基于虚拟边界的平面流场拓扑分析

Planar flow field topology analysis based on virtual boundary

拓扑分析是了解流场结构的重要途径。鉴于传统平面流场拓扑特征提取算法的不足,本文提出了一种新的拓扑分析方法。该方法首先通过边界矢量镜像处理,建立一个带虚拟边界的扩展流场;然后针对扩展流场,按照临界点理论提取拓扑特征。最后,根据流场的实际定义域,对拓扑特征进行裁剪,得到最终的流场拓扑。由于虚拟边界的引入,本文方法能够按照封闭式分界线的检测方式,检测开放式分界线和极限环。此外,本文方法无需任何修改即可用于局部拓扑分析,局部分析结果与全局结果基本一致。测试结果表明,本文方法简化了拓扑特征提取过程,提高了拓扑分析性能。

Topology analysis is an important way to study the structure of flow field. With the drawbacks of some traditional algorithms, a new method is presented in this paper for the topological analysis of planar flow field. In this method, the flow field domain is firstly extended to include a virtual boundary, which is set up by mirroring the vectors at original boundaries. Then, the topological features are extracted from the extended field according to the theory of critical points. The final results of topology are obtained by clipping its components out of the real domain. Contributing to the virtual boundary, this method can detect the open separatrices and limit cycles by the same way as the standard closed ones. Furthermore, it can be applied to local topology analysis without any modification. And the local results are consistent with the global ones except some subtle distinctions. Test results show that it simplifies the topology extraction, and improves the performance of topology analysis.