SciCADE 2013
International Conference on Scientific Computation and Differential Equations
September 16-20, 2013, Valladolid (Spain)

Contributed Talk

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Multiple convective flows in porous annular domains

V. Tsybulin and B. Karasozen

Coexistence of multiple patterns in Lapwood convection (D. Lyubimov) was explained by cosymmetry theory (V. Yudovich). Study of the flows and its bifurcations for this problem requires special numerical methods to preserve cosymmetry in the discrete approximation of underlying system of partial differential equations. We analyze the family of steady convective fluid patterns in annular enclosure filled with a porous medium by the finite-difference method [1]. Results of computation of the families of steady states for two annular domains are given. Non-uniform stability spectra is found for convective patterns belonging to the family of steady states. The continuation of the family up to the appearance of unstable states is done and the scenario with simultaneous instability at three points is detected. So, this bifurcation is being a cosymmetrical effect not a symmetrical one.

[1] B. Karasözen, A.V. Trofimova and V.G. Tsybulin, Natural convection in porous annular domains: Mimetic scheme and family of steady states, J. Comp. Phys. 231 (2012) pp. 2995-3005.

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