This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Feature Extraction of Separation and Attachment Lines *
April-June 1999 (vol. 5 no. 2)
pp. 135-144

Abstract—Separation and attachment lines are topologically significant curves that exist on 2D surfaces in 3D vector fields. Two algorithms are presented, one point-based and one element-based, that extract separation and attachment lines using eigenvalue analysis of a locally linear function. Unlike prior techniques based on piecewise numerical integration, these algorithms use robust analytical tests that can be applied independently to any point in a vector field. The feature extraction is fully automatic and suited to the analysis of large-scale numerical simulations. The strengths and weaknesses of the two algorithms are evaluated using analytic vector fields and also results from computational fluid dynamics (CFD) simulations. We show that both algorithms detect open separation lines–a type of separation that is not captured by conventional vector field topology algorithms.

[1] R.F.W. Bader, Atoms in Molecules–A Quantum Theory. Oxford, U.K.: Oxford Univ. Press, 1990.
[2] F. Brauer and J.A. Nohel, Qualitative Theory of Ordinary Differential Equations. W.A. Benjamin, Inc., pp. 33-95, 1969.
[3] B. Cabral and L.C. Leedom, "Imaging Vector Fields Using Line Integral Convolution," Computer Graphics (SIGGRAPH '93 Proc.), pp. 263-272, 1993.
[4] N.M. Chaderjian and L.B. Schiff, "Navier-Stokes Analysis of a Delta Wing in Static and Dynamic Roll," AIAA-95-1868, AIAA Ann. CFD Meeting 1995.
[5] G.T. Chapman, "Topological Classification of Flow Separation on Three-Dimensional Bodies," AIAA-86-0485, AIAA 24th Aerospace Sciences Meeting, Reno, Nev. 1986.
[6] M.S. Chong, A.E. Perry, and B.J. Cantwell, "A General Classification of Three-Dimensional Flow Fields," Physical Fluids A., vol. 2 pp. 765-777, 1990.
[7] M.S. Chong and A.E. Perry, "Synthesis of Two- and Three-Dimensional Separation Bubbles," Proc. Ninth Australasian Fluid Mechanics Conf., pp. 35-38, Auckland, New Zealand, Dec. 1986.
[8] U. Dallman, "Topological Structures of Three-Dimensional Vortex Flow Separation," AIAA-83-1935 Proc. AIAA 16th Fluid and Plasma Dynamics Conf., 1983.
[9] W.C. de Leuuw, H.-G. Pagendarm, F.H. Post, and B. Walter, "Visual Simulation of Experimental Oil-Flow Visualization by Spot Noise Images from Numerical Simulation," Visualization in Scientific Computing '95, pp. 135-148, Wien, Springer-Verlag, 1995.
[10] L. Forssell, “Visualizing Flow over Curvilinear Grid Surfaces Using Line Integral Convolution,” Proc. IEEE Visualization '94, pp. 240-246, 1994.
[11] A. Globus, C. Levit, and T. Lasinski, "A Tool for Visualizing the Topology of Three-Dimensional Vector Fields," Proc. IEEE Visualization '91, pp. 33-40, 1991.
[12] J. Helman and L. Hesselink,“Surface representation of two- and three-dimensional fluid flow topology,” Proc. Visualization’90, IEEE Computer Society, San Francisco, 1990.
[13] C. Levit, Conf. Scientific Applications of the Connection Machine, NASA Ames Research Center, Moffett Field, Calif., Sept. 1989.
[14] D.N. Kenwright, "Automatic Detection of Open and Closed Separation and Attachment Lines," Proc. IEEE Visualization '98, pp. 151-158, 1998.
[15] M.J. Lighthill, "Attachment and Separation in Three-Dimensional Flow," Laminar Boundary Layers, L. Rosenhead II, ed., vol. 2.6, pp. 72-82, Oxford Univ. Press, 1963.
[16] W. Merzkirch, Flow Visualization. New York: Academic Press, 1974.
[17] H.-G. Pagendarm and B. Walter, "Feature Detection from Vector Quantities in a Numerically Simulated Hypersonic Flow Field in Combination with Experimental Flow Visualization," Proc. Visualization '94, pp. 117-123, 1994.
[18] R.L. Panton, Incompressible Flow. John Wiley&Sons, 1984.
[19] H. Poincare, Oeuvres de Henri Poincare, Tome 1. Paris: Gautheir-Villars, 1928.
[20] G. Scheuermann, H. Hagen, H. Kruger, M. Menzel, and A. Rockwood, Visualization of Higher-Order Singularities in Vector Field Proc. Visualization '97, pp. 67-74, Oct. 1997.
[21] H.-W. Shen and D.L. Kao, “Uflic: A Line Integral Convolution Algorithm for Visualizing Unsteady Flows,” Proc. Visualization '97, pp. 317-322, 1997.
[22] M. Tobak and D.J. Peake, "Topology of Three-Dimensional Separated Flows," Ann. Review of Fluid Mechanics, vol. 14, pp. 61-85, 1982.
[23] J.J. van Wijk, “Spot Noise-Texture Synthesis for Data Visualization,” Computer Graphics (SIGGRAPH '91 Proc.), T.W. Sederberg, ed., vol. 25, pp. 309-318, July 1991.
[24] K.C. Wang, "Separation Patterns of a Boundary Layer Over an Inclined Body," AIAA J., vol. 10, no. 8, pp. 1,044-1,050, 1972.
[25] K.C. Wang, H.C. Zhou, C.H. Hu, and S. Harrington, "Three-Dimensional Separated Flow Structure Over Prolate Spheroids," Proc. R. Soc. London, A 421, pp. 73-90, 1990.
[26] J.Z. Wu, J.W. Gu, and J.M. Wu, "Steady Three-Dimensional Fluid Particle Separation from Arbitrary Smooth Surface and Formation of Free Vortex Layers," AIAA-87-2348, AIAA Ann. CFD Meeting, 1987.
[27] H.X. Zhang, Chinese J. of Aerodynamics, no. 4,Beijing, Peoples Republic of China, Dec. 1985.
[28] D. Zwillinger, Handbook of Differential Equations, second ed. Academic Press, pp. 360-363, 1957.

Index Terms:
Vector field visualization, vector field topology, flow visualization, feature detection, flow separation, separation line.
Citation:
David N. Kenwright, Chris Henze, Creon Levit, "Feature Extraction of Separation and Attachment Lines *," IEEE Transactions on Visualization and Computer Graphics, vol. 5, no. 2, pp. 135-144, April-June 1999, doi:10.1109/2945.773805
Usage of this product signifies your acceptance of the Terms of Use.