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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.

Fonareva A. V., Gaydukov R. K.

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 which the double-deck structure exists is performed.

Gaydukov R. K., Fonareva A. V., 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 ...

Added: September 2, 2019

Gaydukov R., 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

Gaydukov R., Russian Journal of Nonlinear Dynamics 2024 Vol. 20 No. 1 P. 113-125

The problem of flow of a non-Newtonian viscous fluid with power-law rheological properties
along a semi-infinite plate with a small localized irregularity on the surface is considered for large
Reynolds numbers. The asymptotic solution with double-deck structure of the boundary layer is
constructed. The numerical simulation of the flow in the region near the surface was performed
for different ...

Added: December 26, 2023

LIUDMILA I. KUZMINA, Osipov Y., International Journal for Computational Civil and Structural Engineering 2020 Vol. 16 No. 4 P. 50-56

Filtration of suspension in a porous medium is actual in the construction of tunnels and underground structures.
A model of deep bed filtration with size-exclusion mechanism of particle capture is considered. The inverse filtration
problem – finding the Langmuir coefficient from a given concentration of suspended particles at the porous medium outlet is solved using the asymptotic solution ...

Added: July 2, 2021

Chernyshev V. L., Hilberdink T., Nazaikinskii V. E., Russian Journal of Mathematical Physics 2020 Vol. 27 No. 4 P. 456-468

We find the logarithmic asymptotics as T tends to infinity of the number of partitions of positive numbers not exceeded T into sums of positive numbers t_j with j less or equal k, where the counting function of t_j grows as a power of j. The asymptotics is uniform with respect to k. ...

Added: October 31, 2020

Gaydukov R. K., Borisov D. I., Mathematical notes 2016 Vol. 99 No. 5 P. 636-642

A fluid flow along a semi-infinite plate with small periodic irregularities on the surface is considered for large Reynolds numbers. The boundary layer has a double-deck structure: a thin boundary layer (“lower deck”) and a classical Prandtl boundary layer (“upper deck”). The aim of this paper is to prove the existence and uniqueness of the ...

Added: May 18, 2016

Gaydukov R. K., Indian Journal of Pure and Applied Mathematics 2024 P. 1-18

The paper is deals with the heat transfer in the laminar flow of a viscous incompressible fluid along a plate with a small heated localized irregularity. It is well known that double- and triple-deck structures of the boundary layer arise in such flow problems. These structures make it possible, among other things, to describe the phenomenon of ...

Added: May 21, 2024

Danilov V., Gaydukov R., 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 ...

Added: September 3, 2015

L.I. Kuzmina, Osipov Y. V., 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

Protasov V., 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

Gaydukov R., Fonareva A. V., 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 ...

Added: November 14, 2021

V. G. Danilov, R. K. Gaydukov, Russian Journal of Mathematical Physics 2022 Vol. 29 No. 4 P. 431-455

A problem of a nonstationary incompressible viscous fluid ow along a plate with small fast-oscillating irregularities on the surface for a large Reynolds number is considered by using rigorous methods of mathematical physics. Depending on the scales of irregularities in the problem under study, there arises a solution that describes the double-deck or triple-deck structure boundary layers on ...

Added: August 19, 2020

Gaydukov R., Сибирский журнал вычислительной математики 2022 Т. 15 № 2 С. 97-109

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 ...

Added: June 10, 2020

Gaydukov R., European Journal of Mechanics - B/Fluids 2018 Vol. 71 P. 59-65

We consider the problem of flow of a viscous compressible subsonic fluid along a flat plate with small localized (hump-type) 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 the flow in the thin boundary ...

Added: November 20, 2017

V.L. Chernyshev, Minenkov D. S., Nazaikinskii V. E., Functional Analysis and Its Applications 2016 Vol. 50 No. 4 P. 291-307

We find the asymptotics of the element counting function for an additive arithmetic semigroup with exponential growth of the counting function of prime generators. ...

Added: October 18, 2015

Danilov V., Gaydukov R., 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. ...

Added: September 27, 2015

Grushin V. V., 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. ...

Added: January 13, 2018

Л.И. Кузьмина, Осипов Ю. В., 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 ...

Added: August 3, 2014

Danilov V. G., Gaydukov R. K., 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

Gaydukov R., Danilov V., 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

Ludmila I. Kuzmina, Osipov Y., Vetoshkin N., International Journal for Computational Civil and Structural Engineering 2018 Vol. 14 No. 1 P. 92-101

The filtration problem in a porous medium is an important part of underground hydromechanics. Filtration of suspensions and colloids determines the processes of strengthening the soil and creating waterproof walls in the ground while building the foundations of buildings and underground structures. It is assumed that the formation of a deposit is dominated by the ...

Added: July 1, 2018

Grushin V. V., 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

Badanin A., Korotyaev E., Mathematische Nachrichten 2020 Vol. 293 P. 210-225

We consider fourth order ordinary differential operators on the half-line and on the
line, where the perturbation has compactly supported coefficients. The Fredholm
determinant for this operator is an analytic function in the whole complex plane without
zero.We describe the determinant at zero.We show that in the generic case it has
a pole of order 4 in the case ...

Added: February 5, 2021

V. S. Samovol, Moscow Mathematical Journal 2018 Vol. 18 No. 2 P. 387-402

In the article the solutions of Emden–Fowler-type equa- tions of any order are studied using methods of power geometry. It is shown that these methods can be successfully applied in the study of asymptotic behaviour of the solutions. Also, we find conditions for the existence (nonexistence) of solutions of new types having non- power (power-logarithmic) asymptotics. ...

Added: July 25, 2018