Efficient linear, stabilized, second-order time marching schemes for an anisotropic phase field dendritic crystal growth model
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作者:
Yang, Xiaofeng
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机构:
Hunan Normal Univ, Coll Math & Stat, MOE, Key Lab HPC SIP, Changsha 410081, Hunan, Peoples R China
Univ South Carolina, Dept Math, Columbia, SC 29208 USAHunan Normal Univ, Coll Math & Stat, MOE, Key Lab HPC SIP, Changsha 410081, Hunan, Peoples R China
Yang, Xiaofeng
[1
,2
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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
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.
机构:
State Key Laboratory of Solidification Processing,Northwestern Polytechnical UniversityState Key Laboratory of Solidification Processing,Northwestern Polytechnical University
陈铮
张静
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State Key Laboratory of Solidification Processing,Northwestern Polytechnical UniversityState Key Laboratory of Solidification Processing,Northwestern Polytechnical University
机构:
Shaanxi Normal Univ, Sch Math & Stat, Xian 710119, Shaanxi, Peoples R ChinaShaanxi Normal Univ, Sch Math & Stat, Xian 710119, Shaanxi, Peoples R China
Bu, Linlin
Wu, Jianhua
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机构:
Shaanxi Normal Univ, Sch Math & Stat, Xian 710119, Shaanxi, Peoples R ChinaShaanxi Normal Univ, Sch Math & Stat, Xian 710119, Shaanxi, Peoples R China
Wu, Jianhua
Mei, Liquan
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机构:
Xi An Jiao Tong Univ, Sch Math & Stat, Xian 710049, Shaanxi, Peoples R ChinaShaanxi Normal Univ, Sch Math & Stat, Xian 710119, Shaanxi, Peoples R China
Mei, Liquan
Wang, Ying
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机构:
Xian Univ Architecture & Technol, Sch Sci, Xian 710055, Shaanxi, Peoples R ChinaShaanxi Normal Univ, Sch Math & Stat, Xian 710119, Shaanxi, Peoples R China
机构:
Hong Kong Polytech Univ, Dept Appl Math, Kowloon, Hong Kong, Peoples R ChinaHong Kong Polytech Univ, Dept Appl Math, Kowloon, Hong Kong, Peoples R China
Qiao, Zhonghua
Sun, Zhi-Zhong
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机构:
Southeast Univ, Dept Math, Nanjing 210096, Jiangsu, Peoples R ChinaHong Kong Polytech Univ, Dept Appl Math, Kowloon, Hong Kong, Peoples R China
Sun, Zhi-Zhong
Zhang, Zhengru
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机构:
Beijing Normal Univ, Minist Educ, Lab Math & Complex Syst, Beijing 100875, Peoples R China
Beijing Normal Univ, Sch Math Sci, Beijing 100875, Peoples R ChinaHong Kong Polytech Univ, Dept Appl Math, Kowloon, Hong Kong, Peoples R China
机构:
Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China
York Univ, Dept Math & Stat, Toronto, ON M3J 1P3, CanadaShandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China
Liang, Dong
Sun, Guanying
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机构:
Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R ChinaShandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China
Sun, Guanying
Wang, Wenqia
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机构:
Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R ChinaShandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China