PLANE STEADY VORTEX SUBMODEL OF IDEAL GAS

The ideal gas submodel invariant with respect to time translation and space translation in one direction has four integrals in the case of vortex motion. For the stream function and the specific volume, a system of third-order nonlinear differential equations with one arbitrary element containing the equation of state and arbitrary functions of the integrals was obtained. Equivalence transformations for the arbitrary element were found. The group classification problem was solved. The optimal system of dissimilar subalgebras for Lie algebras from group classification was obtained. Examples of invariant solutions describing vortex gas flow with variable entropy, including a point source or sink, are considered. Analogs of simple waves were obtained for some two-dimensional subalgebras.