Abstract

The Second Rank Invariant Submodels for the Special Compressible Fluid

V.G.Volkov (Theoretical Physics Department, Bashkir State Pedagogical University, Ufa, Russia)

e-mail: theorphys@bspu.ru

The model of gasdynamics with the special state equation has been considered. This model corresponds to the motion of a compressible fluid at the large pressure and high temperature. The optimal system of admitted subalgebra of this gasdynamic model is known. An invariant submodel of the second rank is generated with the help of some two-dimensional subalgebra. We consider twelve subalgebra. Three invariants which depend linearly on the coordinates of the velocity are found. One invariant is linear on the entropy and one invariant is also a linear function of the density. Every invariant submodel has been reduced to the canonical form by use of a special choice of invariants. Two submodels of the evolutionary forms and ten submodels of the stationary forms are considered. One can notice the following: Firstly, the factors at the derivative of pressure are always positive. Secondly, the right-hand sides of equations are linearly dependent on the coordinates of the velocity in the Cartesian coordinates. Thirdly, if the subalgebra has the operator of the rotation then cylindrical coordinates are more preferable. On the contrary, if the operator of the rotation is absent in the subalgebra then Cartesian coordinates may be applied. The results of the invariant submodels calculations are accumulated in a table.

Section : 12