Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Exact analytic solutions describing unsteady plane gas flows with shocks of arbitrary strength

Authors: P. L. Sachdev, Neelam Gupta and D. S. Ahluwalia
Journal: Quart. Appl. Math. 50 (1992), 677-726
MSC: Primary 76N15; Secondary 35L67, 76L05
DOI: https://doi.org/10.1090/qam/1193662
MathSciNet review: MR1193662
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Abstract: Several classes of exact analytic solutions for one-dimensional plane gas-dynamic equations describing piston-driven shocks propagating into inhomogeneous media are presented. These solutions are obtained by writing the conservation forms of the basic equations, and hence using their equivalent differential forms. These forms enable introduction of special coordinate systems which make it possible to exactly satisfy boundary conditions at the shock and at the piston. Previous results of Sachdev and Reddy [1] and Ustinov [2, 3] are recovered as special cases. Several representative solutions are shown graphically. Strong shocks as well as shocks of arbitrary strength and characteristic fronts are considered.

References [Enhancements On Off] (What's this?)

  • [1] P. L. Sachdev and A. Venkataswamy Reddy, Some exact solutions describing unsteady plane gas flows with shocks, Quart. Appl. Math. 40, 249-272 (1982) MR 678197
  • [2] M. D. Ustinov, Ideal gas flow behind a finite-amplitude shock wave, Izv. Akad. Nauk. SSSR Mekh. Zhidk. Gaza 2 no. 1, 88-90 (1967)
  • [3] M. D. Ustinov, Some one-dimensional unsteady adiabatic gas flows with plane symmetry, Izv. Akad. Nauk SSSR Mekh. Zhidk. Gaza 21 no. 5, 758-765 (1987)
  • [4] J. A. Steketee, Unsteady rectilinear flows of a non-homentropic gas, Acta Astronaut. 6, 413-434 (1979)
  • [5] J. A. Steketee, Homogeneous solutions of the Lagrangian equations of motion (Notes on the unsteady rectilinear motion of a perfect gas III), Report LR-258, Dept. of Aerospace Engineering, Delft University of Technology, Delft, 1977.

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DOI: https://doi.org/10.1090/qam/1193662
Article copyright: © Copyright 1992 American Mathematical Society

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