A high-order WENO finite difference scheme for the equations of ideal magnetohydrodynamics

被引:232
作者
Jiang, GS
Wu, CC
机构
[1] NYU, Courant Inst, New York, NY 10012 USA
[2] Univ Calif Los Angeles, Dept Phys & Astron, Los Angeles, CA 90095 USA
基金
美国国家航空航天局; 美国国家科学基金会;
关键词
magnetohydrodynamics; essentially non-oscillatory scheme;
D O I
10.1006/jcph.1999.6207
中图分类号
TP39 [计算机的应用];
学科分类号
081203 ; 0835 ;
摘要
We present a high-order accurate weighted essentially non-oscillatory (WENO) finite difference scheme for solving the equations of ideal magnetohydrodynamics (MHD). This scheme is a direct extension of a WENO scheme, which has been successfully applied to hydrodynamic problems. The WENO scheme follows the same idea of an essentially non-oscillatory (ENO) scheme with an advantage of achieving higher-order accuracy with fewer computations. Both ENO and WENO can be easily applied to two and three spatial dimensions by evaluating the fluxes dimension-by-dimension. Details of the WENO scheme as well as the construction of a suitable eigen-system, which can properly decompose various families of MHD waves and handle the degenerate situations, are presented. Numerical results are shown to perform well for the one-dimensional Brio-Wu Riemann problems, the two-dimensional Kelvin-Helmholtz instability problems, and the two-dimensional Orszag-Tang MHD vortex system. They also demonstrate the importance of maintaining the divergence free condition for the magnetic field in achieving numerical stability. The tests also show the advantages of using the higher-order scheme. The new 5th-order WENO MHD code can attain an accuracy comparable with that of the second-order schemes with many fewer grid points. (C) 1999 Academic Press.
引用
收藏
页码:561 / 594
页数:34
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