Analysis of a FEM-MCM Discretization for the 2D/3D stochastic closed-loop geothermal system
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866914969645219840 |
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| author | Qin, Yi Gao, Xinyue Chen, Lele Jiang, Liangliang Chen, Zhangxin Li, Jian |
| author_facet | Qin, Yi Gao, Xinyue Chen, Lele Jiang, Liangliang Chen, Zhangxin Li, Jian |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_11849 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Analysis of a FEM-MCM Discretization for the 2D/3D stochastic closed-loop geothermal system Qin, Yi Gao, Xinyue Chen, Lele Jiang, Liangliang Chen, Zhangxin Li, Jian Numerical Analysis Analysis of PDEs 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. |
| title | Analysis of a FEM-MCM Discretization for the 2D/3D stochastic closed-loop geothermal system |
| topic | Numerical Analysis Analysis of PDEs |
| url | https://arxiv.org/abs/2304.11849 |