Using Characteristic Structures for Enhanced Flow Visualization

The computer-assisted investigation of flow data can be eased by the visualization of topological information about the flow. Especially, when empirical models or numerical results from flow simulation are investigated, often the first step of analysis is to search structural elements, like fixed points, separatrices, etc. The work presented in this paper focuses on the visualization of 3D dynamical systems (comparable to numerical flow data) on the basis of results which are obtained by automatic analysis of the flow topology. Fixed points are determined and the Jacobian matrix of the flow is investigated at these points of phase space to obtain the associated stable and/or unstable invariant sets. Furthermore, this paper presents how Poincaré maps are used to visualize structural information about cyclic flow data together with direct visualization cues like stream lines or stream surfaces.