Efficient and Energy Stable Scheme for an Anisotropic Phase-Field Dendritic Crystal Growth Model Using the Scalar Auxiliary Variable (SAV) Approach
Year: 2020
Author: Xiaofeng Yang
Journal of Mathematical Study, Vol. 53 (2020), Iss. 2 : pp. 212–236
Abstract
The phase-field dendritic crystal growth model is a highly nonlinear system that couples the anisotropic Allen-Cahn type equation and the heat equation. By combining the recently developed SAV (Scalar Auxiliary Variable) method with the linear stabilization approach, as well as a special decoupling technique, we arrive at a totally decoupled, linear, and unconditionally energy stable scheme for solving the dendritic model. We prove its unconditional energy stability rigorously and present various numerical simulations to demonstrate the stability and accuracy.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v53n2.20.05
Journal of Mathematical Study, Vol. 53 (2020), Iss. 2 : pp. 212–236
Published online: 2020-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 25
Keywords: Phase-field dendritic stabilized-SAV method anisotropy Allen-Cahn decoupled.