Upscaling of unsaturated flow in fractured porous media
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2018
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| _version_ | 1866914999655464960 |
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| author | List, Florian Kumar, Kundan Pop, Iuliu Sorin Radu, Florin A. |
| author_facet | List, Florian Kumar, Kundan Pop, Iuliu Sorin Radu, Florin A. |
| contents | In this work, we consider a mathematical model for flow in a unsaturated porous medium containing a fracture. In all subdomains (the fracture and the adjacent matrix blocks) the flow is governed by Richards' equation. The submodels are coupled by physical transmission conditions expressing the continuity of the normal fluxes and of the pressures. We start by analyzing the case of a fracture having a fixed width-length ratio, called $\varepsilon > 0$. Then we take the limit $\varepsilon \to 0$ and give a rigorous proof for the convergence towards effective models. This is done in different regimes, depending on how the ratio of porosities and permeabilities in the fracture, respectively matrix scale with respect to $\varepsilon$, and leads to a variety of effective models. Numerical simulations confirm the theoretical upscaling results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1807_05993 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Upscaling of unsaturated flow in fractured porous media List, Florian Kumar, Kundan Pop, Iuliu Sorin Radu, Florin A. Numerical Analysis In this work, we consider a mathematical model for flow in a unsaturated porous medium containing a fracture. In all subdomains (the fracture and the adjacent matrix blocks) the flow is governed by Richards' equation. The submodels are coupled by physical transmission conditions expressing the continuity of the normal fluxes and of the pressures. We start by analyzing the case of a fracture having a fixed width-length ratio, called $\varepsilon > 0$. Then we take the limit $\varepsilon \to 0$ and give a rigorous proof for the convergence towards effective models. This is done in different regimes, depending on how the ratio of porosities and permeabilities in the fracture, respectively matrix scale with respect to $\varepsilon$, and leads to a variety of effective models. Numerical simulations confirm the theoretical upscaling results. |
| title | Upscaling of unsaturated flow in fractured porous media |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/1807.05993 |