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On a Dirichlet problem for the Darcy-Forchheimer-Brinkman system with application to lid-driven porous cavity flow with internal square block

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  • Papuc, Ioan

Abstract

In this paper we are concerned with both theoretical and numerical study of a Dirichlet boundary value problem for the nonlinear Darcy-Forchheimer-Brinkman system on a bounded Lipschitz domain in Rn(n=2,3). Using the potential theory technique we obtain a well-posed theorem which implies the existence and uniqueness of a weak solution for the aforementioned Dirichlet problem when the boundary data belongs to a L2-based Sobolev space. A numerical investigation of the flow of a viscous fluid through a two dimensional lid-driven porous cavity with a solid square block is performed. The effect of the dimension and position of the internal obstacle on the flow behaviour is analysed.

Suggested Citation

  • Papuc, Ioan, 2021. "On a Dirichlet problem for the Darcy-Forchheimer-Brinkman system with application to lid-driven porous cavity flow with internal square block," Applied Mathematics and Computation, Elsevier, vol. 402(C).
    • Handle: RePEc:eee:apmaco:v:402:y:2021:i:c:s0096300320308596
    DOI: 10.1016/j.amc.2020.125906
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    1. Gutt, Robert & Groşan, Teodor, 2015. "On the lid-driven problem in a porous cavity. A theoretical and numerical approach," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 1070-1082.
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