Staggered grids for three-dimensional convection of a multicomponent fluid in a porous medium

  • Authors:

  • BüLent KarasöZen;Andrew D. Nemtsev;Vyacheslav G. Tsybulin

  • Affiliations:

  • Department of Mathematics and Institute of Applied Mathematics, Middle East Technical University, 06531 Ankara, Turkey;Department of Computational Mathematics and Mathematical Physics, Southern Federal University, Rostov-on-Don, Russia;Department of Computational Mathematics and Mathematical Physics, Southern Federal University, Rostov-on-Don, Russia

  • Venue:
  • Computers & Mathematics with Applications
  • Year:
  • 2012

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Abstract

Convection in a porous medium may produce strong nonuniqueness of patterns. We study this phenomena for the case of a multicomponent fluid and develop a mimetic finite-difference scheme for the three-dimensional problem. Discretization of the Darcy equations in the primitive variables is based on staggered grids with five types of nodes and on a special approximation of nonlinear terms. This scheme is applied to the computer study of flows in a porous parallelepiped filled by a two-component fluid and with two adiabatic lateral planes. We found that the continuous family of steady stable states exists in the case of a rather thin enclosure. When the depth is increased, only isolated convective regimes may be stable. We demonstrate that the non-mimetic approximation of nonlinear terms leads to the destruction of the continuous family of steady states.