<<O>>  Difference Topic DZ06mmfv1dmhdAbstract (r1.5 - 16 May 2006 - ArthurVanDam)
META TOPICPARENT Publications
A. van Dam and P.A. Zegeling.
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<		 A Robust Moving Mesh Finite Volume Method applied to 1D Hyperbolic Conservation Laws from Magnetohydrodynamics. Preprint 1332. Dept. of Mathematics, Utrecht University, July 2005. (submitted)
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>		 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:

 (PDF )
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<		 To appear in Journal of Computational Physics, 2006.

Abstract

In this paper we describe a one-dimensional adaptive moving mesh method and
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 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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META TOPICMOVED ArthurVanDam? date="1147785835" from="Arthur.DZ05mmfv1dmhdAbstract" to="Arthur.DZ06mmfv1dmhdAbstract"
 <<O>>  Difference Topic DZ06mmfv1dmhdAbstract (r1.4 - 25 Dec 2005 - ArthurVanDam)
META TOPICPARENT Publications
A. van Dam and P.A. Zegeling. A Robust Moving Mesh Finite Volume Method applied to 1D Hyperbolic Conservation Laws from Magnetohydrodynamics. Preprint 1332. Dept. of Mathematics, Utrecht University, July 2005. (submitted)
(PDF )
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<		 NOTE : The above preprint is currently under revision, for eventual acceptation for Journal of Computational Physics. Please come back at the end of 2005 for a final version.
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>		 To appear in Journal of Computational Physics, 2006.

Abstract

In this paper we describe a one-dimensional adaptive moving mesh method and
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 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
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<		 extra costs. The results of several numerical experiments are presented,
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>		 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.
 <<O>>  Difference Topic DZ06mmfv1dmhdAbstract (r1.3 - 09 Oct 2005 - ArthurVanDam)
META TOPICPARENT Publications
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<		 Arthur van Dam and P.A. Zegeling.
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>		 A. van Dam and P.A. Zegeling.

A Robust Moving Mesh Finite Volume Method applied to 1D Hyperbolic Conservation Laws from Magnetohydrodynamics. Preprint 1332. Dept. of Mathematics, Utrecht University, July 2005. (submitted)
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<		 (PDF )
>
>		 (PDF )
NOTE : The above preprint is currently under revision, for eventual acceptation for Journal of Computational Physics. Please come back at the end of 2005 for a final version.

Abstract

In this paper we describe a one-dimensional adaptive moving mesh method and
 <<O>>  Difference Topic DZ06mmfv1dmhdAbstract (r1.2 - 10 Aug 2005 - ArthurVanDam)
META TOPICPARENT Publications
Arthur van Dam and P.A. Zegeling. A Robust Moving Mesh Finite Volume Method applied to 1D Hyperbolic Conservation Laws from Magnetohydrodynamics. Preprint 1332. Dept. of Mathematics, Utrecht University, July 2005. (submitted)
Changed:
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<		 (PDF (not available yet) )
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>		 (PDF )

Abstract

In this paper we describe a one-dimensional adaptive moving mesh method and
 <<O>>  Difference Topic DZ06mmfv1dmhdAbstract (r1.1 - 27 Jul 2005 - ArthurVanDam)
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META TOPICPARENT Publications
Arthur van Dam and P.A. Zegeling. A Robust Moving Mesh Finite Volume Method applied to 1D Hyperbolic Conservation Laws from Magnetohydrodynamics. Preprint 1332. Dept. of Mathematics, Utrecht University, July 2005. (submitted)
(PDF (not available yet) )

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 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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Revision r1.1 - 27 Jul 2005 - 10:29 - ArthurVanDam
Revision r1.5 - 16 May 2006 - 13:24 - ArthurVanDam