Труды Института механики им. Р.Р. Мавлютова
Электронный научный журнал | Electronic Scientific Journal
Proceedings of the Mavlyutov Institute of Mechanics
Found all solutions invariant submodel of grade 2 evolution type for the polytropic gas with the assumption of a linear dependence of the radial component of the velocity from the spatial coordinates.
a submodel of rank two,
linear velocity field,
For the equations of gas dynamics with General equation of state is known to all 27 invariant submodels of a rank of two. Known exact solutions only for certain submodels. Classification of exact solutions to the rest of the submodels is not complete.
Objective: to Examine the invariant submodel grade 2 evolutionary type in a cylindrical coordinate system, built on the subalgebra 2.10. Find all the solutions for the polytropic gas with the assumption of a linear dependence of the radial component of the velocity from the spatial coordinates.
Methods: used the methods of group analysis and solutions of differential equations.
Results: we find explicit formulas for functions of velocity, density and pressure.
Conclusions: the obtained explicit formulas describing the motion of gas particles. To reveal the peculiarities of this movement.