Unconditionally energy stable large time stepping method for the L~2-gradient flow based ternary phase-field model with precise nonlocal volume conservation

摘要

We consider numerical approximations for solving a new, Allen-Cahn type ternary phase-field model. We first formulate a phase-field model from an energetic variational formulation based on the L-2-gradient flow and add three nonlocal Lagrange multipliers to the system to conserve the volume for each phase. Then, by combining the SAV approach with the stabilization technique, where a crucial linear stabilization term is added to enhance the stability and keep the required accuracy thus allowing large time steps, we arrive at a decoupled, linear, non-iterative, and volume-conserved scheme. This scheme is unconditionally energy stable and requires solving only four linear second-order elliptic equations with constant coefficients. We further prove energy stability and present numerous 2D and 3D numerical simulations to show accuracy and stability. (C) 2019 Elsevier B.V. All rights reserved.