A submodel of helical motions in gas dynamics

An invariant submodel, constructed in a subalgebra from the sum of a rotation and a displacement [1], is considered within the framework of the PODMODELI program. A group classification is carried out and the optimal system of subalgebras, which is compared with the optimal system of the basic model is calculated. Furthermore, the system of equations of the submodel is reduced to a symmetric hyperbolic form. Simple solutions of this system, with pressure and density which depend solely on time, are considered. The characteristics, the characteristic conoid, trajectories and strong discontinuities are calculated for these simple solutions. The necessary conditions for the existence of a solution without a singularity on the axis are derived. (C) 1996 Elsevier Science Ltd.