A visual fluctuation splitting scheme for magnetohydrodynamics with a new sonic fix and Euler limit

  • Authors:

  • Necdet Aslan

  • Affiliations:

  • Physics Department, Yeditepe University, Kaytsdagi, 81120 Istanbul, Turkey

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2004

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Abstract

This paper presents a two dimensional visual computer code developed to solve magnetohydrodynamic (MHD) equations. This code runs on structured and unstructured triangles and operates by a fluctuation splitting (FS) scheme. The FS scheme originally introduced by Roe [in: K.W. Morton, M.J. Baines (Eds.), Numerical Methods for Fluid Dynamics II, Academic Press, New York, 1982] to solve Euler equations was extended by Aslan [J. Comput. Phys. 153 (1999) 437] for solving ideal MHD equations. Aslan's method included a wave model, called MHD-A, consisting of slow and fast magneto-acoustic waves as well as an entropy and artificial magnetic monopole wave. In this work, Aslan's method was extended to include external sources, a new sonic fix, and a careful normalization in the Euler limit. It is shown by numerical experiments that VIS-MHD-A is able to work accurately for a wide range of problems including discontinuities, shock structures, and problems including smooth solutions (e.g., Rayleigh-Taylor and Kelvin-Helmholtz instability).