Global Mhd Simulations of Space Plasma Environments: Heliosphere, Comets, Magnetospheres of Planets and Satellites

Magnetohydrodynamics (MHD) provides an approximate description of a great variety of processes in space physics. Accurate numerical solutions of the MHD equations are still a challenge, but in the past decade a number of robust methods have appeared. Once these techniques made the direct solution of MHD equations feasible, a number of global three-dimensional models were designed and applied to many space physics objects. The range of these objects is truly astonishing, including active galactic nuclei, the heliosphere, the solar corona, and the solar wind interaction with planets, satellites, and comets. Outside the realm of space physics, MHD theory has been applied to such diverse problems as laboratory plasmas and electromagnetic casting of liquid metals. In this paper we present a broad spectrum of models of different phenomena in space science developed in the recent years at the University of Michigan. Although the physical systems addressed by these models are different, they all use the MHD equations as a unifying basis. 1. Mathematical Basis of the Models The global models that we are presenting here are based on a recently developed code that solves the ideal MHD equations. It is understood that these equations represent a simplified description of the physics involved in space science applications, for example, they neglect kinetic effects, ignore resistivity and diffusion, and treat the ions and electrons as a single fluid. The main benefit of solving the MHD equations is that they are simple enough to be solved over a large domain with a reasonable amount of computing resources, while at the same time being realistic enough that models lead to correct physical insights. Below we outline the MHD equations and the numerical method used to solve them. The ideal MHD equations are: