Group Analysis of the Plane Steady Vortex Submodel of Ideal Gas with Varying Entropy

Salavat Khabirov
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Salavat Khabirov: Mavlyutov Institute of Mechanics UFRC RAS, 71 Pr. Oktyabrya, 450054 Ufa, Russia

Mathematics, 2021, vol. 9, issue 16, 1-15

Abstract: The submodel of ideal gas motion being invariant with respect to the time translation and the space translation by one direct has 4 integrals in the case of vortex flows with the varying entropy. The system of nonlinear differential equations of the third order with one arbitrary element was obtained for a stream function and a specific volume. This element contains from the state equation and arbitrary functions of the integrals. The equivalent transformations were found for arbitrary element. The problem of the group classification was solved when admitted algebra was expanded for 8 cases of arbitrary element. The optimal systems of dissimilar subalgebras were obtained for the Lie algebras from the group classification. The example of the invariant vortex motion from the point source or sink was done. The regular partial invariant submodel was considered for the 2-dimensional subalgebra. It describes the turn of a vortex flow in the strip and on the plane with asymptotes for the stream line.

Keywords: vortex gas flow; varying entropy; group analysis; optimal system of subalgebras; invariant solution; regular partial invariant solution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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