Similarity solutions for two‐phase fluids models

Abstract

The algebraic properties of drift–flux two‐phase fluids models without gravitational and wall friction forces are studied. More precisely, for the two fluids we consider an equation of state of polytropic gases. We perform a classification scheme of the unknown parameters of the model to determine all the possible admitted Lie symmetries. We find that in the most general case the dynamical system of hyperbolic equations is invariant under the action of a four‐dimensional Lie algebra, while the larger number of admitted Lie symmetries is 6. For each admitted Lie algebra the one‐dimensional optimal system is derived which is applied for the determination of all the unique similarity transformations which lead to similarity solutions. Our results are compared with that of previous studies from where we see that most of the solutions presented in this study have not been found before in the literature.