A second order accurate SAV numerical method for the nonlocal ternary conservative Allen-Cahn model

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.