Journal
INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION
Volume 24, Issue 5, Pages 1705-1718Publisher
WALTER DE GRUYTER GMBH
DOI: 10.1515/ijnsns-2022-0126
Keywords
exact solutions; invariants; Lie symmetries; optimal system; two-phase flow
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This paper presents a symmetry classification study of the hyperbolic system of partial differential equations describing a drift-flux two-phase flow in a one-dimensional pipe. The results show that the fluid equations are invariant under the elements of a three-dimensional Lie algebra for general polytropic indices, but additional Lie point symmetries occur for specific values of the polytropic indices. The one-dimensional systems are investigated in each case, with similarity transformations used to reduce the fluid equations into a system of ordinary differential equations. Exact solutions are derived and the reduced systems are studied numerically.
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.
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