Visualization of Nonlinear Vector Field Topology IV
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Contents |
Summary
Fluid flows, especially of air and water, play an essential role in mechanical engineering and other disciplines. Besides physical experiments, numerical simulation is used in most applications. Scientific visualization maps the numerical results into computer graphics to simplify the evaluation of the simulation by engineers and researchers. Good numerical methods allow for error bounds, but an exact calculation of values is usually impossible. Since topological methods are sensible to small errors, a part of the project deals with more robust topological analysis of computational fluid dynamics data, so that inprecise data allows robust analysis and visualization of the topological flow structure. The second part of the project aims at a better visualization of important spatial vortex structures and the robust detection of attachment and separation structures. The previous projects (Visualization of nonlinear vector field topology I-III) have shown that stream surfaces can help with the visualization of these important phenomena, so we intend to improve our stream surface algorithm with respect to precision and graphical representation.
Duration
- since June 2008
Funding
Deutsche Forschungsgemeinschaft (DFG)
Research assistants:
- Dipl.-Inf. Dominic Schneider
- Dipl.-Math. Wieland Reich
Former
- Dr. Alexander Wiebel
Publications:
- Christoph Garth, Alexander Wiebel, Xavier Tricoche, Ken Joy, Gerik Scheuermann. Lagrangian Visualization of Flow-Embedded Surface Structures. Computer Graphics Forum, 27(3), pages 1007-1014. May, 2008.
Abstract: The notions of Finite-Time Lyapunov Exponent (FTLE) and Lagrangian Coherent Structures provide a strong framework for the analysis and visualization of complex technical flows. Their definition is simple and intuitive, and they are built on a deep theoretical foundation. We apply these concepts to enable the analysis of flows in the immediate vicinity of the boundaries of flow-embedded objects by limiting the Lagrangian analysis to surfaces closely neighboring these boundaries. To this purpose, we present an approach to approximate FTLE fields over such surfaces. Furthermore, we achieve an effective depiction of boundary-related flow structures such as separation and attachment over object boundaries and specific insight into the surrounding flow using several specifically chosen visualization techniques. We document the applicability of our methods by presenting a number of application examples.