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

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Abstract | References | 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.

**[1]**H. Bateman, Proc. Nat. Acad. Sci. U.S.A.**24**, 246-251 (1938)**[2]**A. Haar, Math. Ann.**100**, 481-502 (1928)**[3]**R. C. Prim, J. Appl. Phys.**20**, 448-450 (1949)**[4]**H. S. Tsien,*Two-dimensional subsonic flow of compressible fluids*, J. Aero. Sci.**6**, 399-407 (1939) MR**0003135****[5]**H. Bateman, Quart. Appl. Math.**1**, 281-298 (1944) MR**0009686****[6]**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) MR**0128246****[7]**G. Power and A. Tunbridge,*Reciprocal properties in magnetogasdynamics*, ZAMM**43**, 191-197 (1963) MR**0153249****[8]**G. Power and D. Walker,*Some reciprocal relations in rotational magnetogasdynamic flow*, ZAMP**15**, 2, 144-154 (1964) MR**0167127****[9]**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)**[10]**P. Smith,*An extension of the substitution principle to certain unsteady gas flows*, Arch. Rat. Mech Anal.**15**, 147-153 (1964) MR**0154519****[11]**E. D. Tomilov,*On the method of invariant transformations of the gas-dynamic equations*, P.M.M.**29**, 959-960 (1965)**[12]**v. A. Rykov, On an exact solution of the equations of magnetogasdynamics of finite conductivity, P. M. M.**29**, 178-181 (1965)**[13]**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)**[14]**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)**[15]**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) MR**0049731****[16]**L. I. Sedov,*On the integration of the equations of one-dimensional motion of a gas*, DAN SSSR**90**, 5 (1953) MR**0057111****[17]**C. Rogers,*Reciprocal relations in non-steady one-dimensional gasdynamics*, ZAMP**19**, 1, 58-63 (1968)**[18]**C. Rogers,*Invariant transformations in non-steady gasdynamics and magnetogasdynamics*, ZAMP**20**, 3, 370-382 (1969)

Additional Information

DOI:
https://doi.org/10.1090/qam/99682

Article copyright:
© Copyright 1974
American Mathematical Society