This investigation addresses a systematic numerical method based on the finite volume method and a full multigrid technique to study two-dimensional and three-dimensional flow of an incompressible fluid inside a cavity driven by the motion of the upper lid. Quantitative aspects of two and three dimensional flows in lid-driven cavities are analyzed by encompassing descriptive Reynolds numbers Re bounded by 1000 and 8000 for 2D case, 100 and 1000 for 3D case. Furthermore, the effects of inner spherical shape on fluid flow characteristics have been also investigated. An analysis of the flow evolution demonstrates that, by further increasing Reynolds beyond a certain critical value, the steady flow becomes unstable and bifurcates to the unsteady flow. Results show that the transition to the unsteady regime follows the classical scheme of a Hopf bifurcation, giving rise to a perfectly periodic state. Flow periodicity has been verified through time history plots for the velocity compo...

中文翻译：

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预测由位于中心的圆和球引起的2D和3D盖子驱动的空腔的非稳态

这项研究提出了一种基于有限体积法和完全多网格技术的系统数值方法，以研究由上盖运动驱动的腔体内不可压缩流体的二维和三维流动。通过包含描述性的雷诺数Re（对于2D情况为1000和8000，对于3D情况为100和1000）来分析盖驱动腔中二维和三维流动的定量方面。此外，还研究了内部球形形状对流体流动特性的影响。对流动演化的分析表明，通过进一步增加雷诺数超过一定的临界值，稳定流变得不稳定，并分叉为不稳定流。结果表明，向不稳定状态的过渡遵循经典的Hopf分叉方案，从而产生了一个完美的周期性状态。流量周期性已通过时间历史图进行了速度成分的验证。