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Published in:
2011 | OriginalPaper | Chapter
Convection in a Porous Medium and Mimetic Scheme in Polar Coordinates
Authors : Bülent Karasözen, Anastasia Trofimova, Vyacheslav Tsybulin
Published in: Computer Algebra in Scientific Computing
Publisher: Springer Berlin Heidelberg
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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.