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Stability criterion for small perturbations for a quasi-gasdynamic system of equations

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Abstract

The stability of small perturbations against a constant background is studied for a system of quasi-gasdynamic equations in an arbitrary number of space variables. It is established that, for a fixed adiabatic exponent γ, the stability is determined only by the background Mach number, and a necessary and sufficient condition for stability at any Mach number is \(\gamma \leqslant \bar \gamma \), where \(\bar \gamma \approx 6.2479\). The proof is based on a direct analysis of the corresponding complex characteristic numbers depending on several parameters. The multidimensional case is successfully reduced to the one-dimensional one. Then, the generalized Routh-Hurwitz criterion is applied in conjunction with analytical calculations based on Mathematica.

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References

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Authors and Affiliations

  1. Moscow Power Engineering Institute (Technical University), Krasnokazarmennaya ul. 14, Moscow, 111250, Russia

    A. A. Zlotnik

  2. Faculty of Computational Mathematics and Cybernetics, Moscow State University, Leninskie gory, Moscow, 119992, Russia

    I. A. Zlotnik

Authors
  1. A. A. Zlotnik
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  2. I. A. Zlotnik
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Original Russian Text © A.A. Zlotnik, I.A. Zlotnik, 2006, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2006, Vol. 46, No. 2, pp. 262–269.

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Zlotnik, A.A., Zlotnik, I.A. Stability criterion for small perturbations for a quasi-gasdynamic system of equations. Comput. Math. and Math. Phys. 46, 251–257 (2006). https://doi.org/10.1134/S0965542506020072

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  • DOI: https://doi.org/10.1134/S0965542506020072

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