A Compressible Fluid Flow with Double-Deck Structure Inside an Axially Symmetric Wavy-Wall Pipe
Russian Journal of Mathematical Physics. 2019. Vol. 26. No. 3. P. 334-343.
The problem of viscous compressible fluid flow in an axially symmetric pipe with small periodic irregularities on the wall is considered for large Reynolds numbers. An asymptotic solution with double-deck structure of the boundary layer and unperturbed core flow is obtained. Numerical investigations of the influence of the density of the core flow on the flow behavior in the near-wall region are presented.
Research target: Mathematics
Priority areas: mathematics
АЛГОРИТМ ЧИСЛЕННОГО РЕШЕНИЯ СИСТЕМЫ УРАВНЕНИЙ ПРАНДТЛЯ С ИНДУЦИРОВАННЫМ ДАВЛЕНИЕМ В ПЕРИОДИЧЕСКОМ СЛУЧАЕ
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A viscous liquid flow along a semi-infinite plate with small periodic irregularities on the surface was considered for large Reynolds numbers. The flow near the plate is described by Prandtl equations with induced pressure which are non-classical PDE, because they contain a limiting term. The main goal is to construct a numerical algorithm for solving these equations with ...
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Nonstationary double-deck structure of boundary layers in compressible flow problem inside a channel with small irregularities on the walls
, , Russian Journal of Mathematical Physics 2021 Vol. 28 No. 2 P. 224-243
A subsonic flow of a viscous compressible fluid in a two-dimensional channel with small periodic or localized irregularities on the walls for large Reynolds numbers is considered. A formal asymptotic solution with double-deck structure of the boundary layer is constructed. A nontrivial time hierarchy is discovered in the decks. An analysis of the scales of irregularities at ...
Added: March 22, 2021
Double-deck structure in the fluid flow problem over plate with small irregularities of time-dependent shape
, European Journal of Mechanics - B/Fluids 2021 Vol. 89 P. 401-410
An asymptotic solution with double-deck boundary layer structure is constructed for the problem of an incompressible fluid flow along a semi-infinite plate with small localized or periodic (fast-oscillating) irregularities on the surface whose shape depends on time. Numerical simulation of flow in the near-plate region is presented for two types of the shape change: oscillations of the ...
Added: January 4, 2021
Double-deck structure of the boundary layer in the problem of flow in an axially symmetric pipe with small irregularities on the wall for large Reynolds numbers
, , Russian Journal of Mathematical Physics 2017 Vol. 24 No. 1 P. 1-18
The problem of flow of a viscous incompressible fluid in an axially symmetric pipe with small irregularities on the wall is considered. An asymptotic solution of the problem with the double-deck structure of the boundary layer and the unperturbed flow in the environment (the “core flow”) is obtained. The results of flow numerical simulation in ...
Added: September 28, 2016
Асимптотики решений задач обтекания несжимаемой жидкостью поверхностей c малыми неровностями при больших числах Рейнольдса
, , Наноструктуры. Математическая физика и моделирование 2016 Т. 15 № 1 С. 5-102
We study the existence conditions for a double-deck structure of a boundary layer in typical problems of incompressible fluid flow along surfaces with small irregularities (periodic or localized) for large Reynolds number. We obtain characteristic scales (a power of a small parameter included in a solution) which lead to the double-deck structure, and we obtain ...
Added: September 27, 2016
Double-deck structure of the boundary layer in the problem of a compressible flow along a plate with small irregularities on the surface
, European Journal of Mechanics - B/Fluids 2017 Vol. 66 P. 102-108
We consider the problem of a viscous compressible subsonic fluid flow along a flat plate with small periodic irregularities on the surface for large Reynolds numbers. We obtain a formal asymptotic solution with double-deck structure of the boundary layer. We present the results of numerical simulation of flow in the thin boundary layer (i.e., in ...
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, , et al., Труды НГТУ им. Р.Е. Алексеева 2012 № 2(95) С. 48-65
Purpose: Numerical modeling of internal baroclinic disturbances of different shapes in a model lake with variable depth, analysis of velocity field of wave-induced current, especially in the near-bed layer. Approach: The study is carried out with the use of numerical full nonlinear nonhydrostatic model for stratified fluid. Findings: The full nonlinear numerical modeling of internal wave dynamics ...
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, Математические заметки 2017 Т. 102 № 6 С. 816-827
Asymptotic formulas are obtained for a class of integrals that are Fourier transforms of rapidly oscillating functions. These formulas contain special functions and generalize the well-known method of stationary phase. ...
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Double-deck structure in the power-law non-Newtonian fluid flow along a plate with small localized irregularities
, Journal of Non-Newtonian Fluid Mechanics 2021
The asymptotic solution with double-deck structure was obtained in the problem of flow of a non-Newtonian fluid with power-law rheological properties along a semi-infinite plate with a small localized irregularity on the surface for large Reynolds numbers. The numerical modeling of the flow in the region near the surface was performed for different fluid indexes. The results of investigations ...
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Necessity of study of the internal waves of large amplitude in the Barents Sea related to their possible catastrophic effects on offshore platforms, powerful transport sediments and bottom erosion, which invariably affects on the overall environmental situation. In this paper, numerical simulation of the generation and propagation of internal waves in the Barents Sea in the framework of ...
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Double-Deck Structure of the Boundary Layer in Problems of Flow around Localized Perturbations on a Plate
, , Mathematical notes 2015 Vol. 98 No. 4 P. 561-571
We consider the problem of a viscous incompressible fluid flow along a flat plate with a small solitary perturbation (of hump, step, or corner type) for large Reynolds numbers. We obtain an asymptotic solution in which the boundary layer has a double-deck structure. ...
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Double-deck structure in the fluid flow induced by a uniformly rotating disk with small symmetric irregularities on its surface
, , European Journal of Mechanics - B/Fluids 2022 Vol. 94 P. 50-59
The problem of a rotating disk with slightly perturbed surface immersed in a viscous fluid is considered. The asymptotic solutions with double-deck structure of the boundary layer are constructed for symmetric periodic and localized types of irregularities on the disk surface for large Reynolds numbers. The paper presents the results of numerical simulations of the flow near the ...
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Асимптотическое поведение собственных значений оператора Шредингера в тонких бесконечных и тонких замкнутых трубках
, Наноструктуры. Математическая физика и моделирование 2012 Т. 7 № 2 С. 17-44
В работе получено асимптотическое разложение собственных значений оператора Лапласа с нулевыми данными Дирихле в бесконечных трубках, т. е. в бесконечных изогнутых цилиндрах с внутренним кручением при равномерном сжатии поперечных сечений, по малому параметру, характеризующему поперечные размеры трубки. Аналогичное разложение получено для оператора Шредингера с учетом магнитного поля для конечных изогнутых трубок. Предложен метод сведения задачи ...
Added: December 24, 2012
, , Russian Journal of Mathematical Physics 2015 Vol. 22 No. 2 P. 161-173
A fluid flow along a plate with small irregularities on the surface is considered for large Reynolds numbers. The boundary layer has a double-deck structure, i.e., both a thin boundary layer and the classical Prandtl boundary layer are present. It is proved that the solution of the boundary-value problem thus obtained exists and is unique ...
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, Mathematics of Computation 2017 Vol. 86 No. 305 P. 1499-1524
For an arbitrary set of nonnegative integers, we consider the Euler binary partition function which equals the total number of binary expansions of an integer with ``digits'' from . By applying the theory of subdivision schemes and refinement equations, the asymptotic behaviour of as is characterized. For all finite , we compute the lower and upper exponents of growth of , find when ...
Added: May 11, 2017
, , Вестник Московского государственного строительного университета 2014 № 7 С. 34-40
A classic pursuit problem is studied in which two material points - a Pursuer and a Pursued - move in a plane at constant speeds. The velocity vector of the Pursued does not change its direction and the velocity vector of the Pursuer turns and always aims at the Pursued. If the Pursuer moves at ...
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, , International Journal for Computational Civil and Structural Engineering 2017 Т. 13 № 1 С. 63-68
Filtration of the suspension in a porous medium with a geometric particle capture mechanism is considered. The porous medium has an initial deposit unevenly distributed across the filter. The nonlinear model of deep bed filtration suggests that the porosity and permeability of the porous medium depend on the deposit. The asymptotics of the movable boundary ...
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The short envelope soliton dynamics in inhomogeneous dispersive media with allowance for stimulated scattering by damped low-frequency waves
, , , Radiophysics and Quantum Electronics 2013 Vol. 56 No. 3 P. 157-166
We consider the soliton dynamics in terms of the extended nonlinear Schr¨odinger equation taking into account the inhomogeneous linear second-order dispersion (SOD) and stimulated scattering by damped low-frequency waves (SSDW). It is shown that the wave number downshift due to SSDW is compensated by an upshift due to the SOD decrease on the spatial coordinate. ...
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, , Russian Journal of Mathematical Physics 2011 Vol. 18 No. 1 P. 10-25
The goal in this paper is to demonstrate a new method for constructing global-in-time approximate (asymptotic) solutions of (pseudodifferential) parabolic equations with a small parameter. We show that, in the leading term, such a solution can be constructed by using characteristics, more precisely, by using solutions of the corresponding Hamiltonian system and without using any ...
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, , Вестник Московского государственного строительного университета 2017 No. 11 P. 1278-1283
Subject: a groundwater filtration affects the strength and stability of underground and hydro-technical constructions. Research objectives: the study of one-dimensional problem of displacement of suspension by the flow of pure water in a porous medium. Materials and methods: when filtering a suspension some particles pass through the porous medium, and some of them are stuck ...
Added: January 6, 2018
О динамических моделях типа Ферхюльста, описываемых линейными дифференциальными уравнениями второго порядка
, Теория. Практика. Инновации 2017 № 9 (21)
In this paper we consider the calculation of a dynamical system described by a second-order differential equation in which a fundamental system of solutions consisting of functions of exponential type is replaced by bounded functions of the Verhulst model. The time dependence of the forces acting on the dynamical system is analyzed, and the obtained ...
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, , , Промышленное и гражданское строительство 2020 № 6 С. 64-68
Filtration problem for a suspension in a porous medium characterize the injection of a liquid grout into porous rock to strengthen loose soil or create waterproof partitions during the construction of tunnels and underground structures. The suspension is injected under pressure into an empty homogeneous porous medium and moves from inlet to outlet. Some particles ...
Added: July 2, 2020
, Математические заметки 2014 Т. 95 № 5 С. 775-789
The paper deals with solutions to Emden-Fowler-type equations of any arbitrary order. The asymptotic properties of solutions to these equations are studied, and a systematic surveyof numerous uncoordinated results of analysis of continuable and noncontinuable solutions is given. ...
Added: April 4, 2014
, , et al., Известия РАН. Физика атмосферы и океана 2015 Т. 51 № 1 С. 103-112
Распространение внутренних солитонов умеренной амплитуды в двухслойном океане переменной глубины исследуется в рамках уравнений Кортевега-де Вриза и Гарднера с переменными коэффициентами. Аналитическое решение получено с использованием асимптотических разложений по малому параметру – уклону дна. Теоретические результаты сопоставляются с численными, полученными в рамках моделирования примитивных уравнений гидродинамики. Обсуждается вероятность сохранения солитонной формы импульса по мере его ...
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