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arXiv · 2003.04812

On the limit of a two-phase flow problem in thin porous media domains of Brinkman-type

Alaa Armiti-Juber
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Abstract

We study the process of two-phase flow in thin porous media domains of Brinkman-type. This is generally described by a model of coupled, mixed-type differential equations of fluids' saturation and pressure. To reduce the model complexity, different approaches that utilize the thin geometry of the domain have been suggested. We focus on a reduced model that is formulated as a single nonlocal evolution equation of saturation. It is derived by applying standard asymptotic analysis to the dimensionless coupled model, however, a rigid mathematical derivation is still lacking. In this paper, we prove that the reduced model is the analytical limit of the coupled two-phase flow model as the geometrical parameter of domain's width--length ratio tends to zero. Precisely, we prove the convergence of weak solutions for the coupled model to a weak solution for the reduced model as the geometrical parameter approaches zero.

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Alaa Armiti-Juber. 2020-03-10. On the limit of a two-phase flow problem in thin porous media domains of Brinkman-type. https://arxiv.org/abs/2003.04812

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