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Numerical simulation of convective motion in an anisotropic porous medium and cosymmetry conservation

Computational Mathematics and Mathematical Physics volume 57, pages 1706–1719 (2017)Cite this article

Abstract

The onset of convection in a porous anisotropic rectangle occupied by a heat-conducting fluid heated from below is analyzed on the basis of the Darcy–Boussinesq model. It is shown that there are combinations of control parameters for which the system has a nontrivial cosymmetry and a one-parameter family of stationary convective regimes branches off from the mechanical equilibrium. For the two-dimensional convection equations in a porous medium, finite-difference approximations preserving the cosymmetry of the original system are developed. Numerical results are presented that demonstrate the formation of a family of convective regimes and its disappearance when the approximations do not inherit the cosymmetry property.

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Authors and Affiliations

  1. Southern Federal University, Rostov-on-Don, 344090, Russia

    M. A. Abdelhafez & V. G. Tsybulin

  2. Sohag University, Sohag, 82524, Arab Republic of Egypt

    M. A. Abdelhafez

Authors
  1. M. A. Abdelhafez
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  2. V. G. Tsybulin
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Correspondence to M. A. Abdelhafez.

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Original Russian Text © M.A. Abdelhafez, V.G. Tsybulin, 2017, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2017, Vol. 57, No. 10, pp. 1734–1748.

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Abdelhafez, M.A., Tsybulin, V.G. Numerical simulation of convective motion in an anisotropic porous medium and cosymmetry conservation. Comput. Math. and Math. Phys. 57, 1706–1719 (2017). https://doi.org/10.1134/S0965542517100025

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  • DOI: https://doi.org/10.1134/S0965542517100025

Keywords

  • convection
  • porous medium
  • anisotropy
  • cosymmetry
  • finite-difference method
  • staggered grids