Труды Института механики им. Р.Р. Мавлютова
Электронный научный журнал | Electronic Scientific Journal
Proceedings of the Mavlyutov Institute of Mechanics
We consider the system of gas dynamics equations with the state equation of the monatomic gas. The system admits a group of transformations with a 14-dimensional Lie algebra. A projective operator is specific to this algebra. We consider the invariant submodel on two-dimensional subalgebra containing the projective operator. For the vorticity-free motions, the submodel is reduced to an overdetermined system of three equations. A particular solution is found for it, physical interpretation is given, and trajectories of gas particles are depicted. The solution gives the gas compression followed by expansion.
Problem: To consider the invariant submodel on two-dimensional subalgebra containing a projective operator for the 14-dimensional Lie algebra admitted by the equations of motion of the monatomic gas. To consider the condition of vorticity-free motion.
Methods: The methods of the theory of differential equations and group analysis are used.
In a study was determined:
1. For vorticity-free motion, the submodel is reduced to an overdetermined system of three equations.
2. For vorticity-free motion, a particular solution is found and its physical interpretation is given.