Convection in a Porous Medium and Mimetic Scheme in Polar Coordinates

Date

2011-09-09

Author

Karasözen, Bülent
Tsybulin, Vyacheslav

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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 steady states is computed and it is demonstrated that this family disappears under non-mimetic approximation.

Subject Keywords

Cosymmetry, Equations

URI

https://hdl.handle.net/11511/54114

Conference Name

13th International Workshop on Computer Algebra in Scientific Computing

Collections

Graduate School of Applied Mathematics, Conference / Seminar

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A Mimetic Finite-Difference Scheme for Convection of Multicomponent Fluid in a Porous Medium Tsybulin, Vyacheslav; Nemtsev, Andrew; Karasözen, Bülent(2009-09-17) A mimetic finite-difference scheme for the equations of three-dimensional convection of a multicomponent fluid in a porous medium is developed. The discretization is based on staggered grids with five types of nodes (velocities, pressure, temperature, and mass fractions) and on a special approximation of nonlinear terms. Computer experiments have revealed the continuous family of steady states in the case of the zero heat fluxes through two opposite lateral planes of parallelepiped.
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.
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. Tsybulin, “Convection in a Porous Medium and Mimetic Scheme in Polar Coordinates,” Kassel, GERMANY, 2011, vol. 6885, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/54114.