A second order, linear, unconditionally stable, Crank–Nicolson–Leapfrog scheme for phase field models of two-phase incompressible flows

In this article we propose a second order, linear, unconditionally stable, implicit–explicit scheme based on the Crank–Nicolson–Leapfrog discretization and the artificial compression method for solving phase field models of two-phase incompressible flows. We show that the scheme is unconditionally long-time stable. Numerical examples are provided to demonstrate the accuracy and long-time stability.