In this paper, we propose and analyze a diffuse interface model for inductionless magnetohydrodynamic fluids. The model couples a convective Cahn-Hilliard equation for the evolution of the interface, the Navier-Stokes system for fluid flow and the possion quation for electrostatics. The model is derived from Onsager's variational principle and conservation laws systematically. We perform formally matched asymptotic expansions and develop several sharp interface models in the limit when the interfacial thickness tends to zero. It is shown that the sharp interface limit of the models are the standard incompressible inductionless magnetohydrodynamic equations coupled with several different interface conditions for different choice of the mobilities. Numerical results verify the convergence of the diffuse interface model with different mobilitiess.

翻译：本文提出并分析了一种用于感应式无磁流体的扩散界面模型。该模型耦合了描述界面演化的对流Cahn-Hilliard方程、流体流动的Navier-Stokes系统以及静电学的Poisson方程。模型基于Onsager变分原理和守恒律系统推导得出。我们通过形式匹配渐近展开，在界面厚度趋近于零的极限情形下发展出多种尖锐界面模型。研究表明，这些模型的尖锐界面极限与标准不可压缩感应式无磁流体方程组耦合若干不同界面条件相对应，具体界面条件取决于迁移率的不同选取。数值结果验证了不同迁移率下扩散界面模型的收敛性。