Academic Report No. 31: A coupled multi-physics model and a decoupled stabilized finite element method for closed-loop geothermal system
School of Mathematical Sciences Academic Report [2025] No. 031
(High-Level University Construction Series Report No. 1054)
Lecture Title: A coupled multi-physics model and a decoupled stabilized finite element method for closed-loop geothermal system
Speaker: Prof. He Xiaoming (Missouri University of Science and Technology)
Date & Time: 11:00 AM–12:00 PM, Wednesday, May 14, 2025
Venue: International Conference Hall A
Abstract: 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.
Additionally, this talk will introduce the graduate programs at Missouri University of Science and Technology (Missouri S&T) from the perspective of the school's research environment support for graduate students.
Biography: He Xiaoming is a professor at Missouri University of Science and Technology, USA. He received his bachelor's and master's degrees from the School of Mathematics, Sichuan University in 2002 and 2005, respectively, and his Ph.D. from the Department of Mathematics, Virginia Tech in 2009. He was a postdoctoral fellow at Florida State University from 2009 to 2010. From 2010 to 2016, he served as an assistant professor at Missouri University of Science and Technology, was promoted to associate professor with tenure in 2016, and became a full professor in 2021. He received the Humboldt Research Fellowship for Experienced Researchers in 2018. He serves as the Managing Editor of the international journal *International Journal of Numerical Analysis & Modeling* in the field of computational mathematics. Since 2012, he has led several research projects funded by the National Science Foundation of the United States and the U.S. Department of Energy. From 2014 to 2016, he served as the first president of the SIAM Central States Section and the chair of the organizing committee for the first two annual conferences. Since 2019, he has been a member of the organizing committee of Midwest Numerical Analysis Day. Since January 2021, he has been a member of the SIAM Committee on Programs and Conferences. Since July 2021, he has served as a Faculty Fellow in the Office of the Vice Chancellor of Research and Innovation at Missouri University of Science and Technology. Professor He Xiaoming's main research areas are computational science and engineering. His research topics include interface problems, computational fluid dynamics, computational electromagnetics, finite element methods, various decoupling algorithms, data assimilation, stochastic partial differential equations, and control problems. By combining computational mathematics with practical engineering applications, he has done a great deal of work in scientific computing and application fields. He has published more than 100 papers in journals such as 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, and Computational Materials Science.
All faculty and students are welcome to attend!
Invited by: He Haijin
School of Mathematical Sciences
April 30, 2025
