A. A. Zlotnik, I. A. Zlotnik, “Stability criterion for small perturbations for a quasi-gasdynamic system of equations”, Zh. Vychisl. Mat. Mat. Fiz., 2006, Volume 46, Number 2,Pages <nobr>262

This article is cited in 5 papers

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

A. A. Zlotnik^a, I. A. Zlotnik^b

^a Faculty of Computational Mathematics and Cybernetics, Moscow State University, Leninskie gory, Moscow, 119992, Russia
^b Faculty of Computational Mathematics and Cybernetics, Moscow State University, Leninskie gory, Moscow, 119992, Russia

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 $\gamma$, the stability is determined only by the background Mach number, and a necessary and sufficient condition for stability at any Mach number is $\gamma\le\bar\gamma$, where $\bar\gamma\approx6.2479$. 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.

Key words: quasi-gasdynamic systems, stability of small perturbations, Routh–Hurwitz criterion, Mathematica.

UDC: 519.634

Received: 26.08.2005