报告题目：Numerical methods for coupled Stokes-Darcy flows with transport

报 告 人：芮洪兴教授（山东大学）

报告时间：2024年9月2日  10:30

报告地点：格物楼数学研究中心528报告厅

报告摘要：

Recent years, there is a intense research in building suitable mathematical and numerical models for coupled flows with a porous medium (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 problems where just velocity and pressure appear in the models. The models describing solute transport in the coupled Stokes and Dary regions appear in a variety of physical phenomena. There are several works to study the existence and stability of the weak solution with viscosity-depending component concentration. The purpose of this talk is to present the numerical methods for the coupled Stokes-Darcy problem with solute transport. We present the model, a weak formulation and then construct mixed finite element methods for the coupled flow problem using the nonconforming 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 finite element method for the coupled problems.

报告人简介：

芮洪兴，山东大学数学学院教授、博士生导师。中国工业与应用数学学会常务理事、中国计算物理学会常务理事，曾任中国计算数学学会常务理事。主要从事偏微分方程数值解法、科学与工程计算、渗流力学、油水资源数值模拟方法及应用软件开发等计算数学与应用数学研究。在有限元方法、混合元方法、有限体积元方法、特征线算法、区域分裂及并行算法、以及油水资源数值模拟方法研究方面发表论文150余篇，其中SCI收录100余篇。近年来芮洪兴教授承担、参与国家自然科学基金重大研究计划培育项目国家重点项目、面上项目、教育部博士点项目、科技部重大专项、中石化课题等20余项，先后获得山东省高校自然科学一等奖（2003）、山东省科学技术奖自然科学二等奖（2015）；并作为主要完成人获教育部自然科学一等奖（2003）、水利部科技进步三等奖（1998）、国家教委科技进步二等奖（1997）各一项。