Planar flow field topology analysis based on virtual boundary

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.