A finite difference method for a conservative Allen-Cahn equation on non-flat surfaces
- Authors
- Kim, Junseok; Jeong, Darae; Yang, Seong-Deog; Choi, Yongho
- Issue Date
- 1-4월-2017
- Publisher
- ACADEMIC PRESS INC ELSEVIER SCIENCE
- Keywords
- Conservative Allen-Cahn equation; Narrow band domain; Closest point method; Space-time-dependent Lagrange multiplier
- Citation
- JOURNAL OF COMPUTATIONAL PHYSICS, v.334, pp.170 - 181
- Indexed
- SCIE
SCOPUS
- Journal Title
- JOURNAL OF COMPUTATIONAL PHYSICS
- Volume
- 334
- Start Page
- 170
- End Page
- 181
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/83792
- DOI
- 10.1016/j.jcp.2016.12.060
- ISSN
- 0021-9991
- Abstract
- We present an efficient numerical scheme for the conservative Allen-Cahn (CAC) equation on various surfaces embedded in a narrow band domain in the three-dimensional Space. We apply a quasi-Neumann boundary condition on the narrow band domain boundary using the closest point method. This boundary treatment allows us to use the standard Cartesian Laplacian operator instead of the Laplace-Beltrami operator. We apply a hybrid operator splitting method for solving the CAC equation. First, we use an explicit Euler method to solve the diffusion term. Second, we solve the nonlinear term by using a closed form solution. Third, we apply a space-time-dependent Lagrange multiplier to conserve the total quantity. The overall scheme is explicit in time and does not need iterative steps; therefore, it is fast. A series of numerical experiments demonstrate the accuracy and efficiency of the proposed hybrid scheme. (C) 2017 Elsevier Inc. All rights reserved.
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