Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 230, Issue 12, Pages 4828-4847Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2011.03.006
Keywords
Ideal magnetohydrodynamic (MHD) equations; Divergence-free magnetic field; Central discontinuous Galerkin methods; High order accuracy; Overlapping meshes
Funding
- NSF [DMS-0652481, DMS-0636358 (RTG), DMS-0847241]
- Alfred P. Sloan Research Fellowship
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [0847241] Funding Source: National Science Foundation
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In this paper, central discontinuous Galerkin methods are developed for solving ideal magnetohydrodynamic (MHD) equations. The methods are based on the original central discontinuous Galerkin methods designed for hyperbolic conservation laws on overlapping meshes, and use different discretization for magnetic induction equations. The resulting schemes carry many features of standard central discontinuous Galerkin methods such as high order accuracy and being free of exact or approximate Riemann solvers. And more importantly, the numerical magnetic field is exactly divergence-free. Such property, desired in reliable simulations of MHD equations, is achieved by first approximating the normal component of the magnetic field through discretizing induction equations on the mesh skeleton, namely, the element interfaces. And then it is followed by an element-by-element divergence-free reconstruction with the matching accuracy. Numerical examples are presented to demonstrate the high order accuracy and the robustness of the schemes. (C) 2011 Elsevier Inc. All rights reserved.
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