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A family of exact solutions of one-dimensional anisentropic flow

  • D. G. Weir (a1)

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).

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References

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(1)Martin, M. H., Quart. Appl. Math. 8 (1950), 137–50.
(2)Pack, D. C., Mon. Not. R. Astr. Soc. 113 (1953), 4351.
(3)Prim, R. C., Naval Ordnance Laboratory Memorandum 9264 (1947), SB Project no. 192.
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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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