A parallel adaptive scheme is described for solving the hyperbolic system of partial-differential equations governing ideal magnetohydrodynamic (MHD) flows in three space dimensions. A cell-centered explicit finite-volume technique is used, incorporating limited solution reconstruction, upwind fluxes based on approximate Riemann solvers, and explicit multi-stage time stepping. This method provides provides accuracy and robustness across a large range of plasma parameters. A flexible block-based hierarchical data structure is used to facilitate dynamic refinement and coarsening of the mesh based on local properties of the solution. This data structure naturally lends itself to domain decomposition, and simplifies the task of load balancing. The resulting scheme scales extremely well on distributed-memory multi-processor architectures. A speed of 342 GFlops has been attained on a 1,490-processor Cray T3E-1200 with near-perfect scalability. The scheme has been developed for use in calculating solar-wind physics, including the interaction of the solar wind with Earth's magnetosphere. Results from the simulation of a coronal mass ejection are presented in this paper.
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