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Topology-guided Visualization of Constrained Vector Fields

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Topology-based Methods in Visualization

Part of the book series: Mathematics and Visualization ((MATHVISUAL))

Summary

In this study we explore ways of using precomputed vector field topology as a guide for interactive feature-based visualization of flow simulation data. Beyond streamline seeding based on critical points, we focus mainly on computing special stream surfaces related to critical points and periodic orbits. We address the special case of divergence-free vector fields which is often met in practical CFD data, and we extend the topological analysis to no-slip boundaries by treating 3D velocity and 2D wall shear stress in a unified way. Finally we apply the proposed techniques to flow simulation data and demonstrate their usefulness for the purpose of studying recirculation and separation phenomena.

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References

  1. Asimov, D.: Notes on the Topology of Vector Fields and Flows. Tech. Report RNR-93-003, NASA Ames Research Center (1993)

    Google Scholar 

  2. Guckenheimer, J., Holmes, P.: Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields. Springer, New York (1983)

    MATH  Google Scholar 

  3. Globus, A., Levit, C., Lasinski, T.: A tool for visualizing the topology of threedimensional vector fields, In Proc. IEEE Visualization 91, 33-40 (1991)

    Google Scholar 

  4. Garth, C., Tricoche, X., Salzbrunn, T., Bobach, T., Scheuermann, G.: Surface Techniques for Vortex Visualization. In: Proceedings of VisSym 2004, 155-164 (2004)

    Google Scholar 

  5. Garth, C., Tricoche, X., Scheuermann, G.: Tracking of Vector Field Singularities in Unstructured 3D Time-Dependent Datasets. In: Proc. IEEE Visualization 2004,329-336 (2004)

    Google Scholar 

  6. Helman, J.L., Hesselink, L.: Representation and Display of Vector Field Topology in Fluid Flow Data Sets, Computer, 22(8), 27-36 (1989).

    Article  Google Scholar 

  7. Hultquist, J.P.M.: Constructing stream surfaces in steady 3D vector fields, In: Proceedings of the 3rd conference on Visualization ’92, 171-178 (1992)

    Google Scholar 

  8. Löffelmann, H., Kucera, T., Gröller, E.: Visualizing Poincaré Maps Together With the Underlying Flow. In: Hege, H.C., Polthier, K. (eds.), Proceedings of the International Workshop on Visualization and Mathematics ’97 315-328 (1998)

    Google Scholar 

  9. de Leeuw, W., van Liere, R.: Collapsing flow topology using area metrics, In: Proc. IEEE Visualization 99, 149-354 (1999)

    Google Scholar 

  10. Mahrous, K. Bennett, J., Scheuermann, G., Hamann, B. Joy, K.I.: Topological Segmentation in Three-Dimensional Vector Fields, IEEE Transactions on Visualization and Computer Graphics, 10(2), 198-205 (2004)

    Article  Google Scholar 

  11. Surana, A., Grunberg, O., Haller, G.: Exact theory of threedimensional flow separation. Part I. Steady separation, J. Fluid Mech., 564, 57-103 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  12. Spohn, A., Mory, M, Hopfinger, E.: Experiments on vortex breakdown in a confined flow generated by a rotating disk, J. Fluid Mech., 370, 73-99 (1998)

    Article  MATH  Google Scholar 

  13. Sotiropoulos, F., Ventikos, Y., Lackey, T.: Chaotic advection in three-dimensional stationary vortex-breakdown bubbles: Sil’nikov’s chaos and the devil’s staircase, J. Fluid Mech., 444, 257-297 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  14. Thompson, M. Hourigan, K.: The sensitivity of steady vortex breakdown bubbles in confined cylinder flows to rotating lid misalignment, J. Fluid Mech., 496,129-138 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  15. Tricoche, X., Garth, C., Kindlmann, G.L., Deines, E., Scheuermann, G., Ruetten, M., Hansen, C.D.: Visualization of Intricate Flow Structures for Vortex Breakdown Analysis. In: Proceedings of IEEE Visualization ’04, 187-194, 2004.

    Google Scholar 

  16. Tricoche, X., Scheuermann, G., Hagen, H.: A topology simplification method for 2D vector fields, In: Proc. IEEE Visualization 2000, 359-366 (2000)

    Google Scholar 

  17. 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, 225-232 (2003)

    Google Scholar 

  18. Ventikos, Y.: The effect of imperfections on the emergence of three-dimensionality in stationary vortex breakdown bubbles, Physics of Fluids, L13-L16 (2002)

    Google Scholar 

  19. Wischgoll, T., Scheuermann, G.: Locating closed streamlines in 3D vector fields, In: D. Ebert, P. Brunet, I. Navazo (eds.), Data Visualisation 2002, Eurographics Association, 227-232 (2002)

    Google Scholar 

  20. Ye, X., Kao, D., Pang, A., Strategy for Scalable Seeding of 3D Streamlines, In: Proceedings of IEEE Visualization ’05, Minneapolis (2005)

    Google Scholar 

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© 2007 Springer-Verlag Berlin Heidelberg

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Peikert, R., Sadlo, F. (2007). Topology-guided Visualization of Constrained Vector Fields. In: Hauser, H., Hagen, H., Theisel, H. (eds) Topology-based Methods in Visualization. Mathematics and Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70823-0_2

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