Analysis of a FEM-MCM Discretization for the 2D/3D stochastic closed-loop geothermal system
Numerical Analysis
2024-10-14 v2 Numerical Analysis
Analysis of PDEs
Abstract
This paper develops a new 2D/3D stochastic closed-loop geothermal system with a random hydraulic conductivity tensor. We use the finite element method (FEM) and the Monte Carlo method (MCM) to discrete physical and probability spaces, respectively. This FEM-MCM method is effective. The stability for velocity and temperature is rigorously proved. Compared with the deterministic closed-loop geothermal system, a same optimal error estimate for approximate velocity and temperature is obtained. Furthermore, a series of numerical experiments were carried out to show this method has better stability and accuracy results.
Keywords
Cite
@article{arxiv.2304.11849,
title = {Analysis of a FEM-MCM Discretization for the 2D/3D stochastic closed-loop geothermal system},
author = {Yi Qin and Xinyue Gao and Lele Chen and Liangliang Jiang and Zhangxin Chen and Jian Li},
journal= {arXiv preprint arXiv:2304.11849},
year = {2024}
}
Comments
26 pages,25 figures