Novel energy dissipative method on the adaptive spatial discretization for the Allen-Cahn equation

• 作者: Jing-Wei Sun Xu Qian Hong Zhang Song-He Song
• 来源期刊: 中国物理B（英文版）
• 年，卷（期）: 2021,（7）
• 所属期刊栏目: GENERAL
• 页码范围: 123-132
• 页数: 10页
• 语种: 英文
• DOI: 10.1088/1674-1056/abe37b

摘要

We propose a novel energy dissipative method for the Allen-Cahn equation on nonuniform grids.For spatial dis-cretization,the classical central difference method is utilized,while the average vector field method is applied for time discretization.Compared with the average vector field method on the uniform mesh,the proposed method can involve fewer grid points and achieve better numerical performance over long time simulation.This is due to the moving mesh method,which can concentrate the grid points more densely where the solution changes drastically.Numerical experi-ments are provided to illustrate the advantages of the proposed concrete adaptive energy dissipative scheme under large time and space steps over a long time.