A fully discrete curve-shortening polygonal evolution law for moving boundary problems

JOURNAL OF COMPUTATIONAL PHYSICS

卷:424

Article

Sakakibara, Koya^1,2  Miyatake, Yuto³ 

[1] Okayama Univ Sci, Fac Sci, Dept Appl Math, Kita Ku, 1-1 Ridaicho, Okayama, Okayama 7000005, Japan

[2] RIKEN ITHEMS, 2-1 Hirosawa, Wako, Saitama 3510198, Japan

[3] Osaka Univ, Cybermedia Ctr, 1-32 Machikaneyama, Toyonaka, Osaka 5600043, Japan

关键词: Moving boundary problems;    Geometric numerical integration;    Discrete gradient method;    Tangential redistribution;   

DOI  :  10.1016/j.jcp.2020.109857

来源: Elsevier

【 摘 要 】

We consider the numerical integration of moving boundary problems with the curve-shortening property, such as the mean curvature flow and Hele-Shaw flow. We propose a fully discrete curve-shortening polygonal evolution law. The proposed evolution law is fully implicit, and the key to the derivation is to devise the definitions of tangent and normal vectors and tangential and normal velocities at each vertex in an implicit manner. Numerical experiments show that the proposed method allows the use of relatively large time step sizes and also captures the area-preserving or dissipative property in good accuracy. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free