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

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Hubbard, M.E., Baines, M., 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 1815-2406

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Abstract/Summary

A distributed Lagrangian moving-mesh finite element method is applied to problems involving changes of phase. The algorithm uses a distributed conservation principle to determine 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 generalization of the original algorithm presented in Applied Numerical Mathematics, 54:450--469 (2005). Having described the details of the generalized 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
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical and Physical Sciences > Department of Mathematics and Statistics
ID Code:18944
Uncontrolled Keywords:Moving mesh method, finite elements, multiphase flows, interface tracking
Publisher:Global Science Press
Publisher Statement:"First published in Communications in Computational Physics in Vol 6 (2009), pp. 595-624 published by Global Science Press," © Copyright 2006, Global Science Press

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