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On Godunov-Type Schemes for Magnetohydrodynamics: 1. A Model System

✍ Scribed by R.S Myong; P.L Roe

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
254 KB
Volume
147
Category
Article
ISSN
0021-9991

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✦ Synopsis

In the light of recent analytical results on the MHD Riemann problem, Godunovtype numerical schemes for magnetohydrodynamics (MHD) are revisited. As the first step, a model system that exactly preserves the MHD hyperbolic singularities is considered. For this model, analytical results on shock waves are summarized and critical problems occurring in developing shock-capturing methods are identified. Using the results, we propose a new way to define fluxes on cell interfaces. It consists of two solvers, one on the well-posed Riemann problem and another on the evolution of AlfvΓ©n waves. Numerical experiments show that the new scheme is more efficient in calculating large-time solutions.

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