Geodesic
Numerical simulation of convective motion in an anisotropic porous medium and cosymmetry conservation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 10, pp. 1734-1747

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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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     author = {M. A. Abdelhafez and V. G. Tsybulin},
     title = {Numerical simulation of convective motion in an anisotropic porous medium and cosymmetry conservation},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1734--1747},
     publisher = {mathdoc},
     volume = {57},
     number = {10},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_10_a10/}
}
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M. A. Abdelhafez; V. G. Tsybulin. Numerical simulation of convective motion in an anisotropic porous medium and cosymmetry conservation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 10, pp. 1734-1747. http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_10_a10/