Viscous Flow Analysis Using the Poincaré Decomposition

  • Philip Beauchamp
  • Luigi Morino
Conference paper


A computational technique for the analysis of two-dimensional viscous fluid flow fields is presented. The technique is based on an exact formulation of the viscous flow problem using the Poincaré decomposition for the velocity field. The numerical method developed is a hybrid technique which employs the boundary integral method to determine the velocity field while the vorticity evolution is determined from a finite-difference technique. The technique has been applied to the transient and steady-state analysis of thin airfoils in arbitrary motion. Comparison with known results have been found to be in good agreement using computational grids that would defeat most other viscous solvers.


Boundary Element Method Viscous Flow Boundary Integral Method Helmholtz Decomposition Velocity Impulse 
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. [1]
    Batchelor, G. K.: An Introduction to Fluid Dynamics, Cambridge University Press, (1967).Google Scholar
  2. [2]
    Beauchamp, P.: “A Potential-Vorticity Decomposition for the Boundary Integral Equation Analysis of Viscous Flows,” Ph. D. Thesis, Graduate School, Division of Engineering and Applied Science, Boston University, Boston, MA, USA, (1990).Google Scholar
  3. [3]
    Lighthill, M. J.: “Introduction to Boundary Layer Theory,” Part II of Laminar Boundary Layers, Ed. L. Rosenhead, Oxford University Press, pp.46-113, (1963).Google Scholar
  4. [4]
    Morino, L.: “Helmholtz Decomposition Revisited: Vorticity Generation and Trailing Edge Condition. Part I — Incompressible Flows,” Computational Mechanics, No. 1, Vol. 1, (1986).Google Scholar
  5. [5]
    Morino, L., and Beauchamp, P.: “A Potential-Vorticity Decomposition for the Boundary-Element Analysis of Viscous Flows,” Eds.: M. Tanaka and T. A. Cruse, Boundary Element Methods in Applied Mechanics, Pergamon Press, New York, NY, USA, (1988).Google Scholar
  6. [6]
    Morino, L.: “Helmholtz and Poincaré Potential-Vorticity Decompositions for the Analysis of Unsteady Compressible Viscous Flows” Developments in Boundary Element Methods, Vol. 6: Nonlinear Problems of Fluid Dynamics, Eds. P.K. Banerjee and L. Morino, Elsevier Applied Science Publishers, Barking, UK, (1990).Google Scholar

Copyright information

© Springer-Verlag Berlin, Heidelberg 1991

Authors and Affiliations

  • Philip Beauchamp
    • 1
  • Luigi Morino
    • 2
  1. 1.General Electric Co.LynnUSA
  2. 2.Università di RomaRomeItaly

Personalised recommendations