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| Auteurs principaux: | , |
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| Format: | Preprint |
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2023
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| Accès en ligne: | https://arxiv.org/abs/2308.03474 |
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| _version_ | 1866909088973062144 |
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| author | Hörl, Maximilian Rohde, Christian |
| author_facet | Hörl, Maximilian Rohde, Christian |
| contents | We consider single-phase flow in a fractured porous medium governed by Darcy's law with spatially varying hydraulic conductivity matrices in both bulk and fractures. The width-to-length ratio of a fracture is of the order of a small parameter $\varepsilon$ and the ratio $K_\mathrm{f}^\star / K_\mathrm{b}^\star$ of the characteristic hydraulic conductivities in the fracture and bulk domains is assumed to scale with $\varepsilon^α$ for a parameter $α\in \mathbb{R}$. The fracture geometry is parameterized by aperture functions on a submanifold of codimension one. Given a fracture, we derive the limit models as $\varepsilon \rightarrow 0$. Depending on the value of $α$, we obtain five different limit models as $\varepsilon \rightarrow 0$, for which we present rigorous convergence results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_03474 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Rigorous Derivation of Discrete Fracture Models for Darcy Flow in the Limit of Vanishing Aperture Hörl, Maximilian Rohde, Christian Analysis of PDEs 76S05, 58J90, 35Q35, 35B40 We consider single-phase flow in a fractured porous medium governed by Darcy's law with spatially varying hydraulic conductivity matrices in both bulk and fractures. The width-to-length ratio of a fracture is of the order of a small parameter $\varepsilon$ and the ratio $K_\mathrm{f}^\star / K_\mathrm{b}^\star$ of the characteristic hydraulic conductivities in the fracture and bulk domains is assumed to scale with $\varepsilon^α$ for a parameter $α\in \mathbb{R}$. The fracture geometry is parameterized by aperture functions on a submanifold of codimension one. Given a fracture, we derive the limit models as $\varepsilon \rightarrow 0$. Depending on the value of $α$, we obtain five different limit models as $\varepsilon \rightarrow 0$, for which we present rigorous convergence results. |
| title | Rigorous Derivation of Discrete Fracture Models for Darcy Flow in the Limit of Vanishing Aperture |
| topic | Analysis of PDEs 76S05, 58J90, 35Q35, 35B40 |
| url | https://arxiv.org/abs/2308.03474 |