论文标题
无感应磁流体动力相位模型的脱钩，线性，无条件的能量稳定和电荷保守的有限元方法
Decoupled, linear, unconditionally energy stable and charge-conservative finite element method for a inductionless magnetohydrodynamic phase-field model
论文作者
论文摘要
在本文中，我们考虑了两相不可压缩的无感应磁性流体动力学问题的扩散界面模型的数值近似。该模型由Cahn-Hilliard方程，Navier-Stokes方程和泊松方程组成。我们提出了一种线性和脱钩的有限元方法，以解决这种高度非线性和多物理系统。在时间变量中，离散化是一阶欧拉半平方法，几种一阶稳定项和耦合项的隐式解释处理的组合。对于空间变量，我们采用有限元离散化，尤其是我们通过Inf-Sup稳定面积混合有限元对近似于电流密度和电势。使用这些技术，该方案仅涉及一系列分离的线性方程，以在每个时间步骤求解。我们表明该方案可证明是质量保守，电荷保守和无条件能量稳定的。进行数值实验以说明所提出方案的特征，准确性和效率。
In this paper, we consider the numerical approximation for a diffuse interface model of the two-phase incompressible inductionless magnetohydrodynamics problem. This model consists of Cahn-Hilliard equations, Navier-Stokes equations and Poisson equation. We propose a linear and decoupled finite element method to solve this highly nonlinear and multi-physics system. For the time variable, the discretization is a combination of first-order Euler semi-implicit scheme, several first-order stabilization terms and implicit-explicit treatments for coupling terms. For the space variables, we adopt the finite element discretization, especially, we approximate the current density and electric potential by inf-sup stable face-volume mixed finite element pairs. With these techniques, the scheme only involves a sequence of decoupled linear equations to solve at each time step. We show that the scheme is provably mass-conservative, charge-conservative and unconditionally energy stable. Numerical experiments are performed to illustrate the features, accuracy and efficiency of the proposed scheme.
