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DOI 10.21662
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Transformations of gas dynamics equations and basis operators of a admitted 11-dimensional Lie algebra. Multiphase Systems. 15 (2020) 3–4. 217–222 (in Russian).
2020. Vol. 15. Issue 3–4, Pp. 217–222
URL: http://mfs.uimech.org/mfs2020.3.133
DOI: 10.21662/mfs2020.3.133
Transformations of gas dynamics equations and basis operators of a admitted 11-dimensional Lie algebra
Siraeva D.T.∗, Yulmukhametova Y.V.∗,∗∗
∗Mavlyutov Institute of Mechanics UFRC RAS, Ufa, Russia
∗∗Ufa State Aviation Technical University, Ufa, Russia

Abstract

In this paper, the gas dynamics equations are considered. The system is closed by a general equation of state. This equations describe a model of an inviscid non-heat-conducting gas motion in the absence of external force fields and external energy sources. The system is invariant under the 11-parameter group with the corresponding 11-dimensional Lie algebra. The gas dynamics equations, equations of motion, and basis operators of the Lie algebra are written in Cartesian, Cylindrical, and Spherical coordinate systems. The steps involved when changing the coordinate system are illustrated in detail.

Keywords

gas dynamics equations,
cylindrical coordinate system,
spherical coordinate system,
operators of 11-dimensional Lie algebra

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