Numerical methods for the moving contact line problem with application on simulating two-phase flow in a coupled region
A numerical method is designed for a phase field model for the moving contact line problem, which consists of a coupled system of the Cahn-Hilliard and Navier-Stokes equations with the generalized Navier boundary condition. In this method, the system is solved in a decoupled way. For the Cahn-Hilliard equations, a convex splitting scheme is used along with a P1-P1 finite element discretization. A linearized semi-implicit P2-P0 mixed finite element method is employed to solve the Navier-Stokes equations. With the help of this method, we study two-phase fluid flow in coupled free flow and porous media regions. The model consists of coupled Cahn-Hilliard and Navier-Stokes equations in the free fluid region and the two-phase Darcy law in the porous medium region. We propose a Robin-Robin domain decomposition method for the coupled Navier-Stokes and Darcy system with the generalized Beavers-Joseph-Saffman condition on the interface between the free flow and the porous media regions. Numerical examples are presented to illustrate the effectiveness of this method.
主讲人Dr Jie Chen
Dr. Chen received his Ph.D. from Nanyang Technological University in 2011. Then he worked in the department of Mathematics of Hong Kong University of Science and Technology as a postdoc. He joined Xi’an Jiaotong University in 2013 and now he is an Associate Professor in School of Mathematics and Statistics in Xi’an Jiaotong University.