In this paper, we analyze the numerical approximation of two-phase magnetohydrodynamic flows. Firstly, an equivalent new system is designed by introducing two scalar auxiliary variables. One of variables is used to linearize the phase field function and the other is used to deal with the highly coupled and nonlinear terms. Secondly, by combining with a novel decoupling technique based on the “zero-energy-contribution” feature and the pressure correction method, the linearized second order BDF numerical scheme, which has the advantage of fully decoupled structure, is constructed. Furthermore, we strictly prove the unconditional energy stability and error analysis of the scheme, and give a detailed implementation procedure that only requires to calculate several linear elliptic equations with constant coefficients. Finally, the results of numerical simulations are presented to validate the rates of convergence and energy stability.

中文翻译：

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两相磁流体动力流的完全解耦线性化二阶精确数值格式

在本文中，我们分析了两相磁流体动力流的数值近似。首先，通过引入两个标量辅助变量设计了一个等效的新系统。其中一个变量用于线性化相场函数，另一个变量用于处理高度耦合和非线性项。其次，结合基于“零能量贡献”特征的新型解耦技术和压力修正方法，构建了具有完全解耦结构优点的线性化二阶BDF数值格式。此外，我们严格证明了该方案的无条件能量稳定性和误差分析，并给出了仅需要计算几个常系数线性椭圆方程的详细实现过程。最后，给出了数值模拟的结果来验证收敛速度和能量稳定性。