Similarity solutions for strong shocks in an ideal gas

Studies in Applied Mathematics

Volumn 114, Issue 4, 2005, Pages 375-394

  Sharma, V D ^b   Arora, Rajan ^a,b  

^a INDIAN INSTITUTE OF TECHNOLOGY BOMBAY   (India)

^b INDIAN INSTITUTE OF TECHNOLOGY   (India)

Author keywords

[No Author keywords available]

Indexed keywords

ARBITRARY CONSTANTS; EXPONENTIALS; GASEOUS MEDIA; IDEAL GAS; IMPLODING SHOCKS; LIE-GROUPS; POWER-LAW; SELF-SIMILAR SOLUTION; SIMILARITY SOLUTION; STATE-DEPENDENT;

LIE GROUPS;

EID: 17444381624     PISSN: 00222526     EISSN: None     Source Type: Journal    
DOI: 10.1111/j.0022-2526.2005.01557.x     Document Type: Article

References (17)

1. G. GUDERLEY, Starke kugelige und zylindrische Verdichtungsstosse in der Nahe des Kugelmittelpunktes bzw der Zylinderachse, Luftfahrtforschung 19:302-312 (1942).
2. A. SAKURAI, On the problem of a shock wave arriving at the edge of a gas, Commun. Pure Appl. Math. 13:353-370 (1960).
3. Y. B. ZELDOVICH and Y. P. RAIZER, Physics of Shock Waves and High Temperature Hydrodynamic Phenomena, Vol. II, Academic Press, New York, 1967.
4. R. B. LAZARUS, Self-similar solutions for converging shocks and collapsing cavities, SIAM J. Numer. Anal. 18:316-371 (1981).
5. M. VANDYKE and A. J. GUTTMANN, The converging shock wave from a spherical or cylindrical piston, J. Fluid Mech. 120:451-462 (1982).
6. P. HAFNER, Strong convergent shock waves near the center of convergence: A power series solution, SIAM J. Appl. Math. 48:1244-1261 (1988).
7. V. D. SHARMA and C. RADHA, Similarity solutions for converging shocks in a relaxing gas, Int. J. Engng. Sci. 33:535-553 (1995).
8. G. MADHUMITA and V. D. SHARMA, Propagation of strong converging shock waves in a gas of variable density, J. Engng. Math. 46:55-68 (2003).
9. S. STEEB, Similarity solutions of the Euler equation and the Navier-Stokes equation in two space dimensions, Int. J. Theor. Phys. 24:255-265 (1985).
10. G. W. BLUMAN and J. D. COLE, Similarity Methods for Differential Equations, Springer, Berlin, 1974.
11. J. D. LOGAN, Applied Mathematics: A Contemporary Approach, Wiley Interscience, New York, 1987.
12. G. W. BLUMAN and S. KUMEI, Symmetries and Differential Equations, Springer, New York, 1989.
13. W. D. HAYES, Self-similar strong shocks in an exponential medium, J. Fluid Mech. 32:305-315 (1968).
14. G. B. WHITHAM, Linear and NonLinear Waves, Wiley Interscience, New York, 1974.
15. R. RAVINDRAN, Strong shock approximation in the new theory of shock dynamics, Quart. J. Mech. Appl. Math. 50:251-259 (1997).
16. V. D. SHARMA and C. RADHA, One dimensional planar and nonplanar shock waves in a relaxing gas, Phys. Fluids 6:2177-2190 (1994).
17. G. MADHUMITA and V. D. SHARMA, Imploding cylindrical and spherical shock waves in a nonideal medium, J. Hyperbolic Diff. Equa. 1(3):521-530 (2004).