Non-Oscillatory Finite Compact Scheme for the Equations of Ideal Magnetohydrodynamics

Abstract:

Although the equations of ideal Magnetohydrodynamics (MHD) is a non-strictly hyperbolic system, they have a wave-like structure analogous to that of the hydrodynamics equations, various numerical schemes for hydrodynamics equations have been extended to solve the MHD equations. The finite compact (FC) scheme treats the discontinuity as the internal boundary and avoids the global dependence of the traditional compact schemes. By using a parameter-free shock detecting method, the computational domain is divided into a series of smooth regions and shock wave regions. In the shock wave regions, the shock capturing scheme is used to construct the numerical flux, and in the smooth regions the compact scheme is used, the flux of shock wave region is automatically the boundary formulation of the compact scheme. Hence, the FC scheme can resolve shock essentially non-oscillatory and achieve high order of accuracy in smooth region. This paper develops the non-oscillation finite compact scheme for the ideal MHD equations.

• Periodical: Applied Mechanics and Materials (Volume 432)
• Pages: 157-162
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.432.157
• Online since: September 2013
• Authors: Li Liu, Yi Qing Shen
• Keywords: Deal Magnetohydrodynamics, Finite Compact Scheme, Weighted Essentially Non-Oscillatory Scheme

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