A.van Dam and P.A. Zegeling. A robust moving mesh finite volume method applied to 1D hyperbolic conservation laws from magnetohydrodynamics. Journal of Computational Physics, Vol. 216, Issue 2, pp. 526--546, 2006.
(doi: 10.1016/j.jcp.2005.12.014) - (BibTeX)
Also available as Preprint 1332. Dept. of Mathematics, Utrecht University, July 2005:
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Abstract

In this paper we describe a one-dimensional adaptive moving mesh method and its application to hyperbolic conservation laws from magnetohydrodynamics (MHD). The method is robust, because it employs automatic control of mesh adaptation when a new model is considered, without manually-set parameters. Adaptive meshes are a common tool for increasing the accuracy and reducing computational costs when solving time-dependent partial differential equations (PDEs). Mesh points are moved towards locations where they are needed the most. To obtain a time-dependent adaptive mesh, monitor functions are used to automatically `monitor' the importance of the various parts of the domain, by assigning a `weight'-value to each location. Based on the equidistribution principle, all mesh points are distributed according to their assigned weights. We use a sophisticated monitor function that tracks both small, local phenomena as well as large shocks in the same solution. The combination of the moving mesh method and a high-resolution finite volume solver for hyperbolic PDEs yields a serious gain in accuracy at relatively no extra costs. The results of several numerical experiments -- including comparisons with h-refinement -- are presented, which cover many intriguing aspects typifying nonlinear magnetofluid dynamics, with higher accuracy than often seen in similar publications.

Keywords: moving mesh, adaptive mesh refinement, monitor function, finite volumes, conservation laws, magnetohydrodynamics
PACS: 02.70.Bf 52.30.Cv 52.35.Bj 52.35.Tc 52.65.Kj
MSC 2000: 35L60 35L65 65M50 76L05 76M12 76W05

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