勷勤数学•专家报告

题      目：Some Numerical methods for coupled Stokes-Darcy flow with transport

报  告  人：芮洪兴 教授  (邀请人：钟柳强)

                                   山东大学

时      间：4月15日  11：00-12：00

地     点：数科院西楼二楼会议室

报告人简介:

       芮洪兴，山东大学二级教授、博士生导师，主要从事偏微分方程数值方法、多孔介质渗流及流体的数值计算及应用研究。在SINUM，Numer Math，Math Comp，M3AS,CMAME，JCP，JFM等顶级期刊发表多篇高水平论文。主持国家自然科学基金重点项目等，曾获教育部自然科学二等奖，山东省自然科学二等奖、一等奖等。现任山东工业与应用数学学会副理事长、山东数学会计算数学专委会主任。曾任中国工业与应用数学学会常务理事兼油水资源数值方法专委会主任、中国计算数学学会常务理事等。

摘      要：

       Recent years, there is a intense research in building suitable mathematical and numerical models for coupled flows  with a porous medium region (Darcy) and a free fluid region (Stokes). Many kinds of numerical methods have been studied deeply. But most of them just consider the single component flow problem. The models describing solute transport in the coupled Stokes and Darcy regions appear in a variety of physical phenomena. The purpose of this talk is to present the numerical methods for the coupled Stokes-Darcy problem with solute transport where the fluid visoscity depending on the concentration. We present the model, a weak formulation and then construct mixed finite element methods for the coupled flow problem using the piecewise linear Crouzeix-Raviart element for the velocity and piecewise constant for pressure. And we use classical piecewise linear finite element for concentration. We also present a pressure-robust mixed finite element method for the coupled problems. Numerical analysis is presented for the constructed numerical methods

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