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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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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...
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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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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.