Applications of invariant transformations in one-dimensional non-steady gasdynamics
Authors:
S. P. Castell and C. Rogers
Journal:
Quart. Appl. Math. 32 (1974), 241-251
DOI:
https://doi.org/10.1090/qam/99682
MathSciNet review:
QAM99682
Full-text PDF Free Access
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Additional Information
Abstract: Certain reciprocal and adjoint transformations available for one-dimensional non-steady gasdynamic flow are applied to an existing solution to construct new exact solutions of the governing equations. The particle trajectories and the pressure-density relations on these trajectories are calculated. An application of the adjoint transformation in studying the flow between a piston and a non-uniform shock wave is indicated.
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v. A. Rykov, On an exact solution of the equations of magnetogasdynamics of finite conductivity, P. M. M. 29, 178–181 (1965)
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C. Rogers, Reciprocal relations in non-steady one-dimensional gasdynamics, ZAMP 19, 1, 58–63 (1968)
C. Rogers, Invariant transformations in non-steady gasdynamics and magnetogasdynamics, ZAMP 20, 3, 370–382 (1969)
H. Bateman, Proc. Nat. Acad. Sci. U.S.A. 24, 246–251 (1938)
A. Haar, Math. Ann. 100, 481–502 (1928)
R. C. Prim, J. Appl. Phys. 20, 448–450 (1949)
H. S. Tsien, Two-dimensional subsonic flow of compressible fluids, J. Aero. Sci. 6, 399–407 (1939)
H. Bateman, Quart. Appl. Math. 1, 281–298 (1944)
G. Power and P. Smith, Applications of a reciprocal properly to subsonic flow, Appl. Sci. Res. A8, 386–392 (1959); Reciprocal properties of plane gas flows, J. Math. Mech. 10, 349–361 (1961)
G. Power and A. Tunbridge, Reciprocal properties in magnetogasdynamics, ZAMM 43, 191–197 (1963)
G. Power and D. Walker, Some reciprocal relations in rotational magnetogasdynamic flow, ZAMP 15, 2, 144–154 (1964)
A. A. Nikol’skii, Invariant transformations of the equations of motion of an ideal monatomic gas and new classes of their exact solution, P.M.M. 27, 740–756 (1963)
P. Smith, An extension of the substitution principle to certain unsteady gas flows, Arch. Rat. Mech Anal. 15, 147–153 (1964)
E. D. Tomilov, On the method of invariant transformations of the gas-dynamic equations, P.M.M. 29, 959–960 (1965)
v. A. Rykov, On an exact solution of the equations of magnetogasdynamics of finite conductivity, P. M. M. 29, 178–181 (1965)
M. D. Ustinov, Transformation and some solutions of the equations of motion of an ideal gas, Izv. AN SSSR Mekh. Zhid. I Gaza (Fluid Dynamics) 3, 68–74 (1966); Ideal gas flow behind a finite-amplitude shock wave, Izv. AN SSSR Mekh. Zhid. I Gaza 2, 1, 88–90 (1967)
L. A. Movsesian, On an invariant transformation of equations of one-dimensional unsteady motion of an ideal compressible fluid, P.M.M. 31, 137–141 (1967)
M. H. Martin, A new approach to problems in two-dimensional flow, Quart. Appl. Math. 8, 137–150 (1950); The propagation of a plane shock into a quiet atmosphere, Canadian J. Math. 5, 37–39 (1953)
L. I. Sedov, On the integration of the equations of one-dimensional motion of a gas, DAN SSSR 90, 5 (1953)
C. Rogers, Reciprocal relations in non-steady one-dimensional gasdynamics, ZAMP 19, 1, 58–63 (1968)
C. Rogers, Invariant transformations in non-steady gasdynamics and magnetogasdynamics, ZAMP 20, 3, 370–382 (1969)
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Article copyright:
© Copyright 1974
American Mathematical Society