题目：Modeling and numerical simulations of two-phase flow in karstic geometry
时间：2018 年 07 月 9 日（星期一）16：00-18：00
报告摘要： Multiphase flow phenomena are ubiquitous. In some applications such as flows in unconfined karst aquifers, karst oil reservoir, proton membrane exchange fuel cell, multiphase flows in conduits, and in porous media must be considered together. Geometric configurations that contain both conduit and porous media are termed karstic geometry. In this talk, we derive a diffuse interface model for two-phase flow in karstic geometry utilizing Onsager's extremum principle. The model together with the interface boundary conditions satisfies a physically important energy law. We show that the model admits a global finite-energy weak solution which agrees with the regular solution provided the regular solution exists. Then we present a decoupled unconditionally energy-stable numerical scheme for solving this diffuse interface model. Extensions to more general case will be discussed as well. 报告人简介： Dr. Han obtains his PhD in Applied and Computational Mathematics from the Florida State University in 2015, under the supervision of Prof. Xiaoming Wang. He then joins the Department of Mathematics at Indiana University as a Zorn postdoctoral fellow mentored by Prof. Roger Temam. Currently, Dr. Han works as a tenure-track assistant professor in Missouri University of Science and Technology. Dr. Han's research is centered around applied analysis, numerical analysis and computation of partial differential equations from fluid dynamics. In particular he is working on the mathematical validity of Prandtl boundary layer theory; modeling, analysis and numerical simulations of multiphase flow phenomena; and flow instabilities.