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Analyzing Vortex Breakdown Flow Structures by Assignment of Colors to Tensor Invariants
September-October 2006 (vol. 12 no. 5)
pp. 1189-1196
Topological methods are often used to describe flow structures in fluid dynamics and topological flow field analysis usually relies on the invariants of the associated tensor fields. A visual impression of the local properties of tensor fields is often complex and the search of a suitable technique for achieving this is an ongoing topic in visualization. This paper introduces and assesses a method of representing the topological properties of tensor fields and their respective flow patterns with the use of colors. First, a tensor norm is introduced, which preserves the properties of the tensor and assigns the tensor invariants to values of the RGB color space. Secondly, the RGB colors of the tensor invariants are transferred to corresponding hue values as an alternative color representation. The vectorial tensor invariants field is reduced to a scalar hue field and visualization of iso-surfaces of this hue value field allows us to identify locations with equivalent flow topology. Additionally highlighting by the maximum of the eigenvalue difference field reflects the magnitude of the structural change of the flow. The method is applied on a vortex breakdown flow structure inside a cylinder with a rotating lid.
[1] BakkerP. G., Bifurcations in Flow Patterns. PhD thesis, Delft University of Tech nology, 1988
[2] BauerD., PeikertR., Vortex Tracking in Scale-Space. In: Joint EURO-GRAPHICS — IEEE TCVG Symposium on Visualization (2002), pp. 233–240, 2002
[3] CabralB., LeedomL., Imaging Vector Fields Using Line Integral Convolution. In SIGGRAPH '93 Conf. Proc., pp. 263–272, 1993
[4] ChongM. S., PerryA. E., CantwellB. J., A general classification of three-dimensional flow fields. Phys. Fluids A, vol. 2 (5), pp. 261–265, 1990
[5] DelmarcelleT., HesselinkL., The topology of second-order tensor fields. In Proc. of the Conf. on Visualization '94, pp. 140–148, 1994
[6] EscudierM. P., Observations of the flow produced in a cylindrical container by a rotating endwall. Exps. in Fluids, vol. 2, pp. 189–196, 1984
[7] FairchildM. D., Color Appearance Models, Addison-Wesley, Reading, MA, 1998
[8] FishkinK., A Fast HSL-to-RGB Transform, Pixar Inc., January 1989, from "Graphics Gems", Academic Press, 1990
[9] GlassnerA. S., How to Derive a Spectrum from an RGB Triblet, IEEE Computer Graphics and Applications, vol. 9 (4), pp. 95–99, 1989
[10] HelmanJ., HesselinkL., Visualizing vector field topology in fluid flows. IEEE Computer Graphics and Applications, vol. 11 (3), pp. 36–46, 1991
[11] HotzI., FengL., HagenH., HamannB., JeremicB., and JoyK., Physically Based Methods for Tensor Field Visualization. In Proc. of the IEEE Visualization '04 Conf., pp. 123–130, 2004
[12] InterranteV., GroschC., Visualizing 3D Flow. IEEE Computer Graphics and Applications, vol. 18 (4), pp. 49–53, 1998
[13] LiP. P., SiegelH., Visualization of Earthquake Simulation Data. In Proc. of NASA Earth Science Technology Conf., 2004
[14] KenwrightD. N., HenzeC., LevitC., Feature extraction of separation and attachment lines. In IEEE Transactions on Visualization and Computer Graphics, 5 (2), pp. 135–144, 1999
[15] de LeeuwW. C., van WijkJ. J., A Probe for Local Flow Field Visualization. In Proc. of the Visualization '93 Conf., pp. 39–45, 1993
[16] ReynW. J., Classification and Description of the Singular Points of a System of Three Linear Differential Equations. ZAMP, vol. 15, 1964
[17] RüttenM., Topological Analysis of the Vortex Breakdown in a Closed Cylinder with a Rotating Lid, In Proc. of the European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2004, Jyvskyl, Finland, 2004
[18] ScheuermannG., HagenH., KrugerH., MenzelM., RockwoodA., Visualization of higher order singularities in vector fields. In Proc. of IEEE Visualization '97 Conf., pp. 67–74, 1997
[19] TheiselH., RsslCh., SeidelH.-P., Using Feature Flow Fields for Topological Comparison of Vector Fields, In Proc. of the Conf. on Vision, Modeling and Visualization '03, pp. 521–528, 2003
[20] TheiselH., WeinkaufT., Vector Field Metrics based on Distance Measures of First Order Critical Points, Proc. WSCG'2002, The 10-th International Conf. in Central Europe on Computer Graphics, Visualization and Computer Vision, Plzen, Czech Republic, 2002
[21] TheiselH., WeinkaufT., HegeH.-C., SeidelH.-P., Stream Line and Path Line Orientated Topology for 2D Time-Dependent Vector Fields, In Proc. of IEEE Visualization '04 Conf., pp. 321–328, 2004
[22] TricocheX., GarthC., KindlmannG., DeinesE., ScheuermannG., RttenM., HansenC., Visualization of Intricate Flow Structures for Vortex Breakdown Analysis. In Proc. of the IEEE Visualization '04 Conf., pp. 187–194, 2004
[23] TricocheX., GarthC., BobachT., ScheuermannG., RttenM., Accurate and Efficient Visualization of Flow Structures in a Delta Wing Simulation. AIAA Paper 2004–2153, in Proc. of 34th AIAA Fluid Dynamics Conference and Exhibit, Portland, OR, 2004
[24] ZhengX. and PangA., HyperLIC, In Proc. of the IEEE Visualization '03 Conference, pp. 249–256, 2003
[25] ZhukovL., MusethK., BreenD., BarrA. H., WhitakerR., Level Set Segmentation and Modeling of DT-MRI Human Brain Data. Journal of Electronic Imaging, vol. 12, pp. 125–133, 2003
[26] van WijkJ.J., Spot noise-Texture Synthesis for Data Visualization, in Computer Graphics. In Proc. of SIGGRAPH '91, T.W. Sederberg, Editor., Las Vegas, Nevada, pp. 309–318, 1991
Index Terms:
Flow visualization, Tensor field Topology, Invariants
Citation:
Markus Rütten, Min S. Chong, "Analyzing Vortex Breakdown Flow Structures by Assignment of Colors to Tensor Invariants," IEEE Transactions on Visualization and Computer Graphics, vol. 12, no. 5, pp. 1189-1196, Sept. 2006, doi:10.1109/TVCG.2006.119
