Visualizing Vector Field Topology in Fluid Flows
May/June 1991 (vol. 11 no. 3)
pp. 36-46
DOI Bookmark:
http://doi.ieeecomputersociety.org/10.1109/38.79452
Methods for automating the analysis and display of vector field topology in general, and flow topology in particular, are described. By using techniques to extract and visualize topological information, it is possible to combine the simplicity of schematic depictions with the quantitative accuracy of curves and surfaces computed directly from the data. Two-dimensional vector field topology is discussed, covering critical points and time-dependent flows, to provide a basis for the examination of topology in three-dimensional separated flows. Surface topology and separation structures in three-dimensional flows are then addressed. The construction of representations of tangent surfaces that are accurate, as well as efficient to compute and display, is examined, covering tessellation, clipping, and refinement. Locating, characterizing, and displaying three-dimensional critical points are considered. 1. P. Buning and J. Steger, "Graphics and Flow Visualization in Computational Fluid Dynamics,"Proc. AIAA 7th Computational Fluid Dynamics Conf., American Institute of Aeronautics and Astronautics, New York, 1985, pp.162-170.2. M. Tobak and D.J. Peake, "Topology of 3D Separated Flows,"Ann. Rev. Fluid Mechanics, Vol. 14, 1982, pp. 61-85.3. U. Dallmann, "Topological Structures of 3D Flow Separation," Tech. Report DFVLR-IB 221-82 A 07. German Research Institute for Aerospace. Göttingen, Germany, Apr. 1983.4. A.E. Perry and M.S. Chong, "A Description of Eddying Motions and Flow Patterns Using Critical Point Concepts,"Ann. Rev. Fluid Mechanics, 1987, pp. 125-156.5. J.L. Helman and L. Hesselink, "Automated Analysis of Fluid Flow Topology,"3D Visualization and Display Technologies(Proc. SPIE), Vol. 1083, SPIE, Bellingham, Wash., Jan. 1989, pp. 825-835.6. J.L. Helman and L. Hesselink, "Representation and Display of Vector Field Topology in Fluid Flow Data Sets,"Computer, Vol. 22, No. 8, Aug. 1989, pp. 27-36.7. S. Rogers and D. Kwak, "An Upwind Differencing Scheme for Time Accurate Incompressible Navier-Stokes Equations,"Proc. AIAA 6th Applied Aerodynamics Conference, American Institute of Aeronautics and Astronautics, New York, June 1988, pp. 492-502.8. S.X. Ying, L.B. Schiff, and J.L. Steger, "A Numerical Study of 3D Separated Flow Past a Hemisphere Cylinder,"Proc. AIAA 19th Fluid Dynamics, Plasma Dynamics and Lasers Conf., American Institute of Aeronautics and Astronautics, June 1987, paper 87-1207.9. H. Fuchs. Z. M. Kedem, and S. P. Uselton, "Optimal surface reconstruction from planar contours,"Commun. ACM, vol. 20, Oct. 1977.10. P. Maillot, "Three Dimensional Homogeneous Clipping of Triangular Strips," Tech. Report, Sun Microsystems, Mountain View, Calif.. Oct. 1990.11. A. Blaquiere,Nonlinear System Analysis, Academic, New York, 1966.12. M.S. Chong, A.E. Perry, and B.J. Cantwell, "A General Classification of 3D Flow Fields,"Physics of Fluids Ann., Vol. 2, No. 5, May 1990, pp. 765-777.
Citation:
James L. Helman, Lambertus Hesselink, "Visualizing Vector Field Topology in Fluid Flows," IEEE Computer Graphics and Applications, vol. 11, no. 3, pp. 36-46, May/June 1991, doi:10.1109/38.79452
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