Труды Института механики им. Р.Р. Мавлютова

ISSN 2542–0380

Электронный научный журнал | Electronic Scientific Journal

Proceedings of the Mavlyutov Institute of Mechanics

Yulmukhametova Yu.V. The solution of the hydrodynamic submodels of rank 2 with rotation Proceedings of the Mavlyutov Institute of Mechanics. 2016. 11(1). 20–23.

2016. Vol. 11. Issue 1, Pp. 20–23
URL: http://proc.uimech.org/uim2016.1.004,en
DOI: 10.21662/uim2016.1.004

The solution of the hydrodynamic submodels of rank 2 with rotation

Yulmukhametova Yu.V.

Mavlyutov Institute of Mechanics, Ufa

Abstract

Found all solutions invariant submodel of grade 2 evolution type for the polytropic gas with the assumption of a linear dependence of the radial component of the velocity from the spatial coordinates.

Keywords

gas dynamics,
a submodel of rank two,
linear velocity field,
polytropic gas

Article outline

For the equations of gas dynamics with General equation of state is known to all 27 invariant submodels of a rank of two. Known exact solutions only for certain submodels. Classification of exact solutions to the rest of the submodels is not complete.

Objective: to Examine the invariant submodel grade 2 evolutionary type in a cylindrical coordinate system, built on the subalgebra 2.10. Find all the solutions for the polytropic gas with the assumption of a linear dependence of the radial component of the velocity from the spatial coordinates.

Methods: used the methods of group analysis and solutions of differential equations.

Results: we find explicit formulas for functions of velocity, density and pressure.

Conclusions: the obtained explicit formulas describing the motion of gas particles. To reveal the peculiarities of this movement.