Efficient linear, stabilized, second-order time marching schemes for an anisotropic phase field dendritic crystal growth model

被引:56
|
作者
Yang, Xiaofeng [1 ,2 ]
机构
[1] Hunan Normal Univ, Coll Math & Stat, MOE, Key Lab HPC SIP, Changsha 410081, Hunan, Peoples R China
[2] Univ South Carolina, Dept Math, Columbia, SC 29208 USA
基金
美国国家科学基金会;
关键词
Phase-field; Dendritic; Stabilization; IEQ method; Anisotropy; Allen-Cahn; ENERGY STABLE SCHEMES; NUMERICAL APPROXIMATIONS; STEPPING METHODS; GRADIENT FLOWS; ALLEN-CAHN; SIMULATIONS; ACCURATE; 1ST;
D O I
10.1016/j.cma.2018.12.012
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
We consider numerical approximations for a phase field dendritic crystal growth model, which is a highly nonlinear system that couples the anisotropic Allen-Cahn type equation and the heat equation together. We propose two efficient, linear, second-order time marching schemes. The first one is based on the linear stabilization approach where all nonlinear terms are treated explicitly and one only needs to solve two linear and decoupled second-order equations. The second one combines the recently developed Invariant Energy Quadratization approach with the linear stabilization technique. Two linear stabilization terms, which are shown to be crucial to remove the oscillations caused by the anisotropic coefficients numerically, are added to enhance the stability while keeping the required accuracy. We further show the obtained linear system is well-posed and prove its unconditional energy stability rigorously. Various 2D and 3D numerical simulations are implemented to demonstrate the stability and accuracy of the schemes. (C) 2018 Elsevier B.V. All rights reserved.
引用
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页码:316 / 339
页数:24
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