Stream Surface Generation for Fluid Flow Solutions on Curvilinear Grids

  • Allen Van Gelder
Conference paper
Part of the Eurographics book series (EUROGRAPH)


A istream surface in a steady-state three-dimensional fluid flow vector field is a surface across which there is no flow. Stream surfaces can be useful for visualization because the amount of data presented in one visualization can be confined to a manageable quantity in a physically meaningful way.

This paper describes a method for generation of stream surfaces, given a threedimensional vector field defined on a curvilinear grid. The method can be characterized as semi-global; that is, it tries to find a surface that satisfies constraints over a region, expressed as integrals (actually sums, due to discreteness), rather than locally propagating the solution of a differential equation.

The solution is formulated as a series of quadratic minimization problems in n variables, where nis the cross-wind resolution of the grid. An efficient solution method is developed that exploits the fact that the matrix of each quadratic form is tridiagonal and symmetric. Significant numerical issues are addressed, including degeneracies in the tridiagonal matrix and degeneracies in the grid, both of which are typical for the applications envisioned.


Height Field Stream Surface Bilinear Model Computational Space Curvilinear Grid 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [FWJ98]
    D. Feng, C. Wenli, and S. Jiaoying. Stream surface construction using mass conservative interpolation. J. Computer Science and Technology, 13(suppl.issue):45–53, 1998.MATHGoogle Scholar
  2. [Hul92]
    J. P. M. Hultquist. Constructing stream surfaces in steady 3D vector fields. In Proceedings of Visualization’ 92, pages 171–178, Boston, MA, October 1992. IEEE.Google Scholar
  3. [Ken93]
    D. N. Kenwright. Dual Stream Function Methods for Generating Three-Dimensional Streamlines. PhD thesis, Department of Mechanical Engineering, University of Aukland, New Zealand, August 1993.Google Scholar
  4. [KHL99]
    D. N. Kenwright, C. Henze, and C. Levit. Feature extraction of separation and attachment lines. IEEE Trans. Visualization and Computer Graphics, 5(2):135–144, 1999.CrossRefGoogle Scholar
  5. [KM92]
    D. N. Kenwright and G. D. Mallinson. A 3-D streamline tracking algorithm using dual stream functions. In Visualization’ 92, pages 62–68. IEEE, October 1992.Google Scholar
  6. [KM96]
    D. Knight and G. D. Mallinson. Visualizing unstructured flow data using dual stream functions. IEEE Trans. Visualization and Computer Graphics, 2(4):355–363, 1996.CrossRefGoogle Scholar
  7. [Lam32]
    Horace Lamb. Hydrodynamics. Dover, 6th edition, 1932.Google Scholar
  8. [vW93]
    J. J. van Wijk. Implicit stream surfaces. In Visualization’ 93, pages 245–252, San Jose, CA, 1993. IEEE Comput. Soc. Press.Google Scholar

Copyright information

© Springer-Verlag Wien 2001

Authors and Affiliations

  • Allen Van Gelder
    • 1
  1. 1.Computer Science DepartmentUniversity of CaliforniaSanta CruzUSA

Personalised recommendations