Efficient computation of dendritic growth with r-adaptive finite element methods

Authors:
Heyu Wang;Ruo Li;Tao Tang
Affiliations:
Department of Mathematics, Zhejiang University, 310027 Hangzhou, China and Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Kowloon, Hong Kong;LMAM and School of Mathematical Sciences, Peking University, 100871 Beijing, China;Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Kowloon, Hong Kong
Venue:
Journal of Computational Physics
Year:
2008

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Abstract

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.