A Finite Element Method for Computing Transonic Potential Flow

  • S. A. Jepps
Part of the Notes on Numerical Fluid Mechanics book series (NONUFM, volume 3)


The finite element method has gained widespread acceptance as a technique for solving elliptic partial differential equations, where its ability to handle quite general geometries has proved an advantage over finite differences. For the steady flow of an inviscid fluid, the governing equations are elliptic as long as the flow speed is everywhere subsonic. In such cases the effects of compressibility are generally small, and results of adequate accuracy for engineering purposes can be obtained by applying approximate corrections to the solution obtained for incompressible flow. However, incompressible flow can be calculated using the so-called panel method or boundary integral equation approach. Because it reduces the problem from one of solving for an entire field to that of solving for quantities on the boundary, the latter approach is more efficient than either finite elements or finite differences. This fact has prevented the widespread use of finite elements for purely subsonic flow. Attention has therefore recently focused on the possibility of using the finite element method to treat flows which are not purely subsonic, and which thus contain regions in which the governing equation is hyperbolic. This paper describes one such attempt which makes use of the ‘artificial compressibility’ concept developed in ref. 1.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1).
    M. Hafez, J. South and E. Murman Artificial Compressibility Methods for Numerical Solution of Transonic Full Potential Equation. Paper presented at AIAA 11th Fluid and Plasma Dynamics Conference, Seattle, July 1978.Google Scholar
  2. 2).
    A. Eberle Eine Methode finiter Elemente zur Berechnung der transsonischen Potential-Strömung um Profile. MBB Bericht Nr UFE 1352 (6), Sept. 1977.Google Scholar
  3. 3).
    S. A. Jepps Application of the Finite Element Method to Aerodynamics BAe (Warton) Report No. Ae/A/6Q2 March 1979Google Scholar
  4. 4).
    J. F. Thompson, F. C. Thames and C. W. Mastin Automatic Numerical Generation of Body-Fitted Curvilinear Coordinate Systems for Fields Containing Any Number of Arbitrary Two-Dimensional Bodies. Journal of Computational Physics 15, 299 (1974)ADSzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Fachmedien Wiesbaden 1981

Authors and Affiliations

  • S. A. Jepps

There are no affiliations available

Personalised recommendations