Symmetric Solutions for System of unsteady flow of a polytropic gas

Abstract

The machinery of Lie theory (groups and algebras) is applied to the system of equation governing the unsteady flow of a polytropic gas. The action on solutions of transformation groups which leave the equations invariant is considered. Using the invariants of the transformation group, symmetry reductions are achieved in both the steady state and unsteady cases. Various symmetry reductions are obtained and reduce the system of partial differential equations to the system of ordinary equations which we can obtain the complete solutions of each case and the numerical solutions were done.