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,我们提议采用基于Crank-Nicolson跳跃-分流时间分解的第二种顺序,即线性、无条件稳定的分解方法,以解决Allen-Cahn-Navier-Stokes两阶段压抑性流动的相位模型。ACNS系统通过人工压缩法和分解法分解法分解,引入一个指数式的星标辅助变量。我们证明这两种算法都是无条件长期稳定的。我们提供了数字实例,以核实汇合率和无条件的稳定。