Regular submodels of types (1,2) and (1,1) of the equations of gas dynamics

Partially invariant solutions of types (1, 2) and (1, 1) for gas-dynamic equations are regularly divided into two classes: for the first class, the invariant independent variable is the time, i.e., this class contains barochronic solutions, and for the second class, the invariant variable necessarily depends on spatial coordinates. The barochronic submodel of gas-dynamic equations, as well as a passive subsystem for solutions of the second class, is integrated in finite form. In the latter case, the invariant subsystem is reduced to an ordinary differential equation and quadratures. Integration of the submodels is illustrated by a number of examples. The following common properties of barochronic gas flows are described: rectilinear trajectories of gas particles, the possibility of collapse of density on a manifold, and stratification of the space of events. Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 2, pp. 40–49, March–April, 1999.