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

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arxiv 2304.11849 v2 pith:DIHK2ZVZ submitted 2023-04-24 math.NA cs.NAmath.AP

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

Yi Qin , Xinyue Gao , Lele Chen , Liangliang Jiang , Zhangxin Chen , Jian Li This is my paper
classification math.NA cs.NAmath.AP
keywords methodclosed-loopgeothermalsystemfem-mcmstabilitystochastictemperature
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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.

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