Detecting Topologically Relevant Structures in Flows by Surface Integrals

Abstract

Gauss’ theorem, which relates the flow through a surface to the vector field inside the surface, is an important tool in Flow Visualization. We are exploit the fact that the theorem can be further refined on polygonal cells and construct a process that encodes the particle movement through the boundary facets of these cells using transition matrices. By pure power iteration of transition matrices, various topological features, such as separation and invariant sets, can be extracted without having to rely on the classical techniques, e.g., interpolation, differentiation and numerical streamline integration. We will apply our method to steady vector fields with a focus on three dimensions.