Preprint 2003-062

Non-Oscillatory Central Schemes for One- and Two-Dimensional MHD Equations. I.

Jorge Balbas, Eitan Tadmor, and Cheng-Chin Wu

Abstract: In this paper we utilize a family of high-resolution, non-oscillatory central schemes for the approximate solution of the equations of ideal magnetohydrodynamics (MHD) in one- and two-space dimensions. We present several prototype problems. Solutions of one-dimensional shock-tube problems is carried out using second- and third-order central schemes [nessayahu-tadmor:2nd, JCP 87, (1990), p. 408- ] , [liu-tadmor:3rd, Numer. Math. 79, (1998), p. 397- ], and we use the second-order central scheme [jiang-tadmor:multid, SISSC 19 (1998), p. 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 eigen-structure 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. The one- and two-dimensional computations reported in this paper demonstrate the remarkable versatility of central schemes as black-box, Jacobian-free MHD solvers.

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Jorge Balbas, <>
Eitan Tadmor, <>
Cheng-Chin Wu, <>
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<> September 27 2003.

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