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Destruction of the family of steady states in the planar problem of Darcy convection
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Date
2008-08-25
Author
Tsybulin, V. G.
Karasözen, Bülent
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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 under different perturbations of boundary conditions (heat sources, infiltration). Two scenario of the family of equilibria are found: the transformation to a limit cycle and the formation of isolated convective patterns.
Subject Keywords
Darcy convection
,
Porous medium
,
Families of equilibria
,
Cosymmetry
,
Finite-difference method
URI
https://hdl.handle.net/11511/30540
Journal
PHYSICS LETTERS A
DOI
https://doi.org/10.1016/j.physleta.2008.07.006
Collections
Graduate School of Applied Mathematics, Article
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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.
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V. G. Tsybulin and B. Karasözen, “Destruction of the family of steady states in the planar problem of Darcy convection,”
PHYSICS LETTERS A
, pp. 5639–5643, 2008, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/30540.