Multiple solutions and stability of confined convective and swirling flows a continuing challenge
نویسندگان
چکیده
Our recent results on stability and multiplicity of ̄ow states for con®ned ̄ows of an incompressible Newtonian ̄uid are surveyed. The considered laminar ̄ows 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 ̄ow 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 ̄ow states can be expected. This means that at such ̄ow 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 ®elds. Several numerical experiments were performed comparing the present and other formulations, each of which con®rmed the computational ef®ciency of the present approach over other classical numerical methods.
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تاریخ انتشار 2004