4.7 Article

An unsplit staggered mesh scheme for multidimensional magnetohydrodynamics

期刊

JOURNAL OF COMPUTATIONAL PHYSICS
卷 228, 期 4, 页码 952-975

出版社

ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2008.08.026

关键词

MHD; Magnetohydrodynamics; Constrained transport; Corner transport upwind; Unsplit scheme; Staggered mesh; High-order Godunov method

资金

  1. National Science Foundation ITR [DMS-0219282]
  2. US Department of Energy [8523820]

向作者/读者索取更多资源

We introduce an unsplit staggered mesh scheme (USM) for multidimensional magnetohydrodynamics (MHD) that uses a constrained transport (CT) method with high-order Codunov fluxes and incorporates a new data reconstruction-evolution algorithm for second-order MHD interface states. In this new algorithm, the USM scheme includes so-called multidimensional MHD terms, proportional to del.B, in a dimensionally-unsplit way in a single update. This data reconstruction-evolution step, extended from the corner transport upwind (CTU) approach of Colella, maintains in-plane dynamics very well, as shown by the advection of a very weak magnetic field loop in 2D. This data reconstruction-evolution algorithm is also of advantage in its consistency and simplicity when extended to 3D. The scheme maintains the del.B = 0 constraint by solving a set of discrete induction equations using the standard CT approach, where the accuracy of the computed electric field directly influences the quality of the magnetic field solution. We address the lack of proper dissipative behavior in the simple electric field averaging scheme and present a new modified electric field construction (MEC) that includes multidimensional derivative information and enhances solution accuracy. A series of comparison studies demonstrates the excellent performance of the full USM-MEC scheme for many stringent multidimensional MHD test problems chosen from the literature. The scheme is implemented and currently freely available in the University of Chicago ASC FLASH Center's FLASH3 release. (C) 2008 Elsevier Inc. All rights reserved.

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