Non-Oscillatory Central Schemes for One- and Two-Dimensional MHD Equations
CALIFORNIA STATE UNIV LOS ANGELES DEPT OF MATHEMATICS
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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 19, 18, and we use the second-order central scheme 11 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.
- Theoretical Mathematics
- Plasma Physics and Magnetohydrodynamics