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A moving-mesh finite element method and its application to the numerical solution of phase-change problems

Baines, M.J., Hubbard, M.E., Jimack, P.K. and Mahmood, R. (2009) A moving-mesh finite element method and its application to the numerical solution of phase-change problems. Communications in Computational Physics, 6 (3). pp. 595-624. ISSN 1991-7120

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Abstract

A distributed Lagrangian moving-mesh finite element method is applied to problems involving changes of phase. The algorithm uses a distributed conservation principle to de- termine nodal mesh velocities, which are then used to move the nodes. The nodal values are obtained from an ALE (Arbitrary Lagrangian-Eulerian) equation, which represents a gener- alisation of the original algorithm presented in Applied Numerical Mathematics, 54:450–469 (2005). Having described the details of the generalised algorithm it is validated on two test cases from the original paper and is then applied to one-phase and, for the first time, two- phase Stefan problems in one and two space dimensions, paying particular attention to the implementation of the interface boundary conditions. Results are presented to demonstrate the accuracy and the effectiveness of the method, including comparisons against analytical solutions where available.

Item Type: Article
Copyright, Publisher and Additional Information: © 2009 Global-Science Press. This is an author produced version of a paper published in 'Communications in Computational Physics'. Uploaded in accordance with the publisher's self-archiving policy.
Academic Units: The University of Leeds > Faculty of Engineering (Leeds) > School of Computing (Leeds)
Depositing User: Miss Jamie Grant
Date Deposited: 16 Mar 2009 16:06
Last Modified: 08 Feb 2013 17:06
Published Version: http://www.global-sci.com/issue/abstract/readabs.p...
Status: Published
Publisher: Global Science Press
URI: http://eprints.whiterose.ac.uk/id/eprint/7947

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