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A ‘Pseudo-Viscosity’ Method for Calculating Two-Dimensional Flow Fields

Published online by Cambridge University Press:  07 June 2016

F. Walkden  and
J. E. Sellars
F. Walkden
Affiliation:
Royal College of Advanced Technology, Salford
J. E. Sellars
Affiliation:
Royal College of Advanced Technology, Salford
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Summary

A scheme that uses an implicit system of finite-difference equations to obtain solutions of the equations governing the two-dimensional supersonic motion of an inviscid gas is described. The method relies on pseudo-viscosity in order to calculate shock waves. Compared with characteristics methods, pseudo-viscosity methods have certain advantages. For example, shock waves are calculated automatically without special procedures and pseudo-viscosity methods are easily generalised so that problems with three or more independent variables may be considered. Pseudo-viscosity methods have not been used extensively in the field of aerodynamics, partly because of the difficulty in obtaining sufficiently accurate solutions in the neighbourhood of a boundary. The main purpose of this paper is to show how this difficulty can be overcome. The problem of integrating the equations of motion when a boundary condition has to be satisfied on an arbitrary curve is considered. Streamlines are used as one of the independent variables so that the boundary curve is a coordinate curve, and the equations of motion are used in a form which leads to a simple procedure at the wall. For a given system of partial differential equations it is possible to introduce pseudo-viscous terms in many ways, not all of which are satisfactory. The results presented show that the method proposed in this paper is adequate. The calculated results are accurate and vary smoothly in the neighbourhood of the boundary.

Type
Research Article
Information
Aeronautical Quarterly , Volume 17 , Issue 3 , August 1966 , pp. 285 - 301
Copyright
Copyright © Royal Aeronautical Society. 1966

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References

1. Von Neumann, J. and Richtmyer, R. D. A method for the numerical calculation of hydro-dynamic shocks. Journal of Applied Physics, Vol. 21, p. 232, 1950.CrossRefGoogle Scholar
2. Evans, M. W. and Harlow, F. W. The particle-in-cell method for hydrodynamic calculation. Los Alamos M.S. LA2139, 1957.Google Scholar
3. Kolsky, H. A method for the numerical solution of transient hydrodynamic shock problems in two space dimensions. Los Alamos LA1867, 1954.Google Scholar
4. Lax, P. D. Weak solutions of non-linear hyperbolic equations and their numerical computation. Communications in Pure and Applied Mathematics, Vol. 7, p. 159, 1954.CrossRefGoogle Scholar
5. Walkden, F. On the numerical calculation of three-dimensional supersonic flows. PhD Thesis, Manchester University, 1959.Google Scholar
6. Courant, R., Isaacson, E. and Rees, M. On the solution of non-linear hyperbolic differential equations by finite differences. Communications in Pure and Applied Mathematics, Vol. 5, p. 243, 1952.CrossRefGoogle Scholar
7. Stratton, J. R. Electromagnetic theory. McGraw-Hill, New York, 1941.Google Scholar
8. Richtmyer, R. D. Difference methods for initial value problems. Interscience Publishers, New York, 1957.Google Scholar
9. Walkden, F. and Howie, J. M. A new method for calculating the supersonic flow past a body. Unpublished Ministry of Aviation Note, 1962.Google Scholar