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Volume 15, Issue 2
Phase Field Models Versus Parametric Front Tracking Methods: Are They Accurate and Computationally Efficient?

John W. Barrett, Harald Garcke & Robert Nürnberg

DOI: 10.4208/cicp.190313.010813a

Commun. Comput. Phys., 15 (2014), pp. 506-555.

Published online: 2014-02

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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.

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@Article{CiCP-15-506, author = {John W. Barrett, Harald Garcke and Robert Nürnberg}, title = {Phase Field Models Versus Parametric Front Tracking Methods: Are They Accurate and Computationally Efficient?}, journal = {Communications in Computational Physics}, year = {2014}, volume = {15}, number = {2}, pages = {506--555}, 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.190313.010813a}, url = {http://global-sci.org/intro/article_detail/cicp/7104.html} }
TY - JOUR T1 - Phase Field Models Versus Parametric Front Tracking Methods: Are They Accurate and Computationally Efficient? AU - John W. Barrett, Harald Garcke & Robert Nürnberg JO - Communications in Computational Physics VL - 2 SP - 506 EP - 555 PY - 2014 DA - 2014/02 SN - 15 DO - http://doi.org/10.4208/cicp.190313.010813a UR - https://global-sci.org/intro/article_detail/cicp/7104.html KW - AB -

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.

John W. Barrett, Harald Garcke and Robert Nürnberg. (2014). Phase Field Models Versus Parametric Front Tracking Methods: Are They Accurate and Computationally Efficient?. Communications in Computational Physics. 15 (2). 506-555. doi:10.4208/cicp.190313.010813a
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