SIAM Journal on Scientific Computing, Volume 42, Issue 4, Page B951-B982, January 2020.
The purpose of this article is to propose and analyze a new coupled multiphysics 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. Four numerical experiments are provided to demonstrate the applicability of the proposed model and the accuracy of the numerical method.

中文翻译：

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闭环地热系统的多物理场耦合模型和稳定有限元解耦方法

SIAM科学计算杂志，第42卷，第4期，第B951-B982页，2020年1月。
本文的目的是为闭环地热系统提出并分析一种新的耦合多物理场模型和一种解耦稳定有限元方法，该方法主要由地下热交换管道网络组成，用于从地热储层中提取地热。 。新的数学模型考虑了两个不同流动区域之间的热传递，即地热储层中的多孔介质流和管道中的自由流。分别考虑了达西定律和Navier-Stokes方程来控制这两个区域中的流动，而将热方程与流动方程耦合在一起来描述这两个区域中的热传递。此外，在两个区域之间的接口上，考虑了四个物理上有效的界面条件，以描述温度和热通量的连续性以及闭环地热系统的无流体连通特征。在变分公式中，添加了带有罚分参数的界面稳定项，以克服有限元离散化过程中由于界面条件引起的可能的数值不稳定的困难。为了准确有效地求解所提出的模型，我们开发了一种稳定的解耦有限元方法，该方法不仅解耦两个流动区域，而且还解耦了每个区域的热场和流场。证明了所提方法的稳定性。提供了四个数值实验，以证明所提出模型的适用性和数值方法的准确性。