APPLICATIONS OF THE GROUP OF EQUATIONS OF MOTION OF A POLYTROPIC GAS

The machinery of Lie theory (groups and algebras) is applied to the sy stem of equations governing the unsteady flow of a polytropic gas. The action on solutions of transformation groups which leave the equation s invariant is considered. Using the invariants of the transformation groups, various symmetry reductions are achieved in both the steady st ate and the unsteady cases. These reduce the system of partial differe ntial equations to systems of ordinary differential equations for whic h some closed-form solutions are obtained. It is then illustrated how each solution in the steady case gives rise to time-dependent solution s.