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Mimetic discretization of two-dimensional Darcy convection

We consider discretization of the planar convection of the incompressible fluid in a porous medium filling rectangular enclosure. This problem belongs to the class of cosymmetric systems and admits an existence of a continuous family of steady states in the phase space. Mimetic finite-difference schemes for the primitive variables equation are developed. The connection of a derived staggered discretization with a finite-difference approach based on the stream function and temperature equations is established. Computations of continuous cosymmetric families of steady states are presented for the case of uniform and nonuniform grids. (c) 2005 Elsevier B.V. All rights reserved.