Hydrodynamics coupled phase field models have intricate difficulties to solve numerically as they feature high nonlinearity and great complexity in coupling. In this paper, we propose two second order, linear, unconditionally stable decoupling methods based on the Crank--Nicolson leap-frog time discretization for solving the Allen--Cahn--Navier--Stokes (ACNS) phase field model of two-phase incompressible flows. The ACNS system is decoupled via the artificial compression method and a splitting approach by introducing an exponential scalar auxiliary variable. We prove both algorithms are unconditionally long time stable. Numerical examples are provided to verify the convergence rate and unconditional stability.

翻译：水文动力学和相交场模型在数字上难以解决,因为它们具有高度非线性和高度复杂的结合。在本文件中,我们建议采用基于Crank-Nicolson跳跃分流时间分解法的第二种顺序,即线性、无条件稳定的分解方法,以解决Allen-Cahn-Navier-Stokes(ACNS)两阶段压缩流的相位模型。ACNS系统通过人工压缩法和分解法分解法分解。我们证明两种算法都无条件长期稳定。提供了数字实例,以核实汇合率和无条件稳定。