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A high-order WENO finite difference scheme for the equations of ideal magnetohydrodynamics. (English) Zbl 0937.76051
We present a high-order accurate weighted essentially non-oscillatory (WENO) finite difference scheme for solving the equations of ideal magnetohydrodynamics (MHD). We discuss details of the WENO scheme as well as the construction of a suitable eigensystem, which can properly decompose various families of MHD waves and handle the degenerate situations. Numerical results are shown for one-dimensional Brio-Wu Riemann problem, two-dimensional Kelvin-Helmholtz instability problem, and two-dimensional Orszag-Tang MHD vortex system. \(\copyright\) Academic Press.

MSC:
76M20 Finite difference methods applied to problems in fluid mechanics
76W05 Magnetohydrodynamics and electrohydrodynamics
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