T.I. Gombosi, K.G. Powell, D.I. De Zeeuw, C.R. Clauer, K.C. Hansen,
W.B. Manchester, A.J. Ridley, I.I. Roussev, 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 of the challenges for
global MHD (magnetohydrodynamics) modeling of the space environment.
These include mathematical formulation and discretization of the
governing equations, regions of relativistic Alfein speed,
and controlling the divergence of the magnetic field.
The second part concentrates on modern solution methods.
These include high-resolution upwind schemes, block-based adaptive
grids, and domain decomposition for parallel computing.
The third part describes the application of the code to space
weather simulation.

**Keywords**:
magnetohydrodynamics,
adaptive MHD, space weather, geoscience, Cartesian adaptive
grid, adaptive blocks, parallel data structures,
parallel computing,
scientific computing

**Complete paper**.
This paper appears in
*Computers in Science and Engineering* 6 (2004), pp. 14-35.

- My work in modeling climate, atmospheric, and space systems: papers and an overview of research.
- My work in parallel computing: papers, and an overview of research.
- General parallel computing: an explanation of parallel computing, a tutorial, Parallel Computing 101, and a list of resources

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