Abstract
Scenarios of the development of continuous families of steady-state regimes branching off from mechanical equilibrium are investigated for the plane problem of filtrational convection of a multicomponent fluid saturating a porous block of rectangular cross-section. Convection of two- and three-component fluids is considered and unidirectional and differently directed vertical temperature and concentration gradients are analyzed. A new scenario of the formation of a continuous family of steady-state solutions realized in the case of oscillatory instability of mechanical equilibrium is studied.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
G. Z. Gershuni, E. M. Zhukhovitskii, and A. A. Nepomnyashchii Stability of Convective Flows[in Russian], Nauka, Moscow (1989).
D. A. Nield and A. Bejan, Convection in Porous Media, Springer, N.Y., etc. (1999).
D. V. Lyubimov, "Convective motions in a porous medium heated from below," Zh. Prikl. Mekh. Tekh. Fiz., No. 2, 131 (1975).
V. I. Yudovich, "Cosymmetry, degeneration of solutions of operator equations and the onset of convective flow in a porous medium," Mat. Zametki, 49, No. 5, 142 (1991).
V. I. Yudovich, "Secondary cycle of equilibria in a system with cosymmetry, its creation by bifurcation and im-possibility of symmetric treatment of it," Chaos, 5, 402 (1995).
V. I. Yudovich, "Bifurcation relating to the generation of a cycle from the family of equilibria of a dynamical system and its prolongation," Prikl. Mat. Mekh., 62, 22 (1998).
L. G. Kurakin and V. I. Yudovich, "Bifurcation accompanying monotonic instability of an equilibrium of a cosym-metric dynamical system," Chaos, 10, 311 (2000).
L. G. Kurakin and V. I. Yudovich, "Bifurcation associated with monotonic loss of stability of equilibrium of a cosymmetric dynamical system," Dokl. Ross. Akad. Nauk, 372, 29 (2000).
L. G. Kurakin and V. I. Yudovich, "Branching of 2D tori off an equilibrium of a cosymmetric system (codimen-sion-1 bifurcation)," Chaos, 11, 780 (2001).
V. I. Yudovich, "Cosymmetry and convection of a multicomponent fluid in a porous medium," I zv. Vuzov. Severo-Kavkazs. Region. Estestv. Nauki. Spetsvypusk. Mat. Modelirovanie, 174 (2001.
O. Yu. Kantur and V. G. Tsibulin, "Spectral-difference method of calculating convective flows of a fluid through a porous medium and conservation of cosymmetry," Zhurn. Vychislit. Matematiki i Mat. Fiziki, bf 42, 913 (2002).
V. N. Govorukhin, "Numerical investigation of loss of stability by secondary steady-state regimes in the Darcy plane convection problem," Dokl. Ross. Akad. Nauk, 363, 772 (1998).
V. N. Govorukhin, "Analysis of families of secondary steady-state regimes in the problem of plane convection flow through a porous medium in a rectangular vessel," Izv. Ros. Akad. Nauk, Mekh. Zhidk. Gaza, No. 5, 53 (1999).
B. Karasözen and V. G. Tsybulin, "Finite-difference approximations and cosymmetry conservation in filtration convection problem," Phys. LettersA, 262, 321 (1999).
O. Yu. Kantur and V. G. Tsibulin, "Calculation of families of steady-state regimes of filtration convection in a narrow vessel," Zh. Prikl. Mekh. Tekh. Fiz., 44, No. 2, 92 (2003).
Rights and permissions
About this article
Cite this article
Kantur, O.Y., Tsibulin, V.G. Numerical Investigation of the Plane Problem of Convection of a Multicomponent Fluid in a Porous Medium. Fluid Dynamics 39, 464–473 (2004). https://doi.org/10.1023/B:FLUI.0000038565.09347.ac
Issue Date:
DOI: https://doi.org/10.1023/B:FLUI.0000038565.09347.ac