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Staggered grids for three-dimensional convection of a multicomponent fluid in a porous medium
Date
2012-09-01
Author
Karasözen, Bülent
Tsybulin, Vyacheslav G.
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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.
Subject Keywords
Convective patterns
,
Darcy law
,
Cosymmetry
,
Finite-differences
,
Staggered grids
,
Multicomponent fluid
URI
https://hdl.handle.net/11511/31592
Journal
COMPUTERS & MATHEMATICS WITH APPLICATIONS
DOI
https://doi.org/10.1016/j.camwa.2012.02.007
Collections
Graduate School of Applied Mathematics, Article
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Cosymmetric families of steady states in Darcy convection and their collision
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The planar natural convection of an incompressible fluid in a porous medium is considered. We study the selection of steady states under temperature perturbations on the boundary. A selection map is introduced in order to analyze the selection of a steady state from a continuous family of equilibria which exists under zero boundary conditions. The results of finite-difference modeling for a rectangular enclosure are presented.
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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.