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Asymptotic equations of gas dynamics: qualitative analysis, construction of solutions, and applications
P. A. Vel'misov, J. À. Tamarova, E. P. Semånova Ulyanovsk State Technical University
Abstract:
In this paper, we propose asymptotic expansions for the velocity potential and obtain asymptotic equations of gas dynamics for irrotational isentropic flows of an ideal gas: an equation of linear theory, a nonlinear equation for supersonic flows, and a nonlinear transonic equation. We construct some exact particular solutions for the asymptotic nonlinear transonic equation, which takes into account transverse perturbations. Based on a linear asymptotic equation, we examine the dynamic stability of an elastic deformable element of a channel at a subsonic flow rate of a gas or liquid. The study of stability is carried out in a statement corresponding to small perturbations of a homogeneous flow and small deformations of an elastic element, and is based on the construction of a positive definite functional. Sufficient stability conditions are obtained.
Keywords:
aerodynamics, partial differential equation, asymptotic expansion, transonic gas flow, channel, de Laval nozzle, aerohydroelasticity, dynamic stability.
Citation:
P. A. Vel'misov, J. À. Tamarova, E. P. Semånova, “Asymptotic equations of gas dynamics: qualitative analysis, construction of solutions, and applications”, Proceedings of the IV International Scientific Conference "Actual Problems of Applied Mathematics".
Kabardino-Balkar Republic, Nalchik, Elbrus Region, May 22–26, 2018. Part I, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 165, VINITI, Moscow, 2019, 47–62
Linking options:
https://www.mathnet.ru/eng/into466 https://www.mathnet.ru/eng/into/v165/p47
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Abstract page: | 188 | Full-text PDF : | 78 | References: | 22 | First page: | 2 |
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