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Extension of the piecewise parabolic method to multidimensional ideal magnetohydrodynamics. (English) Zbl 0813.76058
The multidimensional scheme is constructed from a one-dimensional functioning code based on the dimensional splitting method. The functioning code is built upon a nonlinear Riemann solver for ideal MHD equations developed by the authors. The correctness of the scheme is tested in the steepening of waves in both one- and two-dimensional situations and in various MHD shock-tube problems which involve all the discontinuities in ideal MHD.

76M20 Finite difference methods applied to problems in fluid mechanics
76W05 Magnetohydrodynamics and electrohydrodynamics
76L05 Shock waves and blast waves in fluid mechanics
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