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A solution-adaptive upwind scheme for ideal magnetohydrodynamics. (English) Zbl 0952.76045
Summary: We present a computational scheme for compressible magnetohydrodynamics (MHD). The scheme uses a high-resolution upwinding based on an approximate Riemann solver for MHD and limited reconstruction, an optimally smoothing multi-stage time-stepping, and solution-adaptive refinement and coarsening. In addition, we present a method for increasing the accuracy of the scheme by subtracting off an embedded steady magnetic field. The scheme is validated by comparison with exact solutions. Results are presented for two three-dimensional interaction of the solar wind with a magnetized planet.

MSC:
76M12 Finite volume methods applied to problems in fluid mechanics
76W05 Magnetohydrodynamics and electrohydrodynamics
85-08 Computational methods for problems pertaining to astronomy and astrophysics
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