Extended symmetry analysis of isothermal no-slip drift flux model

Abstract

We carry out extended symmetry analysis of the hydrodynamic-type system of differential equations modeling an isothermal no-slip drift flux. The maximal Lie invariance algebra of this system is proved to be infinite-dimensional. We also find its complete point symmetry group, including discrete symmetries, using the megaideal-based version of the algebraic method. Optimal lists of one- and twodimensional subalgebras of the above algebra are constructed to obtain groupinvariant solutions. Applying the generalized hodograph method and linearizing the essential subsystem, we represent the general solution of the system under study in terms of solutions of the Klein–Gordon equation. Amongst first-order generalized symmetries, we single out genuinely generalized ones and relate them to Lie symmetries of the essential subsystem. Moreover, we construct infinite families of recursion operators, conservation laws and Hamiltonian structures of the entire system.