Non-oscillatory central schemes for one- and two-dimensional MHD equations: I

  • Authors:

  • Jorge Balbás;Eitan Tadmor;Cheng-Chin Wu

  • Affiliations:

  • Department of Mathematics, University of Calfornia, Los Angeles, CA;Department of Mathematics, Center of Scientific Computation and Mathematical Modeling (CSCAMM) and Institute for Physical Science and Technology (IPST), University of Maryland, MD;Department of Physics and Astronomy, University of California, Los Angeles, CA

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

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Abstract

The computations reported in this paper demonstrate the remarkable versatility of central schemes as black-box, Jacobian-free solvers for ideal magnetohydrodynamics (MHD) equations. Here we utilize a family of high-resolution, non-oscillatory central schemes for the approximate solution of the one- and two-dimensional MHD equations. We present simulations based on staggered grids of several MHD prototype problems. Solution of one-dimensional shock-tube problems is carried out using second- and third-order central schemes [Numer. Math. 79 (1998) 397; J. Comput. Phys. 87 (2) (1990) 408], and we use the second-order central scheme [SIAM J. Sci Comput. 19 (6) (1998) 1892] which is adapted for the solution of the two-dimensional Kelvin-Helmholtz and Orszag-Tang problems. A qualitative comparison reveals an excellent agreement with previous results based on upwind schemes. Central schemes, however, require little knowledge about the eigenstructure of the problem in fact, we even avoid an explicit evaluation of the corresponding Jacobians, while at the same time they eliminate the need for dimensional splitting.