Unconditionally energy-stable decoupled schemes for binary phase field crystal models using staggered temporal grids

Abstract

[1] The binary phase field crystal (BPFC) model has been widely used to study alloy systems and material mixtures. However, most existing energy-stable numerical schemes for the BPFC model require solving coupled nonlinear systems at every time step, which are computationally expensive and often face convergence issues. Moreover, the existence and uniqueness of solutions to these numerical schemes often have strict restrictions on the time step size. To address these issues, we propose a novel, fully decoupled, unconditionally energy-stable time integration scheme for the BPFC model. The key idea is to discretize the two phase field variables on staggered temporal grids, with one on an integer mesh and the other on a half-integer (staggered) mesh. We rigorously prove its unconditional energy stability and verify its second-order accuracy through numerical convergence tests. Numerical simulations demonstrate the robustness and efficiency of the proposed scheme.