Natural convection in porous annular domains: Mimetic scheme and family of steady states

Date

2012-04-01

Author

Karasözen, Bülent
Tsybulin, Vyacheslav G.

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Natural convection of the incompressible fluid in the porous media based on the Darcy hypothesis (Lapwood convection) gives an intriguing branching off of one-parameter family of steady patterns. This scenario may be suppressed in computations when governing equations are approximated by schemes which do not preserve the cosymmetry property. We consider the problem for the annular porous domain in polar coordinates and derive a mimetic finite-difference scheme. This scheme allows to compute the family of convective regimes accurately and to detect the instabilities on some parts of the family.

Subject Keywords

Natural convection, Darcy law, Porous medium, Mimetic scheme, Finite-difference method, Family of steady states, Cosymmetry

URI

https://hdl.handle.net/11511/30165

Journal

JOURNAL OF COMPUTATIONAL PHYSICS

DOI

https://doi.org/10.1016/j.jcp.2012.01.004

Collections

Graduate School of Applied Mathematics, Article

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Convection in a Porous Medium and Mimetic Scheme in Polar Coordinates Karasözen, Bülent; Tsybulin, Vyacheslav (2011-09-09) Analytical investigation of natural convection of the incompressible fluid in the porous media based on the Darcy hypothesis (Lapwood convection) gives intriguing branching off of one-parameter family of convective patterns. This scenario may be suppressed in computations when governing equations are approximated by schemes which do not preserve the cosymmetry property. We consider the problem in polar coordinates and construct a mimetic finite-difference scheme using computer algebra tools. The family of s...
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 ...
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...
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.
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.

Citation Formats

B. Karasözen and V. G. Tsybulin, “Natural convection in porous annular domains: Mimetic scheme and family of steady states,” JOURNAL OF COMPUTATIONAL PHYSICS, pp. 2995–3005, 2012, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/30165.