T.I. Gombosi, D.I. De Zeeuw, K.G. Powell, A.J. Ridley
I.V. Sokolov,
Q.F. Stout,
G. Toth

Center for Space Environment Modeling

University of Michigan

**Abstract**:
The first part of this paper reviews some physics issues representing
major computational challengest for global
MHD models of the space environment.
These issues include:
(i) mathematical formulation and discretization of the governing equations
that ensure the proper jump conditions and propagation speeds,
(ii) regions of relativistic Alfv´en speed,
(iii) regions dominated by strong intrinsic planetary magnetic field
with strong gradients, and
(iv) the religiously debated issue of controling the divergence of the
magnetic field.

The second part of the paper concentrates to modern solution methods that have been developed by the aerodynamics, applied mathematics and DoE communities. Such methods have recently begun to be implemented in space-physics codes, which solve the governing equations for a compressible magnetized 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 to space physics, space physics simulations pose some new challenges. We give a brief review of the state-of-the-art in modern space-physics codes.

Finally, we describe the space physics MHD code developed at the University of Michigan and its recent coupling to a thermosphere-ionosphere and inner magnetosphere model.

**Keywords**:
adaptive mesh refinement, MHD, space weather, geoscience,
adaptive blocks, parallel data structures,
parallel computing,
scientific computing

**Complete paper**.
This paper appears in *Space Plasma Simulation*,
J. Buchner, C.T. Dum, M. Scholer, eds., Lecture Notes in Physics 615,
Springer-Verlag, 2003, pp. 251-279.

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