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





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.

报告学者简介: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2016年在美国密苏里科学技术大学任助理教授,2016年晋升为副教授并获终身教职,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。 从2012年起主持了多项由美国国家科学基金会和美国能源部资助的科研项目。2014-2016年担任SIAM美国中部分会的第一任主席和前两届年会的组织委员会主席。2019年起担任Midwest Numerical Analysis Day的组织委员成员。2021年1月起担任SIAM Committee on Programs and Conferences成员。2021年7月起担任密苏里科技大学Vice Chancellor of Research and Innovation办公室的Faculty Fellow。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。他将计算数学与实际工程应用问题结合起来,在科学计算和应用领域做了大量的工作,在SIAM Journal on Scientific Computing,Journal of Computational Physics,Computer Methods in Applied Mechanics and Engineering, SIAM Journal on Numerical Analysis, Mathematics of Computation,Numerische Mathematik,IEEE Transactions on Plasma Science, Lab on a Chip, Langmuir, Energy & Fuels, Computational Materials Science等杂志发表论文90余篇。