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.

中文翻译：

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用于两相不可压缩流的相场模型的二阶线性无条件稳定的Crank-Nicolson-Leapfrog方案

在本文中，我们提出了基于Crank-Nicolson-Leapfrog离散化和人工压缩方法的二阶，线性，无条件稳定，隐式-显式方案，用于求解两相不可压缩流的相场模型。我们表明该方案是无条件的长期稳定。提供了数值示例来证明其准确性和长期稳定性。