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A family of exact solutions of one-dimensional anisentropic flow

Published online by Cambridge University Press:  24 October 2008

D. G. Weir
D. G. Weir
Affiliation:
Department of MathematicsThe Royal College of Science and TechnologyGlasgow
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Extract

Martin(1) has shown that if the pressure p and the Lagrange variable ψ (ψ = constant on a trajectory) are taken as independent variables, then problems in one-dimensional unsteady flow of an ideal gas reduce to the question of finding solutions of the Monge-Ampère equation

where τ = 1/ρ, ρ being the density, and S = S(ψ) is the specific entropy. Thus the right-hand term is a function of p and ψ depending upon the equation of state and the function S(ψ).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 57 , Issue 4 , October 1961 , pp. 890 - 894
Copyright
Copyright © Cambridge Philosophical Society 1961

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References

REFERENCES

(1)Martin, M. H., Quart. Appl. Math. 8 (1950), 137–50.CrossRefGoogle Scholar
(2)Pack, D. C., Mon. Not. R. Astr. Soc. 113 (1953), 43–51.CrossRefGoogle Scholar
(3)Prim, R. C., Naval Ordnance Laboratory Memorandum 9264 (1947), SB Project no. 192.Google Scholar