摘要：In this presentation, we discuss an efficient numerical approximation for a phase field model of the coupled two-phase free flow and two-phase porous media flow. This model consists of Cahn-Hilliard-Navier-Stokes equations in the free flow region and Cahn-Hilliard-Darcy equations in the porous media region that are coupled by seven interface conditions. The coupled system is decoupled based on the interface conditions and the solution values on the interface from the previous time step. A fully discretized scheme with finite elements for the spatial discretization is developed to solve the decoupled system. In order to deal with the difficulties arising from the interface conditions, the decoupled scheme needs to be constructed appropriately for the interface terms and a modified discrete energy is introduced with an interface component. Furthermore, the scheme is linearized and energy stable. Hence, at each time step one only needs to solve a linear elliptic system for each of the two decoupled equations. Stability of the model and the proposed method is proved. Numerical experiments are presented to illustrate the features of the proposed numerical method and verify the theoretical conclusions.
2005-2009 PhD at Virginia Tech
2009-2010 Postdoctoral research associate at Florida State University
2010-present Associate professor at Missouri University of Science & Technology.