【摘 要】
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Multiple steady solutions and hysteresis phenomenon in the square cavity flows driven by the surface with antisymmet-ric velocity profile are investigated by numerical simulation and bifurcation analysis.A high order spectral element method with the matri
【机 构】
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Institute of Applied Physical and Computational Mathematics,Beijing 100094,China;Department of Moder
论文部分内容阅读
Multiple steady solutions and hysteresis phenomenon in the square cavity flows driven by the surface with antisymmet-ric velocity profile are investigated by numerical simulation and bifurcation analysis.A high order spectral element method with the matrix-free pseudo-arclength technique is used for the steady-state solution and numerical continuation.The com-plex flow pattems beyond the symmetry-breaking at Re (～-) 320 are presented by a bifurcation diagram for Re ＜ 2500.The results of stable symmetric and asymmetric solutions are consistent with those reported in literature,and a new unstable asymmetric branch is obtained besides the stable branches.A novel hysteresis phenomenon is observed in the range of 2208 ＜ Re ＜ 2262,where two pairs of stable and two pairs of unstable asymmetric steady solutions beyond the stable symmetric state coexist.The vortices near the sidewall appear when the Reynolds number increases,which correspond to the bifurcation of topology structure,but not the bifurcation of Navier-Stokes equations.The hysteresis is proposed to be the result of the combined mechanisms of the competition and coalescence of secondary vortices.
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