Analysis of a FEM-MCM Discretization for the 2D/3D stochastic closed-loop geothermal system

04/24/2023

∙

by   Jian Li, et al.

∙

0

∙

share

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.