Extended symmetry analysis of an isothermal no-slip drift flux model

PHYSICA D-NONLINEAR PHENOMENA

卷:402

Article

Opanasenko, Stanislav^1,2  Bihlo, Alexander¹  Popovych, Roman O.^2,3,4  Sergyeyev, Artur⁴ 

[1] Mem Univ Newfoundland, Dept Math & Stat, St John, NF A1C 5S7, Canada

[2] NAS Ukraine, Inst Math, 3 Tereshchenkivska Str, UA-01024 Kiev, Ukraine

[3] Univ Wien, Fak Math, Oskar Morgenstern Pl 1, A-1090 Vienna, Austria

[4] Silesian Univ Opava, Math Inst, Na Rybnicku 1, Opava 74601, Czech Republic

关键词: Hydrodynamic-type system;    Isothermal no-slip drift flux;    Point symmetry;    Exact solution;    Generalized symmetry;    Conservation law;   

DOI  :  10.1016/j.physd.2019.132188

来源: Elsevier

【 摘 要 】

We perform extended group analysis for a 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 the complete point symmetry group of this system, including discrete symmetries, using the megaideal-based version of the algebraic method. Optimal lists of one- and two-dimensional subalgebras of the maximal Lie invariance algebra in question are constructed and employed for obtaining reductions of the system under study. Since this system contains a subsystem of two equations that involves only two of three dependent variables, we also perform group analysis of this subsystem. The latter can be linearized by a composition of a fiber-preserving point transformation with a two-dimensional hodograph transformation to the Klein-Gordon equation. We also employ both the linearization and the generalized hodograph method for constructing the general solution of the entire system under study. We find inter alia genuinely generalized symmetries for this system and present the connection between them and the Lie symmetries of the subsystem we mentioned earlier. Hydrodynamic conservation laws and their generalizations are also constructed. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free