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


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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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).

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