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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Mimetic discretization of two-dimensional Darcy convection Karasözen, Bülent (2005-05-01) 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 establishe...
Cosymmetry preserving finite-difference methods for convection equations in a porous medium Karasözen, Bülent (2005-09-01) The finite-difference discretizations for the planar problem of natural convection of incompressible fluid in a porous medium which preserve the cosymmetry property and discrete symmetries are presented. The equations in stream function and temperature are computed using staggered and non-staggered schemes in uniform and nonuniform rectangular grids. (c) 2004 IMACS. Published by Elsevier B.V. All rights reserved.
Cosymmetric families of steady states in Darcy convection and their collision Karasözen, Bülent (2004-03-15) Natural planar convection of incompressible fluid in a porous medium, the Darcy model is studied. This problem belongs to the class of cosymmetric systems for whose an emergence of a continuous family of steady states (equilibria) is possible. We study the evolution of several families of steady states in the case of wide enclosure and analyze new effects of collision and reorganization of such families.
Selection of steady states in planar Darcy convection Tsybulin, V. G.; Karasözen, Bülent; Ergenc, I. (2006-08-07) 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.

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.