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On the Darcy–Brinkman Flow Through a Channel with Slightly Perturbed Boundary

Transport in Porous Media volume 117, pages 27–44 (2017)Cite this article

Abstract

The goal of this paper is to study the effects of a slightly perturbed boundary on the Darcy–Brinkman flow through a porous channel. We start from a rectangular domain and then perturb the upper part of its boundary by the product of the small parameter \(\epsilon \) and arbitrary smooth function h. Using asymptotic analysis with respect to \(\epsilon \), the effective model has been formally derived. Being in the form of the explicit formulae for the velocity and pressure, the asymptotic approximation clearly shows the nonlocal effects of the small boundary perturbation. The error analysis is also conducted providing the order of accuracy of the asymptotic solution.

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Acknowledgements

The authors have been supported by the Croatian Science Foundation (Project 3955: Mathematical modeling and numerical simulations of processes in thin or porous domains). The authors would like to thank the referee for his/her comments and suggestions that helped to significantly improve the paper.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, University of Zagreb, Bijenička 30, 10000, Zagreb, Croatia

    Eduard Marušić-Paloka & Igor Pažanin

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  1. Eduard Marušić-Paloka
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  2. Igor Pažanin
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Correspondence to Igor Pažanin.

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Marušić-Paloka, E., Pažanin, I. On the Darcy–Brinkman Flow Through a Channel with Slightly Perturbed Boundary. Transp Porous Med 117, 27–44 (2017). https://doi.org/10.1007/s11242-016-0818-4

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  • DOI: https://doi.org/10.1007/s11242-016-0818-4

Keywords

  • Boundary perturbation
  • Darcy–Brinkman equation
  • Asymptotic approximation
  • Error estimates