Dispersion and Group Analysis of Dusty Burgers Equations | Sciact

Dispersion and Group Analysis of Dusty Burgers Equations Научная публикация

Журнал

Lobachevskii Journal of Mathematics
ISSN: 1995-0802 , E-ISSN: 1818-9962

Вых. Данные

Год: 2024, Том: 45, Номер: 1, Страницы: 108-118 Страниц : 11 DOI: 10.1134/s1995080224010505

Ключевые слова

DUSTY GAS, BURGERS EQUATION, MOMENTUM EXCHANGE, DISPERSION ANALYSIS, DISPERSION RELATION, GROUP ANALYSIS, PARTIAL DIFFERENTIAL EQUATION, EFFECTIVE VISCOSITY

Авторы

Stoyanovskaya O.P. ¹ , Turova G.D. ² , Yudina N.M. ³

Организации

1	Lavrentiev Institute of Hydrodynamics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
2	Chelyabinsk State University, Chelyabinsk, Russia
3	Novosibirsk State University, Novosibirsk, Russia

We investigate the system of non-stationary one-dimensional equations consisting of a parabolic Burgers equation for the velocity of a viscous gas and a hyperbolic Hopf equation for the velocity of solid particles. The Burgers and Hopf equations are connected into a system due to relaxation terms simulating the momentum transfer between the carrier phase (gas) and the dispersed phase (particles). The momentum transfer intensity is inversely proportional to the relaxation time of the particle velocity to the gas velocity (stopping time).A dispersion relation is constructed for this system. A particular solution corresponding to the damping of a low-amplitude sound wave is found. For an infinitely short velocity relaxation time, the effective viscosity of the gas-dust medium is derived, which is determined by the viscosity of the gas and the mass fraction of particles in the mixture.The Lie algebra of symmetries of Burgers–Hopf system is found. Invariant submodels with respect to the basis operators of the symmetry algebra are derived. These submodels are explicitly integrated, except for one that defines stationary motion. For this submodel, a code has been developed for the numerical generation of particular solutions of the system. It is shown that the invariant solution determined by this submodel, in the asymptotic case of infinitely short velocity relaxation time also makes it possible to obtain the effective viscosity of the gas-dust mixture. Moreover, this effective viscosity coincides with the viscosity value determined from the dispersion relation.

Stoyanovskaya O.P. , Turova G.D. , Yudina N.M.
Dispersion and Group Analysis of Dusty Burgers Equations
Lobachevskii Journal of Mathematics. 2024. V.45. N1. P.108-118. DOI: 10.1134/s1995080224010505 Scopus РИНЦ OpenAlex

Поступила в редакцию:	21 сент. 2023 г.
Принята к публикации:	5 нояб. 2023 г.

Scopus:	2-s2.0-85192965840
РИНЦ:	67311894
OpenAlex:	W4396799215

Пока нет цитирований