Extraction of Coherent Structures from Natural and Actuated Flows

  • Jens Kasten
  • Tino Weinkauf
  • Christoph Petz
  • Ingrid Hotz
  • Bernd R. Noack
  • Hans-Christian Hege
Part of the Notes on Numerical Fluid Mechanics and Multidisciplinary Design book series (NNFM, volume 108)


We present feature-extraction techniques for numerical and experimental data of complex fluid flows. Focus is placed on efficient analysis and visualization of coherent structures of snapshots, temporal evolution and parameter-dependency of coherent structures. One key enabler are Galilean invariant flow quantities based on pressure, acceleration, vorticity and velocity Jacobians. Other important catalyzers are Lagrangian filters that distill persistent strong particle-fixed features while neglecting weak and short-living ones. The proposed feature extraction framework is exemplified for the time-dependent natural and actuated flow around a high-lift airfoil, as well as other benchmark configurations of the SFB 557.


Feature Extraction Coherent Structure Vortex Core Vortex Region Extremal Line 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Eberly, D.: Ridges in Image and Data Analysis. Kluwer Acadamic Publishers, Dordrecht (1996)zbMATHGoogle Scholar
  2. 2.
    Edelsbrunner, H., Harer, J., Natarajan, V., Pascucci, V.: Morse-smale complexes for piecewise linear 3-manifolds. In: Proc. 19th Sympos. Comput. Geom. 2003, pp. 361–370 (2003)Google Scholar
  3. 3.
    Edelsbrunner, H., Letscher, D., Zomorodian, A.: Topological persistence and simplification. Discrete and Computational Geometry 28, 511–533 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Forman, R.: Morse theory for cell-complexes. Advances in Mathematics 134, 90–145 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Gyulassy, A.: Combinatorial Construction of Morse-Smale Complexes for Data Analysis and Visualization. Ph.D. thesis, University of California, Davis (2008)Google Scholar
  6. 6.
    Kasten, J., Hotz, I., Noack, B.R., Hege, H.-C.: On the extraction of long-living features in unsteady fluid flows. In: TopoInVis 2009. Springer, Heidelberg (2009) (to appear 2010) Google Scholar
  7. 7.
    Kasten, J., Petz, C., Hotz, I., Noack, B.R., Hege, H.-C.: Localized finite-time Lyapunov exponent for unsteady flow analysis. In: Proc. Vision Modeling and Visualization (VMV), pp. 265–274 (2009)Google Scholar
  8. 8.
    Lindeberg, T.: Edge detection and ridge detection with automatic scale selection. International Journal of Computer Vision 30(2), 117–156 (1998)CrossRefGoogle Scholar
  9. 9.
    Peikert, R., Roth, M.: The parallel vectors operator - a vector field visualization primitive. In: Proc. IEEE Visualization 1999, pp. 263–270 (1999)Google Scholar
  10. 10.
    Peikert, R., Sadlo, F.: Height Ridge Computation and Filtering for Visualization. In: IEEE Pacific Visualization Symposium 2008, pp. 119–126 (2008)Google Scholar
  11. 11.
    Petz, C., Kasten, J., Prohaska, S., Hege, H.-C.: Hierarchical vortex regions in swirling flow. Computer Graphics Forum 28, 863–870 (2009)CrossRefGoogle Scholar
  12. 12.
    Pobitzer, A., Peikert, R., Fuchs, R., Schindler, B., Kuhn, A., Theisel, H., Matković, K., Hauser, H.: On the way towards topology-based visualization of unsteady flow – the state of the art. Computer Graphics Forum (2010); Proc. Eurographics 2010 (to appear)Google Scholar
  13. 13.
    Post, F., Vrolijk, B., Hauser, H., Laramee, R., Doleisch, H.: Feature extraction and visualisation of flow fields. In: Proc. Eurographics 2002, State of the Art Reports, pp. 69–100 (2002)Google Scholar
  14. 14.
    Sahner, J.: Extraction of vortex structures in 3d flow fields. Ph.D. thesis, Zuse Institute Berlin and Univ. Magdeburg, Fakultät für Informatik (2009)Google Scholar
  15. 15.
    Sahner, J., Weinkauf, T., Hege, H.-C.: Galilean invariant extraction and iconic representation of vortex core lines. In: Brodlie, K., Duke, K.J.D. (eds.) Proc. Eurographics / IEEE VGTC Symposium on Visualization (EuroVis 2005), Leeds, UK, pp. 151–160 (2005)Google Scholar
  16. 16.
    Sahner, J., Weinkauf, T., Teuber, N., Hege, H.-C.: Vortex and strain skeletons in Eulerian and Lagrangian frames. IEEE Transactions on Visualization and Computer Graphics 13, 980–990 (2007)CrossRefGoogle Scholar
  17. 17.
    Salzbrunn, T., Jänicke, H., Wischgoll, T., Scheuermann, G.: The state of the art in flow visualization: Partition-based techniques. In: SimVis, pp. 75–92 (2008)Google Scholar
  18. 18.
    Schlichting, H.: Boundary-Layer Theory. McGraw-Hill, New York (1979)zbMATHGoogle Scholar
  19. 19.
    Shi, K., Theisel, H., Weinkauf, T., Hauser, H., Hege, H.-C., Seidel, H.P.: Path line oriented topology for periodic 2D time-dependent vector fields. In: Proc. Eurographics / IEEE VGTC Symposium on Visualization (EuroVis 2006), Lisbon, Portugal, pp. 139–146 (2006)Google Scholar
  20. 20.
    Theisel, H., Sahner, J., Weinkauf, T., Hege, H.-C., Seidel, H.P.: Extraction of parallel vector surfaces in 3d time-dependent fields and application to vortex core line tracking. In: Proc. IEEE Visualization 2005, pp. 631–638 (2005)Google Scholar
  21. 21.
    Theisel, H., Weinkauf, T., Hege, H.-C., Seidel, H.P.: Saddle connectors - an approach to visualizing the topological skeleton of complex 3D vector fields. In: Proc. IEEE Visualization 2003, pp. 225–232 (2003)Google Scholar
  22. 22.
    Theisel, H., Weinkauf, T., Hege, H.-C., Seidel, H.P.: Topological methods for 2D time-dependent vector fields based on stream lines and path lines. IEEE Transactions on Visualization and Computer Graphics 11, 383–394 (2005)CrossRefGoogle Scholar
  23. 23.
    Weinkauf, T.: Extraction of topological structures in 2d and 3d vector fields. Ph.D. thesis, Zuse Institute Berlin and Univ. Magdeburg, Informatik (2008)Google Scholar
  24. 24.
    Weinkauf, T., Günther, D.: Separatrix persistence: Extraction of salient edges on surfaces using topological methods. Computer Graphics Forum 28, 1519–1528 (2009)CrossRefGoogle Scholar
  25. 25.
    Weinkauf, T., Sahner, J., Günther, B., Theisel, H., Hege, H.-C., Thiele, F.: Feature-based analysis of a multi-parameter flow simulation. In: Proc. SimVis 2008, Magdeburg, Germany, pp. 237–251 (2008)Google Scholar
  26. 26.
    Weinkauf, T., Sahner, J., Theisel, H., Hege, H.-C.: Cores of swirling particle motion in unsteady flows. IEEE Transactions on Visualization and Computer Graphics 13, 1759–1766 (2007)CrossRefGoogle Scholar
  27. 27.
    Weinkauf, T., Theisel, H., Hege, H.-C., Seidel, H.P.: Boundary switch connectors for topological visualization of complex 3D vector fields. In: Data Visualization 2004. Proc. VisSym 2004, pp. 183–192 (2004)Google Scholar
  28. 28.
    Weinkauf, T., Theisel, H., Hege, H.-C., Seidel, H.P.: Topological structures in two-parameter-dependent 2D vector fields. Computer Graphics Forum 25, 607–616 (2006)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Jens Kasten
    • 1
  • Tino Weinkauf
    • 2
  • Christoph Petz
    • 1
  • Ingrid Hotz
    • 1
  • Bernd R. Noack
    • 3
  • Hans-Christian Hege
    • 1
  1. 1.Zuse Institute Berlin (ZIB)BerlinGermany
  2. 2.Courant Institute of Mathematical SciencesNew York, NYUSA
  3. 3.Institut PprimeCNRS - Université de Poitiers - ENSMA, UPR 3346PoitiersFrance

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