A second order accurate SAV numerical method for the nonlocal ternary conservative Allen-Cahn model. (August 2023)

• Record Type: Journal Article
• Authors: Weng, Zhifeng; Yue, Xiaoqiang; Zhai, Shuying
• Is Part Of: Applied mathematics letters. Volume 142(2023)
• Publication Date: 2023-08
• Subjects: Nonlocal Allen-Cahn model -- Three component -- S-SAV -- Mass conservation -- Energy stability; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2023.108633
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: The nonlocal model has attracted a great attention in materials field for describing various types of material heterogeneities and defects. In this paper, we are concerned with construction of energy stability numerical methods for the nonlocal ternary conservative Allen-Cahn model, two different Lagrange multipliers to enforce conservation of mass are considered, respectively. By employing a stabilized scalar auxiliary variable (S-SAV) approach with second-order backward differentiation formula in temporal, two fast and effective schemes are established. The unconditional energy stability and mass conservation are rigorously derived. Numerical experiments are presented to verify theoretical results and to show the robustness and accuracy of the proposed method.