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Phase Field Models Versus Parametric Front Tracking Methods: Are They Accurate and Computationally Efficient?

Published online by Cambridge University Press:  03 June 2015

John W. Barrett ,
Harald Garcke  and
Robert Nürnberg
John W. Barrett*
Affiliation:
Department of Mathematics, Imperial College London, London, SW7 2AZ, UK
Harald Garcke*
Affiliation:
Fakultät für Mathematik, Universität Regensburg, 93040 Regensburg, Germany
Robert Nürnberg*
Affiliation:
Department of Mathematics, Imperial College London, London, SW7 2AZ, UK
*
Email:[email protected]
Corresponding author.Email:[email protected]
Email:[email protected]
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Abstract

We critically compare the practicality and accuracy of numerical approximations of phase field models and sharp interface models of solidification. Here we focus on Stefan problems, and their quasi-static variants, with applications to crystal growth. New approaches with a high mesh quality for the parametric approximations of the resulting free boundary problems and new stable discretizations of the anisotropic phase field system are taken into account in a comparison involving benchmark problems based on exact solutions of the free boundary problem.

Keywords

35K5535R3535R3753C4465M1265M5065M6074E1074E1574N2080A2282C26Phase field modelsparametric sharp interface methodsStefan problemanisotropysolidificationcrystal growthnumerical simulationsbenchmark problems
Type
Research Article
Information
Communications in Computational Physics , Volume 15 , Issue 2 , February 2014 , pp. 506 - 555
Copyright
Copyright © Global Science Press Limited 2014

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