Lie symmetry analysis for two-phase flow with mass transfer

Abstract We perform a complete symmetry classification for the hyperbolic system of partial differential equations, which describes a drift-flux two-phase flow in a one-dimensional pipe, with a mass-transfer term between the two different phases of the fluid. In addition, we consider the polytropic equation of states parameter and gravitational forces. For general values of the polytropic indices, we find that the fluid equations are invariant under the elements of a three-dimensional Lie algebra. However, additional Lie point symmetries follow for specific values of the polytropic indices. The one-dimensional systems are investigated in each case of the classification scheme, and the similarity transformations are calculated in order to reduce the fluid equations into a system of ordinary differential equations. Exact solutions are derived, while the reduced systems are studied numerically.