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| Format: | Preprint |
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2020
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| Online Access: | https://arxiv.org/abs/2004.07022 |
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| _version_ | 1866914202072907776 |
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| author | Suárez-Grau, Francisco J. |
| author_facet | Suárez-Grau, Francisco J. |
| contents | In this paper we study stationary incompressible Newtonian fluid flow in a thin porous media. The media under consideration is a bounded perforated $3D$ domain confined between two parallel plates. The description of the domain includes two small parameters: $\varepsilon$ representing the distance between pates and $a_\varepsilon$ connected to the microstructure of the domain such that $a_\varepsilon\ll \varepsilon$. We consider the classical setting of perforated media, i.e. $a_\varepsilon$-periodically distributed solid (not connected) obstacles of size $a_\varepsilon$. The goal of this paper is to introduce a version of the unfolding method, depending on both parameters $\varepsilon$ and $a_\varepsilon$, and then to derive the corresponding $2D$ Darcy's law. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2004_07022 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Theoretical derivation of Darcy's law for fluid flow in thin porous media Suárez-Grau, Francisco J. Analysis of PDEs 76A20, 76M50, 35B27, 35Q30 In this paper we study stationary incompressible Newtonian fluid flow in a thin porous media. The media under consideration is a bounded perforated $3D$ domain confined between two parallel plates. The description of the domain includes two small parameters: $\varepsilon$ representing the distance between pates and $a_\varepsilon$ connected to the microstructure of the domain such that $a_\varepsilon\ll \varepsilon$. We consider the classical setting of perforated media, i.e. $a_\varepsilon$-periodically distributed solid (not connected) obstacles of size $a_\varepsilon$. The goal of this paper is to introduce a version of the unfolding method, depending on both parameters $\varepsilon$ and $a_\varepsilon$, and then to derive the corresponding $2D$ Darcy's law. |
| title | Theoretical derivation of Darcy's law for fluid flow in thin porous media |
| topic | Analysis of PDEs 76A20, 76M50, 35B27, 35Q30 |
| url | https://arxiv.org/abs/2004.07022 |