Extension of the piecewise parabolic method to multidimensional ideal magnetohydrodynamics

Wenlong Dai, Paul R. Woodward

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An extension of the piecewise parabolic method to treat multidimensional ideal magnetohydrodynamical equations is presented in this paper. The multidimensional scheme is constructed from a one-dimensional functioning code based on the dimensional splitting method originally suggested by Strang. The functioning code is built upon a nonlinear Riemann solver for ideal MHD equations recently 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. The robust character of the scheme is demonstrated in the shock-tube problems and in the interaction between MHD shocks and a cloud. The results of these problems show that the scheme keeps the principal advantages of a high-order Godunov scheme: Robust operation in the presence of very strong waves, thin shock fronts with little attendant noise generation, and thin contact discontinuity.

Original languageEnglish (US)
Pages (from-to)485-514
Number of pages30
JournalJournal of Computational Physics
Issue number2
StatePublished - Dec 1994


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