Staggered grids for three-dimensional convection of a multicomponent fluid in a porous medium

2012-09-01
Karasözen, Bülent
Tsybulin, Vyacheslav G.
Convection in a porous medium may produce strong nonuniqueness of patterns. we study this phenomena for the case of a multicomponent fluid and develop a mimetic finite-difference scheme for the three-dimensional problem. Discretization of the Darcy equations in the primitive variables is based on staggered grids with five types of nodes and on a special approximation of nonlinear terms. This scheme is applied to the computer study of flows in a porous parallelepiped filled by a two-component fluid and with two adiabatic lateral planes. We found that the continuous family of steady stable states exists in the case of a rather thin enclosure. When the depth is increased, only isolated convective regimes may be stable. We demonstrate that the non-mimetic approximation of nonlinear terms leads to the destruction of the continuous family of steady states.
COMPUTERS & MATHEMATICS WITH APPLICATIONS

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Citation Formats
B. Karasözen and V. G. Tsybulin, “Staggered grids for three-dimensional convection of a multicomponent fluid in a porous medium,” COMPUTERS & MATHEMATICS WITH APPLICATIONS, pp. 1740–1751, 2012, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/31592.