Time-dependent 2-D vector field topology: An approach inspired by lagrangian coherent structures

Computer Graphics Forum

Volumn 29, Issue 1, 2010, Pages 88-100

  Sadlo, F ^a   Weiskopf, D ^a  

^a UNIVERSITY OF STUTTGART   (Germany)

Author keywords

Lagrangian coherent structures; Time dependent vector fields; Vector field topology

Indexed keywords

COMPUTATIONAL FLUID DYNAMICS; LAGRANGE MULTIPLIERS; LYAPUNOV METHODS; TOPOLOGY;

FINITE-TIME LYAPUNOV EXPONENT; LAGRANGIAN COHERENT STRUCTURES; SEPARATRICES; TIME DEPENDENT; TIME-DEPENDENT VECTOR FIELDS; UNSTEADY VECTOR FIELDS; VECTOR FIELD TOPOLOGY; VECTOR FIELDS;

VECTORS;

EID: 76649135858     PISSN: 01677055     EISSN: 14678659     Source Type: Journal    
DOI: 10.1111/j.1467-8659.2009.01546.x     Document Type: Article

References (27)

1. Bürger K., Kondratieva P., Krüger J., Westermann R. : Importance-driven particle techniques for flow visualization. In Proc. of Pacific Vis. Symp. (2008 pp. 71 78.
2. Eberly D., Gardner R., Morse B., Pizer S., Scharlach C. : Ridges for image analysis. J. Math. Imag. Vis. 4, 4 (1994 353 373.
3. Garth C., Krishnan H., Tricoche X., Joy K. I. : Generation of Accurate Integrat Surfaces in Time-Dependent Vector Fields. IEEE Trans. Visual. Comput. Graph. 14, 6 (2008 1404 1411.
4. Garth C., Li G.-S., Tricoche X., Hansen C. D., Hagen H. : Visualization of coherent structures in transient flows. In Topology-Based Methods in Visualization II (2009 Hege H.-C., Polthier K., Scheuermann G. Eds. Springer, Berlin Heidelberg, pp. 1 14.
5. Garth C., Tricoche X., Salzbrunn T., Bobach T., Scheuermann G. : Surface techniques for vortex visualization. In VisSym, 346 (2004 pp. 155 164.
6. Haller G. : Finding finite-time invariant manifolds in two-dimensional velocity fields. Chaos 10, 1 (2000 99 108.
7. Haller G. : Distinguished material surfaces and coherent structures in three-dimensional fluid flows. Physica D 149 2001 248 277.
8. Helman J., Hesselink L. : Representation and display of vector field topology in fluid flow data sets. Computer 22, 8 (1989 27 36.
9. Hultquist J. P. M. : Constructing stream surfaces in steady 3-D vector fields. In Proc. IEEE Visualization '92 (1992 IEEE Computer Society, pp. 171 178.
10. Ide K., Small D., Wiggins S. : Distinguished hyperbolic trajectories in time-dependent fluid flows: analytical and computational approach for velocity fields defined as data sets. Nonlin. Process. Geophys. 9, 3/4 (2002 237 263.
11. Lekien F., Coulliette C., Mariano A. J., Ryan E. H., Shay L. K., Haller G., Marsden J. E. : Pollution release tied to invariant manifolds: A case study for the coast of Florida. Physica D 210, 1 (2005).
12. Löffelmann H., Kučera T., Gröller E. : Visualizing Poincaré maps together with the underlying flow. In Mathematical Visualization (1998 Hege H.-C., Polthier K. Eds Springer Verlag, Berlin Heidelberg New York, pp. 315 328.
13. Löffelmann H., Mroz L., Gröller E., Purgathofer W. : Stream arrows: Enhancing the use of stream-surfaces for the visualization of dynamical systems. Visual Comput. 13 1997 359 369.
14. Mancho A. M., Small D., Wiggins S., Ide K. : Computation of stable and unstable manifolds of hyperbolic trajectories in two-dimensional, aperiodically time-dependent vector fields. Physica D 182 2003 188 222.
15. Peikert R., Sadlo F. : Visualization Methods for Vortex Rings and Vortex Breakdown Bubbles. In Proceedings of the 9th Eurographics/IEEE VGTC Symposium on Visualization (EuroVis'07) (2007 pp. 211 218.
16. Peikert R., Sadlo F. : Height ridge computation and filtering for visualization. In Proc. of Pacific Vis. Symp. (2008 Fujishiro I., Li H., Ma K.-L. Eds. pp. 119 126.
17. Peikert R., Sadlo F. : Flow topology beyond skeletons: visualization of features in recirculating flow. In Topology-Based Methods in Visualization II (2009 Hege H.-C., Polthier K., Scheuermann G. Eds. Springer, Berlin Heidelberg, pp. 145 160.
18. Shadden S. C. : Lagrangian coherent structures (2005). http://www.cds.caltech.edu/∼shawn/LCS-tutorial/contents.html.
19. Sadlo F., Peikert R. : Efficient Visualization of Lagrangian Coherent Structures by Filtered AMR Ridge Extraction. IEEE Trans. Visual. Comput. Graph. 13, 5 (2007 1456 1463.
20. Sadlo F., Peikert R. : Visualizing Lagrangian coherent structures and comparison to vector field topology. In Topology-Based Methods in Visualization II (2009 Hege H.-C., Polthier K., Scheuermann G. Eds. Springer, Berlin Heidelberg, pp. 15 30.
21. Soni B., Thompson D., Machiraju R. : Visualizing particle/flow structure interactions in the small bronchial tubes. IEEE Trans. Visual. Comput. Graph. 14, 6 (2008 1412 1427.
22. Tricoche X., Garth C., Kindlmann G., Deines E., Scheuermann G., Ruetten M., Hansen C. : Visualization of intricate flow structures for vortex breakdown analysis. In Proc. IEEE Visualization '04 (2004 pp. 187 194.
23. Theisel H., Weinkauf T., Hege H.-C., Seidel H.-P. : Saddle connectors - an approach to visualizing the topological skeleton of complex 3-D vector fields. In Proc. IEEE Visualization '03 (2003 pp. 225 232.
24. Weinkauf T., Hege H.-C., Noack B., Schlegel M., Dillmann A. : Coherent structures in a transitional flow around a backward-facing step. Phys. Fluids 15, 9 (2003 S3.
25. Wischgoll T., Scheuermann G. : Detection and visualization of closed streamlines in planar flows. IEEE Trans. Visual. Comput. Graph. 7, 2 (2001 165 172.
26. Wiebel A., Tricoche X., Schneider D., Jaenicke H., Scheuermann G. : Generalized streak lines: Analysis and visualization of boundary induced vortices. IEEE Trans. Visual. Comput. Graph. 13, 6 (2007 1735 1742.
27. Ye X., Kao D., Pang A. : Strategy for scalable seeding of 3-D streamlines. In Proc. IEEE Visualization '05 (2005 pp. 471 478.