Commun. Comput. Phys., 6 (2009), pp. 595-624.


A Moving-Mesh Finite Element Method and its Application to the Numerical Solution of Phase-Change Problems

M. J. Baines 1, M. E. Hubbard 2*, P. K. Jimack 2, R. Mahmood 3

1 Department of Mathematics, The University of Reading, UK.
2 School of Computing, University of Leeds, UK.
3 Computer Division, Pakistan Institute of Nuclear Science and Technology (PINSTECH), Islamabad, Pakistan.

Received 29 August 2008; Accepted (in revised version) 24 December 2008
Available online 6 February 2009

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 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.

AMS subject classifications: 35R35, 65M50, 65M60, 76M10, 76T99
Key words: Moving mesh method, finite elements, multiphase flows, interface tracking.

*Corresponding author.
Email: m.j.baines@reading.ac.uk (M. J. Baines), meh@comp.leeds.ac.uk (M. E. Hubbard), pkj@comp.leeds.ac.uk (P. K. Jimack), dr_rashid_mahmood@yahoo.com (R. Mahmood)
 

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