Mimetic discretization of two-dimensional Darcy convection

Date

2005-05-01

Author

Karasözen, Bülent

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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.

Subject Keywords

Convection, Porous medium, Darcy law, Cosymmetry, Finite-difference method, Staggered grid, Family of equilibria

URI

https://hdl.handle.net/11511/31191

Journal

COMPUTER PHYSICS COMMUNICATIONS

DOI

https://doi.org/10.1016/j.cpc.2004.12.012

Collections

Graduate School of Applied Mathematics, Article

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Staggered grids discretization in three-dimensional Darcy convection Karasözen, Bülent; Tsybulin, V. G. (2008-06-15) We consider three-dimensional convection of an incompressible fluid saturated in a parallelepiped with a porous medium. A mimetic finite-difference scheme for the Darcy convection problem in the primitive variables is developed. It consists of staggered nonuniform grids with five types of nodes, differencing and averaging operators on a two-nodes stencil. The nonlinear terms are approximated using special schemes. Two problems with different boundary conditions are considered to study scenarios of instabili...
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.
Destruction of the family of steady states in the planar problem of Darcy convection Tsybulin, V. G.; Karasözen, Bülent (2008-08-25) We consider natural convection of an incompressible fluid in a porous medium described by the planar Darcy equation. For some boundary conditions, Darcy problem may have non-unique solutions in form of a continuous family of steady states. We are interested in the situation when these boundary conditions are violated. The resulting destruction of the family of steady states is studied via computer experiments based on a mimetic finite-difference approach. Convection in a rectangular enclosure is considered ...
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, “Mimetic discretization of two-dimensional Darcy convection,” COMPUTER PHYSICS COMMUNICATIONS, pp. 203–213, 2005, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/31191.