期刊
JOURNAL OF COMPUTATIONAL PHYSICS
卷 334, 期 -, 页码 170-181出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2016.12.060
关键词
Conservative Allen-Cahn equation; Narrow band domain; Closest point method; Space-time-dependent Lagrange multiplier
资金
- National Research Foundation of Korea (NRF) - Korea government (MSIP) [NRF-2014R1A2A2A01003683]
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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