The Community for Technology Leaders
RSS Icon
Issue No.12 - Dec. (2011 vol.17)
pp: 2080-2087
Jens Kasten , Zuse Institute Berlin
Jan Reininghaus , Zuse Institute Berlin
Ingrid Hotz , Zuse Institute Berlin
Hans-Christian Hege , Zuse Institute Berlin
Acceleration is a fundamental quantity of flow fields that captures Galilean invariant properties of particle motion. Considering the magnitude of this field, minima represent characteristic structures of the flow that can be classified as saddle- or vortex-like. We made the interesting observation that vortex-like minima are enclosed by particularly pronounced ridges. This makes it possible to define boundaries of vortex regions in a parameter-free way. Utilizing scalar field topology, a robust algorithm can be designed to extract such boundaries. They can be arbitrarily shaped. An efficient tracking algorithm allows us to display the temporal evolution of vortices. Various vortex models are used to evaluate the method. We apply our method to two-dimensional model systems from computational fluid dynamics and compare the results to those arising from existing definitions.
Vortex regions, time-dependent flow fields, feature extraction.
Jens Kasten, Jan Reininghaus, Ingrid Hotz, Hans-Christian Hege, "Two-Dimensional Time-Dependent Vortex Regions Based on the Acceleration Magnitude", IEEE Transactions on Visualization & Computer Graphics, vol.17, no. 12, pp. 2080-2087, Dec. 2011, doi:10.1109/TVCG.2011.249
[1] D. C. Banks and B. A. Singer, A predictor-corrector technique for visualizing unsteady flow. IEEE Transactions on Visualization and Computer Graphics, 1 (2): 151–163, 1995.
[2] D. Bauer and R. Peikert, Vortex tracking in scale-space. In D. Ebert, P. Brunet, and I. Navazo, editors, VisSym02 Joint Eurographics - IEEE TCVG Symposium on Visualization, pages 233–240. Eurographics Association, 2002.
[3] D. Bauer, R. Peikert, M. Sato, and M. Sick, A case study in selective visualization of unsteady 3d flow. In VIS '02: Proceedings of the Conference on Visualization '02, pages 525–528, Washington, DC, USA, 2002. IEEE Computer Society.
[4] E. Caraballo, M. Samimy, and J. DeBonis., Low dimensional modeling of flow for closed-loop flow control. In AIAA Paper, volume 59, 41st AIAA Aerospace Science Meeting, January 6-9, 2003, Reno, NV, USA.
[5] R. Fuchs, J. Kemmler, B. Schindler, J. Waser, F. Sadlo, H. Hauser, and R. Peikert, Toward a Lagrangian vector field topology. Computer Graphics Forum, 29 (3): 1163–1172, June 2010.
[6] C. Garth, X. Tricoche, T. Salzbrunn, T. Bobach, and G. Scheuermann, Surface Techniques for Vortex Visualization. In O. Deussen, C. Hansen, D. Keim, and D. Saupe editors, Symposium on Visualization, pages 155– 164, Konstanz, Germany, 2004. Eurographics Association.
[7] C. Garth, X. Tricoche, and G. Scheuermann, Tracking of vector field singularities in unstructured 3d time-dependent datasets. In In Proc. IEEE Visualization 2004, pages 329–336, 2004.
[8] G. Haller, Distinguished material surfaces and coherent structures in three-dimensional fluid flows. Physica D, 149 (4): 248–277, 2001.
[9] G. Haller, An objective definition of a vortex. Journal of Fluid Mechanics, 525: 1–26, 2005.
[10] J. Hunt, Vorticity and vortex dynamics in complex turbulent flows. Trans. Can. Soc. Mech. Eng., 11: 21–35, 1987.
[11] M. Jankun-Kelly, M. Jiang, D. Thompson, and R. Machiraju, Vortex visualization for practical engineering applications. IEEE Transactions on Visualization and Computer Graphics, 12 (5): 957–964, 2006.
[12] J. Jeong and F. Hussain, On the identification of a vortex. Journal of Fluid Mechanics, 285: 69–94, 1995.
[13] J. Kasten, I. Hotz, B. Noack, and H.-C. Hege, On the extraction of long-living features in unsteady fluid flows. In V. P. et al., editor, Topologi-cal Methods in Data Analysis and Visualization. Theory, Algorithms, and Applications., Mathematics and Visualization, pages 115–126. Springer, 2011.
[14] T. S. Lundgren, Strained spiral vortex model for turbulent fine structure. Physics of Fluids, 25 (12): 2193–2203, 1982.
[15] B. Noack, I. Mezi, G. Tadmor, and A. Banaszuk, Optimal mixing in recirculation zones. Physics of Fluids, 16 (4): 867–888, 2004.
[16] B. R. Noack, M. Schlegel, B. Ahlborn, G. Mutschke, M. Morzyski, P. Comte, and G. Tadmor, A finite-time thermodynamics of unsteady fluid flows. Journal Non-Equilibrium Thermodynamics, 33 (2): 103–148, 2008.
[17] C. Petz, J. Kasten, S. Prohaska, and H.-C. Hege, Hierarchical vortex regions in swirling flow. Computer Graphics Forum, 28 (3): 863–870, 2009.
[18] A. Pobitzer, R. Peikert, R. Fuchs, B. Schindler, A. Kuhn, H. Theisel, K. Matkovic, and H. Hauser, On the way towards topology-based visualization of unsteady flow - the state of the art. In EuroGraphics 2010 State of the Art Reports (STARs), pages 137–154, 2010.
[19] F. H. Post, B. Vrolijk, H. Hauser, R. S. Laramee, and H. Doleisch, The state of the art in flow visualisation: Feature extraction and tracking. Computer Graphics Forum, 22 (4): 775–792, 2003.
[20] F. Reinders, I. Sadarjoen, B. Vrolijk, and F. Post, Vortex tracking and visualisation in a flow past a tapered cylinder. Computer Graphics Forum, 21 (4): 675–682, 11 2002.
[21] J. Reininghaus, D. Günther, I. Hotz, S. Prohaska, and H.-C. Hege, TADD: A computational framework for data analysis using discrete Morse theory. In Mathematical Software – ICMS 2010, volume 6327 of Lecture Notes in Computer Science, pages 198–208. Springer, 2010.
[22] J. Reininghaus, J. Kasten, T. Weinkauf, and I. Hotz, Efficient computation of combinatorial feature flow fields. IEEE Transactions on Visualization and Computer Graphics, 2011 (to appear).
[23] V. Rom-Kedar, A. Leonard, and S. Wiggins, An analytical study of transport, mixing and chaos in an unsteady vortical flow. Journal of Fluid Mechanics, 214: 347–394, 1990.
[24] I. A. Sadarjoen and F. H. Post, Geometric methods for vortex extraction. In Joint Eurographics-IEEE TVCG Symposium on Visualization, pages 53–62, 1999.
[25] D. Schneider, A. Wiebel, H. Carr, M. Hlawitschka, and G. Scheuer-mann., Interactive comparison of scalar fields based on largest contours with applications to flow visualization. IEEE Trans Vis Comput Graph, 14 (6): 1475–1482, 2008.
[26] S. C. Shadden, A Dynamical Systems Approach to Unsteady Systems. PhD thesis, California Institute of Technology, Pasadena CA, 2006.
[27] S. Stegmaier, U. Rist, and T. Ertl, Opening the Can of Worms: An Exploration Tool for Vortical Flows. In C. Silva, and E. Gröller, and H. Rushmeier editor, Proceedings of IEEE Visualization '05, pages 463– 470. IEEE, 2005.
[28] P. Tabeling, Two-dimensional turbulence: a physicist approach. Physics Reports, 362 (1): 1 – 62, 2002.
[29] H. Theisel, and H.-P. Seidel, Feature flow fields. In VisSym '03: Proceedings of the Symposium on Data Visualization 2003, pages 141–148, Aire-la-Ville, Switzerland, 2003. Eurographics Association.
[30] A. Tikhonova, C. D. Correa, and K.-L. Ma, An exploratory technique for coherent visualization of time-varying volume data. Computer Graphics Forum, 29 (3): 783–792, 2010.
[31] X. Tricoche, T. Wischgoll, G. Scheuermann, and H. Hagen, Topology tracking for the visualization of time-dependent two-dimensional flows. Computer & Graphics, 26: 249–257, 2002.
[32] M. Wilczek, O. Kamps, and R. Friedrich, Lagrangian investigation of two-dimensional decaying turbulence. Physica D: Nonlinear Phenomena, 237 (14-17): 2090 – 2094, 2008.
[33] C. H. K. Williamson, Vortex dynamics in the cylinder wake. Annual Review of Fluid Mechanics, 28: 477–539, 1996.
4 ms
(Ver 2.0)

Marketing Automation Platform Marketing Automation Tool