Application of Lie groups to compressible model of two-phase flows

This paper presents some exact solutions for the drift-flux model of two-phase flows using Lie group analysis. The analysis involves an isentropic no-slip conservation of mass for each phase and the conservation of momentum for the mixture. The present analysis employs a complete Lie algebra of infinitesimal symmetries. Subsequent to these theoretical analysis a symmetry group is established. The symmetry generators are used for constructing similarity variables which reduce the model equations to a system of ordinary differential equations (ODES). In particular, a general framework is discussed for solving the model equations analytically. As a consequence of this, new classes of exact group-invariant solutions are developed. This provides new insights into the fundamental properties of weak discontinuities and helps one to understand better on existence of solutions. (C) 2015 Elsevier Ltd. All rights reserved.