Convex Splitting Runge–Kutta methods for phase-field models. (1st June 2017)

• Record Type: Journal Article
• Authors: Shin, Jaemin; Lee, Hyun Geun; Lee, June-Yub
• Is Part Of: Computers & mathematics with applications. Volume 73:issue 11(2017)
• Page Start: 2388
• Page End: 2403
• Publication Date: 2017-06-01
• Subjects: Convex splitting -- Implicit–explicit Runge–Kutta -- Allen–Cahn equation -- Cahn–Hilliard equation -- Phase-field crystal equation; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2017.04.004
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: In this paper, we present the Convex Splitting Runge–Kutta (CSRK) methods which provide a simple unified framework to solve phase-field models such as the Allen–Cahn, Cahn–Hilliard, and phase-field crystal equations. The core idea of the CSRK methods is the combination of convex splitting methods and multi-stage implicit–explicit Runge–Kutta methods. Our CSRK methods are high-order accurate in time and we investigate the energy stability numerically. We present numerical experiments to show the accuracy and efficiency of the proposed methods up to the third-order accuracy.