Similarity solutions for two-phase fluids models

TL;DR

This paper classifies the Lie symmetries of two-phase fluid models without gravity, deriving similarity solutions and identifying new solutions not previously documented.

Contribution

It provides a comprehensive symmetry classification and similarity solutions for two-phase fluids models with polytropic gases, expanding existing literature.

Findings

Most solutions are newly identified in this study.

The model admits a four-dimensional Lie algebra of symmetries.

Optimal systems of symmetries are derived for solution generation.

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 equation of states of polytropic gases. We perform a classification scheme of the unknown parameters of the model such that 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 six. 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 found before in the literature.