Interaction of a characteristic shock with a weak discontinuity in a non-ideal gas

Wave Motion

Volumn 44, Issue 5, 2007, Pages 346-354

  Pandey, Manoj ^a   Sharma, V D ^a  

^a INDIAN INSTITUTE OF TECHNOLOGY BOMBAY   (India)

Author keywords

Characteristic shock; Group theoretic method; van der Waals gas; Weak discontinuity

Indexed keywords

ACCELERATION; FLOW OF GASES; SHOCK WAVES; VAN DER WAALS FORCES;

CHARACTERISTIC SHOCK; GROUP THEORETIC METHOD; WEAK DISCONTINUITY;

FLOW INTERACTIONS;

ACCELERATION; FLOW INTERACTIONS; FLOW OF GASES; SHOCK WAVES; VAN DER WAALS FORCES;

AMPLITUDE; EQUATION; GAS FLOW; NUMERICAL METHOD; SHOCK WAVE; THEORETICAL STUDY; WAVE ATTENUATION; WAVE REFLECTION; WAVE VELOCITY;

EID: 33947318071     PISSN: 01652125     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.wavemoti.2006.12.002     Document Type: Article

References (24)

1. Jeffrey A. Quasilinear hyperbolic systems and waves (1976), Pitman, London
2. Brun L. Ondes de xhoc finies dans les soliders elastiques. In: Mandel J., and Brun L. (Eds). Mechanical Waves in Solids (1975), Springer, Vienna
3. Morro A. Interaction of acoustic waves with shock waves in elastic solids. ZAMP 29 (1978) 822-827
4. Morro A. Interaction of waves with shock in Magnetogasdynamics. Acta Mechanica. 35 (1980) 197-213
5. Boillat G., and Ruggeri T. Energy momentum wave velocities and characteristic shocks in Euler's variational equations with application to the Born-infeld theory. J. Math. Phys. 45 (2004) 3468-3478
6. Boillat G., and Ruggeri T. Reflection and transmission of discontinuity waves through a shock wave. General theory including also the case of characteristic shocks. Proc. Roy. Soc. Edin. 83A (1979) 17-24
7. Ruggeri T. Interaction between a discontinuity wave and a shock wave: critical time for the fastest transmitted wave, example of the polytropic fluid. Appl. Anal. 11 (1980) 103-112
8. Virgopia N., and Ferraioli F. On the evolution of characteristic shocks in rotating flows with axial magnetic fields. Continuum Mech. Therm. 6 (1994) 31-49
9. Jena J., and Sharma V.D. On the evolution of a characteristic shock and its interaction with a discontinuity wave in a relaxing gas. In: DeSanto J.A. (Ed). Mathematical and Numerical Aspects of Wave Propagation (1998), SIAM 685-687
10. Radha Ch., Sharma V.D., and Jeffrey A. Interaction of shock waves with discontinuities. Appl. Anal. 50 (1993) 145-166
11. Donato A., and Oliveri F. When non-autonomous equations are equivalent to autonomous ones. Appl. Anal. 58 (1995) 313-323
12. Jena J., and Sharma V.D. Self-similar shocks in a dusty gas. Int. J. Non-Linear Mech. 34 (1999) 313-327
13. Conforto F. Wave feature and group analysis for an axi-symmetric model of dusty gas. Int. J. Non-Linear Mech. 35 (2000) 925-930
14. Bluman G.W., and Kumei S. Symmetries and Differential Equations (1981), Springer, New York
15. Olver P.J. Applications of Lie Groups to Differential Equations (1986), Springer, New York
16. Rogers C., and Ames W.F. Nonlinear Boundary Value Problems in Science and Engineering (1989), Academic Press, New York
17. Pert G.J. Self-similar flow with uniform velocity gradient and their use in modelling the free expansion of polytropic gases. J. Fluid Mech. 100 (1980) 257-277
18. Sharma V.D., Ram R., and Sachdev P. Uniformly valid analytical solution to the problem of decaying shock wave. J. Fluid Mech. 185 (1987) 153-170
19. Clarke J.F. Small amplitude gasdynamic disturbance in an exploding atmosphere. J. Fluid Mech. 89 (1978) 343-355
20. Boillat G. Chocs caractristiques. C.R. Acad. Sci. Paris Ser. A 283 (1976) 409-412
21. Anile A.M., Hunter J.K., Pantano P., and Russo G. Ray Methods for Non-linear Waves in Fluids and Plasmas (1993), Longman Scientific and Technical, UK
22. Boillat G. La propagation des ondes (1965), Gauthier-Villars, Paris
23. Boillat G., and Ruggeri T. On the evolution law of weak discontinuities for hyperbolic quasi-linear systems. Wave Motion 1 2 (1979) 149-152
24. Courant R., and Friedrich K.O. Supersonic Flow and Shock Waves (1976), Springer, New York