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

2012-09-01
Karasözen, Bülent
Nemtsev, Andrew D.
Tsybulin, Vyacheslav G.
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.

Citation Formats
B. Karasözen, A. D. Nemtsev, and V. G. Tsybulin, “Staggered grids for three-dimensional convection of a multicomponent fluid in a porous medium,” COMPUTERS & MATHEMATICS WITH APPLICATIONS, vol. 64, no. 6, pp. 1740–1751, 2012, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/31592.