共查询到20条相似文献,搜索用时 15 毫秒
1.
Electromagnetic fields are often used industrially to controlthe flow of liquid metal, and in particular this review is concernedwth applications of alternating fields. An alternating fieldinduces eddy currents in liquid metal which interact with thefield to give a Lorentz body force which is generally rotationaland which must therefore drive fluid motion. We derive generalexpressions for the Lorentz force, showing that it consistsof both steady and oscillatory components. The flow in a circularcylinder due to a rotating field is discussed in detail, sincethis problem is simple to analyse and illustrates several importantgeneral principles. In the high-frequency limit, the field isconfined to a narrow layer on the surface of the conductor,and we derive approximate methods for calculating the surfacemagnetic pressure andthe induced flow. We also examine the otherextreme of slowly alternating fields. As each problem is studied,we discuss practical applications. 相似文献
2.
K. D. Cherednichenko 《Journal of Mathematical Sciences》2006,138(2):5613-5622
A high-frequency ray theory is presented for a type of small-amplitude waves (termed Scholte-Gogoladze waves), localized in
a thin layer around an interface between elastic and fluid domains. The interface is assumed to be smooth, with typical radii
of curvature much larger than the excitation wavelength. The technique employed in the paper is based on a boundary-layer
version of the classical WKB-expansion (see V. M. Babich and N. Ya. Kirpichnikova, The Boundary-Layer Method in Diffraction
Problems (Springer, Berlin 1979)). Bibliography: 20 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 324, 2005, pp. 229–246. 相似文献
3.
《Applied Mathematics Letters》2005,18(11):1293-1303
We consider the problem of displacement processes in a three-layer fluid in a Hele–Shaw cell modeling enhanced processes of oil recovery by polymer flooding. The middle layer sandwiched between water and oil contains polymer-thickened water. We provide lower bounds on the length of the intermediate layer and on the amount of polymer in the middle layer for stabilizing the leading front to a specified level. We also provide an upper bound on the growth rate of instabilities for a given viscous profile of the middle layer. 相似文献
4.
Jianwen Zhang 《Journal of Mathematical Analysis and Applications》2007,328(1):220-244
We consider the development of the nonstationary boundary layer about a body that gradually starts to move in a resting fluid. Under certain conditions, we construct the solutions for the problem of formation of boundary layer in a pseudo-plastic fluid. The method used here is mainly based on a transformation which reduces the boundary layer system to a boundary value problem for a single quasilinear parabolic equation. 相似文献
5.
Hans Babovsky 《PAMM》2007,7(1):1141101-1141102
We introduce a Boltzmann equation on discrete lattices and demonstrate its applicability for the numerical simulation of flows in the transition regime to fluid dynamics. The application concerns an evaporation condensation where the fluid dynamic flow is ruled by a thin kinetic boundary layer. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
6.
This work is concerned with the boundary layer turbulence, which is an outstanding problem in fluid mechanics. We consider an incompressible viscous fluid in 2D domains with permeable walls. The permeability is described by the Yudovich condition. The goal of the article is to study the fluid behavior at vanishing viscosity (large Reynold’s numbers). We show that the vanishing viscous limit is a solution of the Euler equations with the Yudovich condition on the inflow region of the boundary. 相似文献
7.
An operator splitting approach for the interaction between a fluid and a multilayered poroelastic structure
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Martina Bukač Ivan Yotov Paolo Zunino 《Numerical Methods for Partial Differential Equations》2015,31(4):1054-1100
We develop a loosely coupled fluid‐structure interaction finite element solver based on the Lie operator splitting scheme. The scheme is applied to the interaction between an incompressible, viscous, Newtonian fluid, and a multilayered structure, which consists of a thin elastic layer and a thick poroelastic material. The thin layer is modeled using the linearly elastic Koiter membrane model, while the thick poroelastic layer is modeled as a Biot system. We prove a conditional stability of the scheme and derive error estimates. Theoretical results are supported with numerical examples. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1054–1100, 2015 相似文献
8.
A matrix of fundamental solutions is constructed for the operator governing the high-frequency oscillations of a plate with transverse shear deformation. Important properties of the corresponding wave functions and layer potentials are discussed, as an essential step in the development of numerical boundary element methods. 相似文献
9.
Brian Straughan 《Acta Appl Math》2014,132(1):561-581
We develop a detailed linear instability and nonlinear stability analysis for the situation of convection in a horizontal plane layer of fluid when there is a heat sink/source which is linear in the vertical coordinate which is in the opposite direction to gravity. This can give rise to a scenario where the layer effectively splits into three sublayers. In the lowest one the fluid has a tendency to be convectively unstable while in the intermediate layer it will be gravitationally stable. In the top layer there is again the possibility for the layer to be unstable. This results in a problem where convection may initiate in either the lowest layer, the upmost layer, or perhaps in both sublayers simultaneously. In the last case there is the possibility of resonance between the upmost and lowest layers. In all cases penetrative convection may occur where convective movement in one layer induces motion in an adjacent sublayer. In certain cases the critical Rayleigh number for thermal convection may display a very rapid increase which is much greater than normal. Such behaviour may have application in energy research such as in thermal insulation. 相似文献
10.
We obtain the dispersion relations that describe the spectrum of the “effluent” harmonic antisymmetric normal waves for an
arbitrary direction in the plane of an orthotropic layer surrounded by a viscous or ideally compressible fluid. We present
the results of computation of the lower branches of the dispersion spectrum for elastically equivalent directions of propagation
in a layer of monocrystal Seignette salt in water.
Four figures. Bibliography: 5 titles.
Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 28, 1998, pp. 123–131. 相似文献
11.
12.
We consider nonstationary seepage in a bounded nonhomogeneously anisotropic fissured-porous layer. The layer contains by an imperfect well, which operates with a constant discharge. Formulas for the distribution of fluid pressure are obtained using the Laplace transform and the separation of variables method.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 73, pp. 52–57, 1992. 相似文献
13.
G. V. Golubev 《Journal of Mathematical Sciences》1992,58(3):245-247
We consider the determination of the hydraulic conductivity field of a nonhomogeneous layer with linear seepage of an incompressible fluid in a nonelastic layer. In mathematical terms, the problem is formulated as a Cauchy problem for a partial differential equation of a special form. A theorem is proved which establishes that the solutions obtained for different times are identical.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 57, pp. 67–70, 1985. 相似文献
14.
We give an asymptotic equivalent at infinity of the unbounded solutions of some boundary layer equations arising in fluid mechanics.Received: 24 May 2004 相似文献
15.
O.V. Avramenko 《Journal of Mathematical Sciences》1998,90(1):1887-1890
We present new analytic solutions of the problem of wave propagation in a continuously stratified fluid in the Boussinesq
approximation. We study the propagation of internal waves in an ideal fluid in systems of homogeneous-layer/continuously stratified
layer and homogeneous-layer/continuously stratified half-space type. We obtain the dispersion equations and study several
limiting cases. Bibliography: 2 titles.
Translated fromTeoreticheskaya i Prikladnaya Mekhanika, Vol. 27, 1997, pp. 132–137. 相似文献
16.
This note concerns nonlinear ill‐posedness of the Prandtl equation and an invalidity of asymptotic boundary layer expansions of incompressible fluid flows near a solid boundary. Our analysis is built upon recent remarkable linear illposedness results established by Gérard‐Varet and Dormy and an analysis by Guo and Tice. We show that the asymptotic boundary layer expansion is not valid for nonmonotonic shear layer flows in Sobolev spaces. We also introduce a notion of weak well‐posedness and prove that the nonlinear Prandtl equation is not well‐posed in this sense near nonstationary and nonmonotonic shear flows. On the other hand, we are able to verify that Oleinik's monotonic solutions are well‐posed. © 2011 Wiley Periodicals, Inc. 相似文献
17.
Homogenization provides a reduced model of the acoustic wave propagation through a periodically perforated layer immersed in an inviscid fluid. The shape of the perforation influences some parameters of the non-local transmission condition. We developed and implemented numerically the sensitivity analysis for an optimal design of the perforation. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
18.
Gershon I. Kresin Vladimir G. Maz'ya 《Mathematical Methods in the Applied Sciences》1995,18(14):1095-1131
We study a class of matrix integral operators which appear as limit values of the double layer potentials. We find general representations for the norms and for the essential norms of such operators in the space of continuous vector-valued functions. These representations are specified for boundary integral operators of linear isotropic elasticity theory and hydrodynamics of viscous incompressible fluid under the assumption that there is an angle point on the boundary of a plane domain and a conic point or an edge on the boundary of a three-dimensional domain. 相似文献
19.
We describe the asymptotic behaviour of an incompressible viscous free fluid in contact with a porous layer flow through the porous layer surface. This porous layer has a small thickness and consists of thin channels periodically distributed. Two scales are present in this porous medium, one associated to the periodicity of the distribution of the channels and the other to the size of these channels. Proving estimates on the solution of this Stokes problem, we establish a critical link between these two scales. We prove that the limit problem is a Stokes flow in the free domain with further boundary conditions on the basis of the domain which involve an extra velocity, an extra pressure and two second-order tensors. This limit problem is obtained using Γ-convergence methods. We finally consider the case of a Navier–Stokes flow within this context. 相似文献
20.
In this paper we study the behavior of the stationary magnetic hydrodynamical boundary layer of a dilatant fluid flowing through a porous obstacle. We consider a family of boundary value problems with a small parameter where micro-inhomogeneities are concentrated on the boundary of the domain (the original velocity profile depends on a small parameter). We construct an averaged problem and prove convergence of the solution of the original problem to that of the averaged one. Thus we describe the effective behavior of the micro-inhomogeneous fluid. 相似文献