Topological Analysis and Visualization of Features in Computational Fluid Dynamics Results

Computational Fluid Dynamics (CFD) is a necessary tool in modern mechanical engineering, especially in the aerospace and automotive industry. Solving problems of industrial scale creates large data sets, but without post-processing, many relevant questions can not be answered. Typical questions are vortex formation, vortex shape and position, and attachment or separation of flow on immersed surfaces. These features can be studied by using results from qualitative dynamical system theory like critical points, separatrices, and limit cycles. The talk begins with examples from industry demonstrating the complexity of such features. Topological analysis and visualization based on dynamical systems theory is introduced as a partial answer. The goal is an automatic analysis of CFD data that finds relevant features, calculates their properties and visualizes their position and shape. Towards the end, a notation of local flow is suggested that might open the door for further mathematical treatment of the mentioned flow phenomena.