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High-order and mass conservative methods for the conservative Allen-Cahn equation

Title
High-order and mass conservative methods for the conservative Allen-Cahn equation
Authors
Lee, Hyun Geun
Ewha Authors
이현근
SCOPUS Author ID
이현근scopus
Issue Date
2016
Journal Title
COMPUTERS & MATHEMATICS WITH APPLICATIONS
ISSN
0898-1221JCR Link1873-7668JCR Link
Citation
vol. 72, no. 3, pp. 620 - 631
Keywords
Conservative Allen-Cahn equationHigh-order methodMass conservative methodFourier spectral method
Publisher
PERGAMON-ELSEVIER SCIENCE LTD
Indexed
SCI; SCIE; SCOPUS WOS scopus
Abstract
The conservative Allen-Cahn (AC) equation has been studied analytically and numerically. Our mathematical analysis and numerical experiment, however, show that previous numerical methods are not second-order accurate in time and/or do not conserve the initial mass. The aim of this paper is to propose high-order and mass conservative methods for solving the conservative AC equation. In the methods, we discretize the conservative AC equation by using a Fourier spectral method in space and first-, second-, and third-order implicit-explicit Runge-Kutta schemes in time. We show that the methods inherit the mass conservation, Numerical experiments are presented demonstrating the accuracy and efficiency of proposed methods. (C) 2016 Elsevier Ltd. All rights reserved.
DOI
10.1016/j.camwa.2016.05.011
Appears in Collections:
연구기관 > 수리과학연구소 > Journal papers
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