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报告题目：A coupled multi-physics model and a decoupled stabilized finite element method for closed-loop geothermal system

报告人：何晓明 教授 美国密苏里科技大学

邀请人：董灏

报告时间：2024年7月13日(星期六)下午2:30-5:30

报告地点：235会议室（行政辅楼）

报告人简介：何晓明,美国密苏里科技大学教授。2002年与2005年在四川大学数学学院分别获学士与硕士学位, 2009年在弗吉尼亚理工大学数学系获博士学位, 2009年至 2010年在佛罗里达州立大学作博士后。2010年至今在美国密苏里科技大学任教, 2021年晋升为正教授。2018年获得Humboldt Research Fellowship for Experienced Researchers。担任计算数学领域国际期刊International Journal of Numerical Analysis & Modeling的Managing editor。何晓明教授主要的研究领域是计算科学与工程, 研究问题主要包括界面问题, 计算流体力学, 计算电磁学, 有限元方法, 各类解耦算法, 数据同化, 随机偏微分方程, 控制问题等, 在科学计算和应用领域做了大量的工作, 在SIAM Journal on Scientific Computing, SIAM Journal on Numerical Analysis, Mathematics of Computation, Numerische Mathematik, Journal of Computational Physics, Computer Methods in Applied Mechanics and Engineering, IEEE Transactions on Plasma Science, Computational Materials Science等杂志发表论文 100 余篇。

报告摘要：We propose and analyze a new coupled multi-physics model and a decoupled stabilized finite element method for the closed-loop geothermal system, which mainly consists of a network of underground heat exchange pipelines to extract the geothermal heat from the geothermal reservoir. The new mathematical model considers the heat transfer between two different flow regions, namely the porous media flow in the geothermal reservoir and the free flow in the pipes. Darcy's law and Navier-Stokes equations are considered to govern the flows in these two regions, respectively, while the heat equation is coupled with the flow equations to describe the heat transfer in both regions. Furthermore, on the interface between the two regions, four physically valid interface conditions are considered to describe the continuity of the temperature and the heat flux as well as the no-fluid-communication feature of the closed-loop geothermal system. In the variational formulation, an interface stabilization term with a penalty parameter is added to overcome the difficulty of the possible numerical instability arising from the interface conditions in the finite element discretization. To solve the proposed model accurately and efficiently, we develop a stabilized decoupled finite element method which decouples not only the two flow regions but also the heat field and the flow field in each region. The stability of the proposed method is proved. Numerical experiments are provided to demonstrate the applicability of the proposed model and the accuracy of the numerical method.

主办单位：数学与统计学院