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Homogenization of the Darcy–Lapwood–Brinkman Flow in a Thin Domain with Highly Oscillating Boundaries

Bulletin of the Malaysian Mathematical Sciences Society volume 42, pages 3073–3109 (2019)Cite this article

Abstract

In this paper, we investigate the flow through a thin corrugated domain filled with fluid-saturated porous medium. The porous medium flow is described by the nonlinear Darcy–Lapwood–Brinkman model acknowledging the viscous shear and the inertial effects. The thickness of the domain is assumed to be of the same small order \(\varepsilon \) as the period of the oscillating boundaries. Depending on the magnitude of the permeability with respect to \(\varepsilon \), we rigorously derive different asymptotic models and compare the results with the non-oscillatory case. We employ a homogenization technique based on the adaption of the unfolding method and deduce the influence of the porous structure and boundary oscillations on the effective flow.

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Authors and Affiliations

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

    Igor Pažanin

  2. Departamento de Ecuaciones Diferenciales y Análisis Numérico, Facultad de Matemáticas, Universidad de Sevilla, 41012, Sevilla, Spain

    Francisco Javier Suárez-Grau

Authors
  1. Igor Pažanin
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  2. Francisco Javier Suárez-Grau
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Corresponding author

Correspondence to Francisco Javier Suárez-Grau.

Additional information

Communicated by Yong Zhou.

I. Pažanin: The first author of this paper has been supported by the Croatian Science Foundation (Project 3955: Mathematical modeling and numerical simulations of processes in thin or porous domains). F. J. Suárez-Grau: The second author of this paper has been supported by Ministerio de Economía y Competitividad (Spain), Proyecto Excelencia MTM2014-53309-P.

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Pažanin, I., Suárez-Grau, F.J. Homogenization of the Darcy–Lapwood–Brinkman Flow in a Thin Domain with Highly Oscillating Boundaries. Bull. Malays. Math. Sci. Soc. 42, 3073–3109 (2019). https://doi.org/10.1007/s40840-018-0649-2

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  • DOI: https://doi.org/10.1007/s40840-018-0649-2

Keywords

  • Darcy–Lapwood–Brinkman equation
  • Thin domain
  • Highly oscillating boundary
  • Unfolding method

Mathematics Subject Classification

  • 35B27
  • 35B40
  • 76S05