学术报告

报告人：梅立泉教授 （西安交通大学）

报告题目：Energy Stable Finite Element Method for the Multi-phase Fluid Flow Coupling Model in Different Media Regions

报告时间：10月25日（星期五）10:30-11:30

报告地点：25教18楼报告厅

参加人员：教师、研究生、本科生

报告摘要：We discuss the numerical approximation for the coupling model of fluid flow between fluid region and porous media. This model has been widely used in many fields of science and engineering. 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 need only solve a linear elliptic system for each of the two decoupled equations. Stability of the model and the proposed method is rigorously proved. Numerical experiments are presented to illustrate the features of the proposed numerical method and verify the theoretical conclusions.

报告人简介：梅立泉，生于1969年12月，1997年获得计算数学专业博士学位，现为西安交通大学数学与统计学院教授、博士生导师。中国核学会计算物理学会第5届、第6届理事。主要研究方向：偏微分方程数值解、计算物理、数据挖掘。主持国家自然科学基金4项、973项目子专题1项，共主持参加科研项目11项，获欧洲专利、德国专利两项；已发表学术论文130多篇，其中在“SIAM J. Sci. Comput.”、 “J. Comput. Phys.”、 “Appl. Math. Model.”、“Appl. Math. Lett.”、“Comput. Phys. Commun.”、 “Annals of Phys.”、“Plasma Sources Sci. Tech.”、“Plasma Phys. Cont. Fusion”、“Appl. Math. Comput.”、“Appl. Numer. Math.”、“Comput. Math. Appl.”、 “Phys. Plasmas”、“Phys. Lett. A”等国际知名期刊上发表SCI论文82篇，ESI高被引论文2篇，研究成果被他人多次引用，单篇最高SCI他引138次。