Green, JR, Jimack, PK, Mullis, AM et al. (1 more author) (2011) An Adaptive, Multilevel Scheme for the Implicit Solution of Three-Dimensional Phase-Field Equations. Numerical Methods for Partial Differential Equations, 27 (1). 106 - 120. ISSN 0749-159X
Abstract
Phase-field models, consisting of a set of highly nonlinear coupled parabolic partial differential equations, are widely used for the simulation of a range of solidification phenomena. This article focuses on the numerical solution of one such model, representing anisotropic solidification in three space dimensions. The main contribution of the work is to propose a solution strategy that combines hierarchical mesh adaptivity with implicit time integration and the use of a nonlinear multigrid solver at each step. This strategy is implemented in a general software framework that permits parallel computation in a natural manner. Results are presented that provide both qualitative and quantitative justifications for these choices.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | (c) 2011, Wiley. This is the accepted version of the following article: Green, JR, Jimack, PK, Mullis, AM and Rosam, J (2011) An Adaptive, Multilevel Scheme for the Implicit Solution of Three-Dimensional Phase-Field Equations. Numerical Methods for Partial Differential Equations, 27 (1). 106 - 120. ISSN 0749-159X, which has been published in final form at http://dx.doi.org/10.1002/num.20634 |
Keywords: | Adaptive methods; binary alloy solidification; dendritic growth; fully implicit; load-balancing algorithms; model; multigrid methods; multiscale problems; nonlinear partial differential equations; phase change problems; phase field models; refinement; simulation; solvability theory; solver; stiff systems; systems |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Chemical & Process Engineering (Leeds) > Institute for Materials Research (Leeds) The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 06 May 2014 10:49 |
Last Modified: | 17 Jan 2018 10:03 |
Published Version: | http://dx.doi.org/10.1002/num.20634 |
Status: | Published |
Publisher: | Wiley |
Identification Number: | 10.1002/num.20634 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:78689 |