题目：Recent advances on numerical modeling of two-phase flows in superposed free flow and porous media
报告人：韩道志教授（State University of New York at Buffalo）
In many applications such as contaminant transport in karst aquifers, oil recovery, proton exchange membrane fuel cell technology and cardiovascular modeling, multiphase flows in free flow and in porous media interact with each other, and therefore have to be considered together. In this talk we survey recent advances on the modeling and numerical methods for two-phase flows in superposed free flow and porous media. In particular we derive a quasi-incompressible Cahn-Hilliard diffuse interface model for fluids of mismatched densities. Some open problems in this direction will be discussed. Finally we will show how to establish optimal convergence rates of HDG method for Cahn-Hilliard equations avoiding exponential dependence on the inverse of interfacial width.
Dr. Daozhi Han is an assistant professor in the Department of Mathematics at State University of New York at Buffalo (UB). He obtained his Ph.D in Applied and Computational Math from Florida State University in 2015. Then he held a Zorn Postdoctoral Fellowship in the Department of Mathematics at Indiana University. Prior to joining UB, he was a tenure-track assistant professor at Missouri University of Science and Technology from 2017 to 2022. His research centers around applied analysis, particularly numerical analysis and numerical simulations of partial differential equations from fluid mechanics. His research has been supported by the National Science Foundation and the Simons Foundation.