Computational phase-field modeling

Gomez, Hector; van der Zee, Kristoffer George

Abstract

Phase-field modeling is emerging as a promising tool for the treatment of problems with interfaces. The classical description of interface problems requires the numerical solution of partial differential equations on moving domains in which the domain motions are also unknowns. The computational treatment of these problems requires moving meshes and is very difficult when the moving domains undergo topological changes. Phase-field modeling may be understood as a methodology to reformulate interface problems as equations posed on fixed domains. In some cases, the phase-field model may be shown to converge to the moving-boundary problem as a regularization parameter tends to zero, which shows the mathematical soundness of the approach. However, this is only part of the story because phase-field models do not need to have a moving-boundary problem associated and can be rigorously derived from classical thermomechanics. In this context, the distinguishing feature is that constitutive models depend on the variational derivative of the free energy. In all, phase-field models open the opportunity for the efficient treatment of outstanding problems in computational mechanics, such as, the interaction of a large number of cracks in three dimensions, cavitation, film and nucleate boiling, tumor growth or fully three-dimensional air-water flows with surface tension. In addition, phase-field models bring a new set of challenges for numerical discretization that will excite the computational mechanics community.

Citation

Gomez, H., & van der Zee, K. G. (2017). Computational phase-field modeling. In E. Stein, R. de Borst, & T. J. Hughes (Eds.), Encyclopedia of Computational Mechanics, Second Edition. John Wiley & Sons, Ltd

• Acceptance Date: Nov 26, 2015
• Publication Date: Nov 30, 2017
• Deposit Date: Apr 7, 2016
• Publicly Available Date: Nov 30, 2017
• Peer Reviewed: Peer Reviewed
• Book Title: Encyclopedia of Computational Mechanics, Second Edition
• ISBN: 978-1-119-00379-3
• Public URL: https://nottingham-repository.worktribe.com/output/897296
• Related Public URLs: http://eu.wiley.com/WileyCDA/WileyTitle/productCd-1119003792.html
• Additional Information: This is the submitted version of the following book chapter: Gomez, Hector, van der Zee, Kristoffer George, Computational phase-field modeling in Encyclopedia of Computational Mechanics, 2nd ed., Erwin Stein, Rene de Borst, Thomas J. R. Hughes, which has been published in final form in http://eu.wiley.com/WileyCDA/WileyTitle/productCd-1119003792.html.
• Contract Date: Apr 7, 2016