Asymptotical Solutions in a Reactive non-ideal

Transcription

Asymptotical Solutions in a Reactive non-ideal
Asymptotical Solutions in a Reactive non-ideal
Hydrodynamic medium
Rajan Arora
Indian Institute of Technology Roorkee, Saharanpur Campus,
Saharanpur-247001, U.P., India
rajan [email protected], [email protected]
Using the weakly non-linear geometrical acoustics theory, we obtain the small
amplitude high frequency asymptotic solution to the basic equations governing one dimensional unsteady planar, spherically and cylindrically symmetric
flow in a reactive non-ideal hydrodynamic medium. The transport equations
for the amplitudes of resonantly interacting waves are derived. The evolutionary behavior of non-resonant wave modes culminating into shock waves is also
studied.
References
[1] Y. B. Zel’Dovich, On the theory of the propagation of detonation in
gaseous systems, J. of Experimental and Theoretical Physics of the U.S.S.R.,
10 (1940), pp. 542-568.
[2 ] V. Choquet-Bruhat, Ondes asymptotique et approchees pour systemes
d’equations aux derivees partielles nonlineaires, J. Math. Pures Appl. 48
(1969), pp. 119-158.
[3] J. K. Hunter and J. Keller, Weakly nonlinear high frequency waves, Comm.
Pure Appl. Math., 36 (1983), pp. 547-569.
[4] V. D. Sharma and Gopala Krishna Srinivasan, Wave interaction in a nonequilibrium gas flow, Int. J. Non-linear Mechanics 40, (2005), pp. 10311040.
[5] Rajan Arora, Asymptotical Solutions for vibrationally relaxing gas, Journal of Mathematical Modelling and Analysis, 14(4), (2009), pp. 423-434.

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