Roman Gaydukov

National Research University Higher School of Economics | HSE · Department of Applied Mathematics

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 regio...

В работе излагается общая схема построения многомасштабных асимптотических решений, возникающих в задачах обтекания поверхности с малыми неровностями. Уточняются результаты известных работ по гидродинамике. Библиография: 25 названий.

The stationary problem of a uniformly 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 the symmetric periodic and localized types of irregularities on the disk surface for large Reynolds numbers. The numerical simula...

An asymptotic solution with double-deck boundary layer structure is constructed for the problem of an incompressible fluid flow over 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...

In this chapter, without claiming to be original, we recall some basic notions of the solid-state physics which will be used to construct the mathematical model of the field emission cathode. More detailed descriptions of these facts can be found in any literature on the solid-state physics. Our description is based on [2, 3, 23, 27, 28, 30, 41, 42...

In the first part of this chapter, a numerical algorithm for solving the phase field system is presented with application to the real field emission nanocathode. The second part of this chapter contains the results of numerical simulations. In the third part of this chapter, we present an algorithm for introducing a liquid phase nucleus in the pres...

This chapter is a “mathematical” one. Here we collect the mathematical background related to the mathematical model of phase transition based on the phase field system introduced by G. Caginalp. Sections 3.1 and 3.2 of the chapter contain some preliminaries and considerations about mathematical models from the physical viewpoint. In Sect. 3.3, we g...

This book deals with mathematical modeling, namely, it describes the mathematical model of heat transfer in a silicon cathode of small (nano) dimensions with the possibility of partial melting taken into account. This mathematical model is based on the phase field system, i.e., on a contemporary generalization of Stefan-type free boundary problems....

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...

We consider the stationary 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 t...

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 th...

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 the...

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 station...

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.

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 in the Pr...

This paper presents the results of mathematical modeling of heat transfer in the field emission process in a conic cathode of small dimensions with its possible melting considered. It is shown that the possibility of melting is determined by the cathode vertex angle. The melting is modeled in the framework of the phase field system using the propos...

We consider flow past a flat plate with small periodic irregularities for large Reynolds number. This flow has double-deck boundary layer structure. For oscillations in classical boundary layer we obtained the time-dependent Rayleigh-type equation with some boundary condition. We prove the existence and uniqueness of the stationary solution for the...