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

J 2020

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

SERGYEYEV, Artur, Stanislav OPANASENKO, Alexander BIHLO and Roman POPOVYCH

Basic information

Original name

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

Authors

SERGYEYEV, Artur (804 Ukraine, belonging to the institution), Stanislav OPANASENKO (804 Ukraine, guarantor), Alexander BIHLO (40 Austria) and Roman POPOVYCH (804 Ukraine, belonging to the institution)

Edition

Physica D: Nonlinear Phenomena, Amsterdam, Elsevier B.V. 2020, 0167-2789

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10101 Pure mathematics

Country of publisher

Netherlands

Confidentiality degree

není předmětem státního či obchodního tajemství

References:

Physica D: Nonlinear Phenomena

RIV identification code

RIV/47813059:19610/20:A0000064

Organization unit

Mathematical Institute in Opava

DOI

http://dx.doi.org/10.1016/j.physd.2019.132188

UT WoS

000512219900003

Keywords in English

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

Links

EF16_027/0008521, research and development project. GBP201/12/G028, research and development project.

Změněno: 6/4/2021 14:09, Mgr. Aleš Ryšavý

Abstract

V originále

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.

Citovat

SERGYEYEV, Artur, Stanislav OPANASENKO, Alexander BIHLO and Roman POPOVYCH. Extended symmetry analysis of an isothermal no-slip drift flux model. Physica D: Nonlinear Phenomena. Amsterdam: Elsevier B.V., 2020, vol. 402, No 132188, p. "132188-1"-"132188-16", 16 pp. ISSN 0167-2789. Available from: https://dx.doi.org/10.1016/j.physd.2019.132188.

@article{39680,
   author = {Sergyeyev, Artur and Opanasenko, Stanislav and Bihlo, Alexander and Popovych, Roman},
   article_location = {Amsterdam},
   article_number = {132188},
   doi = {http://dx.doi.org/10.1016/j.physd.2019.132188},
   keywords = {Hydrodynamic-type system; Isothermal no-slip drift flux; Point symmetry; Exact solution; Generalized symmetry; Conservation law},
   language = {eng},
   issn = {0167-2789},
   journal = {Physica D: Nonlinear Phenomena},
   title = {Extended symmetry analysis of an isothermal no-slip drift flux model},
   url = {https://www.sciencedirect.com/science/article/pii/S0167278919301745?via%3Dihub},
   volume = {402},
   year = {2020}
}

TY  - JOUR
ID  - 39680
AU  - Sergyeyev, Artur - Opanasenko, Stanislav - Bihlo, Alexander - Popovych, Roman
PY  - 2020
TI  - Extended symmetry analysis of an isothermal no-slip drift flux model
JF  - Physica D: Nonlinear Phenomena
VL  - 402
IS  - 132188
SP  - "132188-1"-"132188-16"
EP  - "132188-1"-"132188-16"
PB  - Elsevier B.V.
SN  - 01672789
KW  - Hydrodynamic-type system
KW  - Isothermal no-slip drift flux
KW  - Point symmetry
KW  - Exact solution
KW  - Generalized symmetry
KW  - Conservation law
UR  - https://www.sciencedirect.com/science/article/pii/S0167278919301745?via%3Dihub
L2  - https://www.sciencedirect.com/science/article/pii/S0167278919301745?via%3Dihub
N2  - 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.
ER  -

SERGYEYEV, Artur, Stanislav OPANASENKO, Alexander BIHLO and Roman POPOVYCH. Extended symmetry analysis of an isothermal no-slip drift flux model. \textit{Physica D: Nonlinear Phenomena}. Amsterdam: Elsevier B.V., 2020, vol.~402, No~132188, p.~''132188-1''-''132188-16'', 16 pp. ISSN~0167-2789. Available from: https://dx.doi.org/10.1016/j.physd.2019.132188.

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