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.