Study of a 3D Cavity Flow using the Numerical Scheme with High Accuracy

采用高精度、高分辨率的组合式压缩格式对盖驱动矩形腔内三维定常流动进行了数值模拟。研究了展向长径比为1的空腔内的不可压缩流动。0和6。55，宽高比为0。4、0。6、1。0和1。4. 从稳定速度场数据中获得了高精度的流线，并在雷诺数为100 ~ 500的范围内绘制了庞加莱剖面。流线有两种类型：闭合曲线附近的局部流线和混沌流线。在庞加莱剖面中，我们可以通过局部流线在端壁附近的区域找到不变环面椭圆和共振岛的各种结构，通过混沌流线找到不规则分布的点。庞加莱剖面中的结构与一维非自治哈密顿系统相图中的结构相似。特别是，我们发现流线的庞加莱截面随着雷诺数的变化，在3:1和2:1共振中表现出惊人的相似性。当雷诺数大于2:1共振时，得到了整个流动区域的混沌流线。本研究表明，在不同长径比和展向长径比的腔体中，稳定腔体流动普遍存在不变环面和共振破坏。

Numerical simulations are carried out for the three-dimensional steady flow in a lid-driven rectangular cavity using the combined compact scheme with high accuracy and high resolution. We study the incompressible flow in a cavity with spanwise aspect ratio 1. 0 and 6. 55, and aspect ratios 0. 4, 0. 6, 1. 0 and 1. 4. Streamlines are obtained from the steady velocity field data with high accuracy and Poincare sections are plotted from the streamlines for Reynolds numbers ranging from 100 to 500. There are two types of streamlines : localized streamlines near a closed curve and chaotic streamlines. In the Poincare sections we can find various structures of ovals of invariant tori and resonant islands by localized streamlines in the regions near the end-wall and irregularly distributed points by chaotic streamlines. The structures in the Poincare sections are similar to those in the phase portraits of one-dimensional non-autonomous Hamiltonian system. In particular, we found that the Poincare sections of streamlines show striking similarities for the 3 : 1 and 2 : 1 resonances as the Reynolds number is changed. When the Reynolds number is larger than that in the 2 : 1 resonance, we obtained the chaotic streamlines in the whole flow region. The present study show that existence of the invariant tori and disruption by the resonances are generally observed in steady cavity flows in cavities with different aspect ratios and spanwise aspect ratios.