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Anisotropic Problem of Darcy Convection: Family of Steady Flows and Its Disintegration during the Destruction of Cosymmetry

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Fluid convection in a porous rectangle is analyzed on the basis of the Darcy model with regard to anisotropy of the thermal characteristics and the permeability. Relations between the parameters for which the problem belongs to the class of cosymmetric systems are obtained. In this case explicit formulas for the critical numbers of the loss of stability of mechanical equilibrium are derived. Using a finite-difference method that retains the cosymmetry of the problem, families of steady convective regimes are calculated. The destruction of these families is demonstrated by means of the computational experiment in the case of violation of the cosymmetry conditions leading to appearance of a finite number of stationary regimes.

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Correspondence to M. A. Abdelhafez.

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Original Russian Text © M.A. Abdelhafez, V.G. Tsybulin, 2018, published in Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, 2018, No. 6, pp. 19–29.

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Abdelhafez, M.A., Tsybulin, V.G. Anisotropic Problem of Darcy Convection: Family of Steady Flows and Its Disintegration during the Destruction of Cosymmetry. Fluid Dyn 53, 738–749 (2018).

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