High-order and mass conservative methods for the conservative Allen–Cahn equation. (August 2016)

• Record Type: Journal Article
• Authors: Lee, Hyun Geun
• Is Part Of: Computers & mathematics with applications. Volume 72:issue 3(2016)
• Page Start: 620
• Page End: 631
• Publication Date: 2016-08
• Subjects: Conservative Allen–Cahn equation -- High-order method -- Mass conservative method -- Fourier spectral method; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2016.05.011
• Languages: English
• ISSNs: 0898-1221

Abstract

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.