Труды Института механики им. Р.Р. Мавлютова
Электронный научный журнал | Electronic Scientific Journal
Proceedings of the Mavlyutov Institute of Mechanics
The system of gas dynamics equations with the state equation of the monatomic gas admits a group of transformations with a 14-dimensional Lie algebra. A projective operator is specific to this algebra. We consider all one-dimensional subalgebras containing the projective operator. Invariants are calculated and invariant submodel of rank 3 is constructed for each of subalgebras. All submodels are stationary type. They are reduced to the canonical form. Area hyperbolicity of obtained system were specified. Integral entropy is obtained along the flow lines. An ordinary differential equation to the invariant functions is obtained along the flow lines (analogue of a Bernoulli integral for stationary motions). We consider all two-dimensional subalgebras containing projective operator. Invariant submodel of rank 2 stationary type is constructed for each of subalgebras. Submodels are reduced to the canonical form.
gas dynamics equations,