A Darcy law with memory by homogenisation for evolving microstructure
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914712817500160 |
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| author | Wiedemann, David Peter, Malte A. |
| author_facet | Wiedemann, David Peter, Malte A. |
| contents | We consider the homogenisation of the instationary Stokes equations in a porous medium with an a-priori given evolving microstructure. In order to pass to the homogenisation limit, we transform the Stokes equations to a domain with a fixed periodic microstructure. The homogenisation result is a Darcy-type equation with memory term and has the form of an integro-differential equation. The evolving microstructure leads to a time and space dependent permeability coefficient and the local change of the porosity causes an additional source term for the pressure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_08166 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Darcy law with memory by homogenisation for evolving microstructure Wiedemann, David Peter, Malte A. Analysis of PDEs 76M50, 35B27, 76S05, 35R37, 76D07 We consider the homogenisation of the instationary Stokes equations in a porous medium with an a-priori given evolving microstructure. In order to pass to the homogenisation limit, we transform the Stokes equations to a domain with a fixed periodic microstructure. The homogenisation result is a Darcy-type equation with memory term and has the form of an integro-differential equation. The evolving microstructure leads to a time and space dependent permeability coefficient and the local change of the porosity causes an additional source term for the pressure. |
| title | A Darcy law with memory by homogenisation for evolving microstructure |
| topic | Analysis of PDEs 76M50, 35B27, 76S05, 35R37, 76D07 |
| url | https://arxiv.org/abs/2403.08166 |