Plane Steady Vortex Submodel of Ideal Gas
S. V. Khabirov
Mavlyutov Institute of Mechanics, Ufa Federal Research Center, Russian Academy of Sciences, Ufa, Russia
Keywords: vortex gas flows, group analysis, optimal system of subalgebras, invariant solutions, simple waves
Abstract
The ideal gas submodel invariant with respect to time translation and space translation along one direction has four integrals in the case of vortex motion. For the stream function and specific volume, a system of nonlinear differential equations of the third order with one arbitrary element containing the equation of state and arbitrary functions of integrals. Equivalence transformations for an arbitrary element were found. The problem of group classification was solved. The optimal system of dissimilar subalgebras for the Lei algebras from group classification was obtained. Examples of invariant solutions describing vortex gas flow with variable entropy, including a point source or stock are considered. Analogs of simple waves were obtained for some two-dimensional subalgebras.
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