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

Authors: Myong R.S.¹; Roe P.L.²

Source: Journal of Computational Physics, Volume 147, Number 2, December 1998 , pp. 545-567(23)

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Abstract:

In the light of recent analytical results on the MHD Riemann problem, Godunov-type 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 Alfvén waves. Numerical experiments show that the new scheme is more efficient in calculating large-time solutions. Copyright 1998 Academic Press.

Language: English

Document Type: Research article

Affiliations: 1: NASA Goddard Space Flight Center, Mail Stop 930, Greenbelt, Maryland, 20771 2: W. M. Keck Foundation Laboratory for CFD, Department of Aerospace Engineering, University of Michigan, Ann Arbor, Michigan, 48109

Publication date: 1998-12-01