Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 227, Issue 12, Pages 5984-6000Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2008.02.016
Keywords
moving mesh method; phase-field model; finite element method; dendritic growth
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This paper deals with the application of a moving grid method to the solution of a phase-field model for dendritic growth in two- and three-dimensions. A mesh is found as the solution of an optimization problem that automatically includes the boundary conditions and is solved using a multi-grid approach. The governing equations are discretized in space by linear finite elements and a split time-level scheme is used to numerically integrate in time. One novel aspect of the method is the choice of a regularized monitor function. The moving grid method enables us to obtain accurate numerical solutions with much less degree of freedoms. It is demonstrated numerically that the tip velocity obtained by our method is in good agreement with the previously published results. (c) 2008 Elsevier Inc. All rights reserved.
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