An Adaptive Time-Stepping Algorithm for the Allen–Cahn Equation. (16th July 2022)

• Record Type: Journal Article
• Authors: Lee, Chaeyoung; Park, Jintae; Kwak, Soobin; Kim, Sangkwon; Choi, Yongho; Ham, Seokjun; Kim, Junseok
• Other Names: Gu Xian-Ming Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2022(2022)
• Publication Date: 2022-07-16
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2022/2731593
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : In this paper, we present a simple and accurate adaptive time-stepping algorithm for the Allen–Cahn (AC) equation. The AC equation is a nonlinear partial differential equation, which was first proposed by Allen and Cahn for antiphase boundary motion and antiphase domain coarsening. The mathematical equation is a building block for modelling many interesting interfacial phenomena such as dendritic crystal growth, multiphase fluid flows, and motion by mean curvature. The proposed adaptive time-stepping algorithm is based on the Runge–Kutta–Fehlberg method, where the local truncation error is estimated by using fourth- and fifth-order numerical schemes. Computational experiments demonstrate that the proposed time-stepping technique is efficient in multiscale computations, i.e., both the fast and slow dynamics.