A TWO-GRID DECOUPLED FINITE ELEMENT METHOD FOR THE STATIONARY CLOSED-LOOP GEOTHERMAL SYSTEM

Haochen Liu; Pengzhan Huang

doi:10.11948/20220258

2023 Volume 13 Issue 4

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Article navigation > Journal of Applied Analysis & Computation > 2023 > 13(4): 1837-1851

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Haochen Liu, Pengzhan Huang. A TWO-GRID DECOUPLED FINITE ELEMENT METHOD FOR THE STATIONARY CLOSED-LOOP GEOTHERMAL SYSTEM[J]. Journal of Applied Analysis & Computation, 2023, 13(4): 1837-1851. doi: 10.11948/20220258

Citation:

Haochen Liu, Pengzhan Huang. A TWO-GRID DECOUPLED FINITE ELEMENT METHOD FOR THE STATIONARY CLOSED-LOOP GEOTHERMAL SYSTEM[J]. Journal of Applied Analysis & Computation, 2023, 13(4): 1837-1851. doi: 10.11948/20220258

A TWO-GRID DECOUPLED FINITE ELEMENT METHOD FOR THE STATIONARY CLOSED-LOOP GEOTHERMAL SYSTEM

Haochen Liu^1,,
Pengzhan Huang^1, ,

1.
College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China

Author Bio: Email: liuhaochen@stu.xju.edu.cn(H. Liu)
Corresponding author: Email: hpzh@xju.edu.cn(P. Huang)
Fund Project: The authors were supported by the Natural Science Foundation of Xinjiang Province (No. 2021D01E11) and the Natural Science Foundation of China (No. 11861067)

Abstract

Abstract

A two-grid decoupled finite element method is proposed and analyzed for the stationary closed-loop geothermal model, which is coupled by the Navier-Stokes/Darcy equations and the heat equations with some interface conditions. The main idea of the proposed method is to solve the nonlinear problem on a coarse grid to obtain an initial approximation, then solve the decoupled, linear problem on a fine grid. Hence, the original problem is solved by two subsystems using the two-grid technique, which will save computational time. Moreover, the stability of the proposed method is proved, and numerical examples are presented.
- Closed-loop geothermal model /
- finite element method /
- two-grid algorithm /
- decoupled strategy
MSC: 65N30, 35Q35

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References

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