) -VxB E = -u x B (3) For one popular class of schemes, the equa- tions are written in a form in which the gasdy- namic terms are put in divergence form, and