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АЛГОРИТМ ЧИСЛЕННОГО РЕШЕНИЯ СИСТЕМЫ УРАВНЕНИЙ ПРАНДТЛЯ С ИНДУЦИРОВАННЫМ ДАВЛЕНИЕМ В ПЕРИОДИЧЕСКОМ СЛУЧАЕ
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 periodic boundary conditions. The results
of numerical modeling of the flow are presented.
Keywords: численное моделированиеnumerical modelingосреднениедвухпалубная структураaveragingпериодические возмущенияperiodic perturbationsmultideck structures of the boundary layerPrandtl equations with induced pressureуравнения Прандтля с индуцированным давлением
Publication based on the results of:
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. K., 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 ...
Added: July 9, 2017
Талипова Т. Г., Kurkina O. E., Терлецкая Е. В. et al., Экологические системы и приборы 2014 № 3 С. 26-38
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 ...
Added: May 13, 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
Семин С. В., Kurkina O. E., Kurkin A. A. 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 ...
Added: October 6, 2012
M.V.Karasev, E.M.Novikova, Russian Journal of Mathematical Physics 2015 Vol. 22 No. 4 P. 463-468
We study dynamics of a charge in the planar Penning trap in which the direction of magnetic field does not coincide with the trap axis. Under some combined resonance condition on the deviation angle and magnitudes of magnetic and electric fields, the trajectories of a charge are near-periodic. We describe the reduction to a top-like ...
Added: October 22, 2015
Danilov V., Rudnev V., Gaydukov R. et al., М. : Научно-техническое издательство «Горячая линия – Телеком», 2014
A new mathematical model of heat transfer in silicon field emission pointed cathode of small dimensions is constructed which permits taking its partial melting into account. This mathematical model is based on the phase field system, i.e., on a contemporary generalization of Stefan-type problems. The approach used by the authors is not purely mathematical but ...
Added: September 23, 2014
Danilov V., Gaydukov R., Vadim Kretov et al., IEEE Transactions on Electron Devices 2014 Vol. 61 No. 12 P. 4232-4239
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 ...
Added: October 24, 2014
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
Danilov V., European Journal of Mechanics - B/Fluids 2019 Vol. 74 P. 152-158
A stratified liquid with two layers separated by a fast oscillating interface in the case of Raleigh--Taylor instability
is considered. The averaged equations are derived, and it is shown that a mushy region of a certain density appears after averaging. The similarity between this fact and the case of unstable jump decay is discussed. ...
Added: October 21, 2018
Aseeva N., Blyakhman L. G., Logvinova K. V. et al., Труды НГТУ им. Р.Е. Алексеева 2013 № 3(100) С. 37-46
Цель работы: Рассмотрена динамика солитонов в рамках расширенного нелинейного уравнения Шредингера. Учтено как индуцированное рассеяние высокочастотных волн на затухающих низкочастотных волнах, так и неоднородность линейной дисперсии второго порядка.
Научный подход: Исследование проведено как численно, так и аналитически.
Результат: Показано, что смещение пространственного спектра солитона в длинноволновую область, обусловленного индуцированным рассеянием, компенсируется убывающей дисперсией, смещающей спектр солитона в ...
Added: September 24, 2013
Grushin V. V., Dobrokhotov S. Y., Сергеев С. А., Труды Математического института им. В.А. Стеклова РАН 2015 Т. 288 С. 287
Added: December 21, 2015
Blyakhman L. G., Morozov V. P., Tyutin V. V., Труды НГТУ им. Р.Е. Алексеева 2016 № 3 (114) С. 9-15
Цель работы: Исследована динамика двухкомпонентных (векторных) солитонов Давыдова-Скотта(ДС) при пространственно-скоростном рассогласовании высокочастотных (ВЧ) и низкочастотных (НЧ) компонент. Рассмотрение проведено в рамках Захаровского типа системы двух связанных уравнений для ВЧ и НЧ поля. В этой системе ВЧ поле описывается линейным уравнением Шредингера с переменным во времени и пространстве потенциалом, вызванным НЧ компонентой. НЧ компонента в этой ...
Added: October 5, 2016
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
Талипова Т. Г., Kurkina O. E., Rouvinskaya E. 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 ...
Added: November 7, 2013
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
Aseeva N., Gromov E., Tyutin V. V., Chaos 2013 Vol. 23 No. 1 P. 013143-1-013143-6
Solitons dynamics in the frame of the extended nonlinear Schrodinger equation taking into account space stimulated Raman scattering (SSRS), synchronic spatial variation of inhomogeneous second-order dispersion (SOD), and self-phase modulation (SPM) is considered both analytically and numerically. Compensation of soliton Raman self–wave number down shift by synchronically increasing SOD and SPM is shown. Analytical soliton ...
Added: April 4, 2013
Mikheev A. V., 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 ...
Added: September 6, 2017
Anikin A. Y., Brüning J., Dobrokhotov S. et al., Russian Journal of Mathematical Physics 2019 Vol. 26 No. 3 P. 265-276
In this paper, we consider the spectral problem for the magnetic Schrödinger operator on the 2-D plane (x1, x2) with the constant magnetic field normal to this plane and with the potential V having the form of a harmonic oscillator in the direction x1 and periodic with respect to variable x2. Such a potential can ...
Added: September 18, 2019
Fonareva A. V., Gaydukov R. K., 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
Aseeva N., Gromov E., Tyutin V. V., 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. ...
Added: October 8, 2013
Danilov V., Rudnev V., Журнал вычислительной математики и математической физики 2012 Т. 52 № 11 С. 2080-2092
Исследуется эффект локализованного в пространстве и времени возмущения температуры, которое возникает в точке контакта свободных границ в задаче Стефана–Гиббса–Томсона в рамках модели фазового поля. ...
Added: December 24, 2012
Bogachev V., 2020 Vol. 75 No. 3 P. 393-425
Generalizations and refnements are given for results of Kozlov and Treschev on non-uniform averagings in the ergodic theorem in the case of operator semigroups on spaces of integrable functions and semigroups of
measure-preserving transformations. Conditions on the averaging measures are studied under which the averages converge for broad classes of integrable functions. ...
Added: October 23, 2020