A new Allen–Cahn type two-model phase-field crystal model for fcc ordering and its numerical approximation

Abstract

In this paper, we derive a new Allen–Cahn type two-model phase-field crystal model based on the conserved L2-gradient flow approach to describe the face-centered-cubic (fcc) ordering. By adding a nonlocal Lagrange multiplier to the Allen–Cahn dynamics, the total mass conservation can be preserved precisely while satisfying the energy dissipation. This reduces the order of partial differential equations (PDEs) from ten to eight, thus avoids the difficulty of solving higher-order differential equations. Then, we develop efficient and unconditionally energy stable schemes using the stabilized-SAV approach. At each time step, the developed numerical schemes are reduced to decoupled constant-coefficient linear equations, and the unique solvability and unconditional energy stability are strictly proved. Numerical examples are carried out to numerically validate the accuracy and energy stability of the schemes.