Destruction of the family of steady states in the planar problem of Darcy convection

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Tsybulin V. G. , KARASÖZEN B.

PHYSICS LETTERS A, vol.372, no.35, pp.5639-5643, 2008 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 372 Issue: 35
  • Publication Date: 2008
  • Doi Number: 10.1016/j.physleta.2008.07.006
  • Title of Journal : PHYSICS LETTERS A
  • Page Numbers: pp.5639-5643


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. (C) 2008 Elsevier B.V. All rights reserved.