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Multiple solutions and stability of confined convective and swirling flows – a continuing challenge

Alexander Yu. Gelfgat (Department of Fluid Mechanics and Heat Transfer, Faculty of Engineering, Tel‐Aviv University, Tel‐Aviv, Israel)
Pinhas Z. Bar‐Yoseph (Computational Mechanics Laboratory, Faculty of Mechanical Engineering, Technion – Israel Institute of Technology, Haifa, Israel)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 1 March 2004

1442

Abstract

Our recent results on stability and multiplicity of flow states for confined flows of an incompressible Newtonian fluid are surveyed. The considered laminar flows are caused by either thermal, mechanical, or electromagnetic effects and beyond the stability limit exhibit multiplicity of stable, steady or oscillatory, asymptotic states. Stability diagrams as well as examples of multiple flow states are given. It is concluded that beyond the critical value of the characteristic non‐dimensional parameter, and below the threshold to stochastic or turbulent state, multiple stable asymptotic flow states can be expected. This means that at such flow regimes, any computational (experimental) result may be strongly dependent on its initial condition and/or computational (experimental) path. Uncertainties of experimental and numerical modeling, which follow from this conclusion, are discussed. The global spectral Galerkin method using divergence free basis functions has been employed for the spatial approximation of the velocity and temperature fields. Several numerical experiments were performed comparing the present and other formulations, each of which confirmed the computational efficiency of the present approach over other classical numerical methods.

Keywords

Citation

Gelfgat, A.Y. and Bar‐Yoseph, P.Z. (2004), "Multiple solutions and stability of confined convective and swirling flows – a continuing challenge", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 14 No. 2, pp. 213-241. https://doi.org/10.1108/09615530410513818

Publisher

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Emerald Group Publishing Limited

Copyright © 2004, Emerald Group Publishing Limited

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