共查询到20条相似文献,搜索用时 31 毫秒
1.
Large eddy simulations of the flow between a rotating
and a stationary disk have been performed using a dynamic and a
mixed dynamic subgrid-scale model. The simulations were compared
to direct numerical simulation results. The mixed dynamic model
gave better overall predictions than the dynamic model.
Modifications of the near-wall structures caused by the mean flow
three-dimensionality were also investigated. Conditional
averages near strong stress-producing events led to the same
conclusions regarding these modifications as studies of the flow
generated by direct numerical simulation, namely a distinct
asymmetry of the vortices producing sweeps and ejections. 相似文献
2.
Von Kármáns problem of a rotating disk in an
infinite viscous fluid is extended to
the case where the disk surface admits partial slip. The nonlinear similarity equations
are integrated accurately for the full range of slip coefficients.
The effects of slip are discussed. An existence proof is also
given. 相似文献
3.
《Mathematische Nachrichten》2017,290(4):613-631
We consider the initial value problem of the 3D incompressible Boussinesq equations for rotating stratified fluids. We establish the dispersive and the Strichartz estimates for the linear propagator associated with both the rotation and the stable stratification. As an application, we give a simple proof of a unique existence of global in time solutions to our system using just a contraction mapping principle. 相似文献
4.
In this paper, we consider the 3D Boussinesq equations with the incompressibility condition. We obtain a regularity condition for the three-dimensional Boussinesq equations by means of the Littlewood-Paley theory and Bony’s paradifferential calculus. 相似文献
5.
We prove that a smooth solution of the 3D Boussinesq system with zero viscosity in a bounded domain breaks down, if a certain norm of vorticity blows up at the same time. Here this norm is weaker than the bmo-norm. 相似文献
6.
7.
Xiaojing Xu 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(2):677-681
The goal of this work is to study the Boussinesq equations for an incompressible fluid in R2, with diffusion modeled by fractional Laplacian. The existence, the uniqueness and the regularity of solution has been proved. 相似文献
8.
Fattehallah Ghadi Vitoriano Ruas Mohamed Wakrim 《Journal of Computational and Applied Mathematics》2008
In this paper we present a new method to solve the 2D generalized Stokes problem in terms of the stream function and the vorticity. Such problem results, for instance, from the discretization of the evolutionary Stokes system. The difficulty arising from the lack of the boundary conditions for the vorticity is overcome by means of a suitable technique for uncoupling both variables. In order to apply the above technique to the Navier–Stokes equations we linearize the advective term in the vorticity transport equation as described in the development of the paper. We illustrate the good performance of our approach by means of numerical results, obtained for benchmark driven cavity problem solved with classical piecewise linear finite element. 相似文献
9.
James P. Kelliher Milton C. Lopes Filho Helena J. Nussenzveig Lopes 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2009
We study the limiting behavior of viscous incompressible flows when the fluid domain is allowed to expand as the viscosity vanishes. We describe precise conditions under which the limiting flow satisfies the full space Euler equations. The argument is based on truncation and on energy estimates, following the structure of the proof of Kato's criterion for the vanishing viscosity limit. This work complements previous work by the authors, see Iftimie et al. (2009) [5], Kelliher (2008) [8]. 相似文献
10.
M. Hayes S. B. G. O’Brien 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2005,56(5):852-873
A vertical substrate is coated with a thin film of a solution consisting of a volatile viscous liquid and a solid solute. The liquid film thins under gravity while the volatile component simultaneously evaporates. We develop a model to predict the evolving film thickness and in so doing we develop an approximation for the later stages of the well-known dip-coating process.Received: October 10, 2003; revised: May 4 and July 19, 2004 相似文献
11.
In this work, we study the linearized Navier–Stokes equations in an exterior domain of R3 at the steady state, that is, the Oseen equations. We are interested in the existence and the uniqueness of weak, strong and very weak solutions in Lp-theory which makes our work more difficult. Our analysis is based on the principle that linear exterior problems can be solved by combining their properties in the whole space R3 and the properties in bounded domains. Our approach rests on the use of weighted Sobolev spaces. 相似文献
12.
H. H. Sherif M. S. Faltas E. I. Saad 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2008,59(2):293-312
The Stokes axisymmetrical flow caused by a sphere translating in a micropolar fluid perpendicular to a plane wall at an arbitrary
position from the wall is presented using a combined analytical-numerical method. A linear slip, Basset type, boundary condition
on the surface of the sphere has been used. To solve the Stokes equations for the fluid velocity field and the microrotation
vector, a general solution is constructed from fundamental solutions in both cylindrical, and spherical coordinate systems.
Boundary conditions are satisfied first at the plane wall by the Fourier transforms and then on the sphere surface by the
collocation method. The drag acting on the sphere is evaluated with good convergence. Numerical results for the hydrodynamic
drag force and wall effect with respect to the micropolarity, slip parameters and the separation distance parameter between
the sphere and the wall are presented both in tabular and graphical forms. Comparisons are made between the classical fluid
and micropolar fluid.
相似文献
13.
The main purpose of this paper is to justify the Stokes-Blasius law of boundary-layer thickness for the 2-D Boussinesq equations with vanishing diffusivity limit in the half plane, i.e., we shall prove that the boundary-layer thickness is of the value δ(ε)=εα with any α∈(0,1/2) for small diffusivity coefficient ε>0. Moreover, the convergence rates of the vanishing diffusivity limit are also obtained. 相似文献
14.
The existence and uniqueness of solutions to the Euler equations for initial vorticity in BΓ∩Lp0∩Lp1 was proved by Misha Vishik, where BΓ is a borderline Besov space parameterized by the function Γ and 1<p0<2<p1. Vishik established short time existence and uniqueness when Γ(n)=O(logn) and global existence and uniqueness when . For initial vorticity in BΓ∩L2, we establish the vanishing viscosity limit in L2(R2) of solutions of the Navier-Stokes equations to a solution of the Euler equations in the plane, convergence being uniform over short time when Γ(n)=O(logn) and uniform over any finite time when Γ(n)=O(logκn), 0?κ<1, and we give a bound on the rate of convergence. This allows us to extend the class of initial vorticities for which both global existence and uniqueness of solutions to the Euler equations can be established to include BΓ∩L2 when Γ(n)=O(logκn) for 0<κ<1. 相似文献
15.
A.P. Brasil Jr. J.H. Carneiro de Araujo V. Ruas 《Journal of Computational and Applied Mathematics》2008
A three-field finite element scheme designed for solving time-dependent systems of partial differential equations governing viscoelastic flows is introduced. The linearized form of this system is a generalized time-dependent Stokes system. Once a classical time-discretization is performed, the resulting three-field system of equations allows for a stable approximation of velocity, pressure and extra stress tensor, by means of continuous piecewise linear finite elements, in both two and three dimension space. Another advantage of the new formulation is the fact that it implicitly provides an algorithm for the iterative resolution of system non-linearities, in the case of viscoelastic flows. Additionally, convergence in an appropriate sense applying to these three flow fields is demonstrated, for such generalized Stokes system. Numerical results are given in order to illustrate the performance of the new approach. 相似文献
16.
P. D. Weidman A. M. J. Davis D. G. Kubitschek 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2008,59(2):313-332
The simultaneous effects of transpiration through and tangential movement of a semi-infinite flat plate on the self-similar
boundary layer flow driven by uniform shear in the far field is considered. Difficulties with standard shooting techniques
are overcome using Crocco variables which also serve to better elucidate the solution structure. The stabilities of dual,
triple and even quadruple steady flow solutions encountered in different ranges of plate stretching and wall stress are determined
using a linear temporal stability analysis for the self-similar flow.
相似文献
17.
Frédéric Lelièvre 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(17):5902-5919
We discuss a new model (inspired by the work of Vishik and Fursikov) approximating the 3D Navier-Stokes equations, which preserves the scaling as in the Navier-Stokes equations and thus allows the study of self-similar solutions. Using some energy estimates and Leray’s limiting process, we show the existence of a solution of this model in the finite energy case, and the energy equality and inequality fulfilled by it. This approximation can be shown to converge to the Navier-Stokes equations using a mild approach based on the approximated pressure, and the solution satisfies Scheffer’s local energy inequality, an essential tool for proving Caffarelli, Kohn and Nirenberg’s regularity criterion. We also give a partial result of self-similarity satisfied by the approximated solution in the infinite energy case. 相似文献
18.
Anindita Bhattacharyya G. P. Raja Sekhar 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2005,56(3):475-496
An arbitrary Stokes flow of a viscous, incompressible fluid inside a sphere with internal singularities, enclosed by a porous spherical shell, using Brinkmans equation for the flow in the porous region is discussed. At the interface of the clear fluid and porous region stress jump boundary condition for tangential stresses is used. The drag and torque are found by deriving the corresponding Faxens laws. It is found that drag and torque not only change with the varying permeability, but also change for different values of stress jump coefficient. Critical permeability is found for which drag and torque change their behavior. As a limiting case the corresponding Faxens laws for the rigid spherical shell with internal singularities has been obtained.Received: December 17, 2002; revised: February 3, 2004 相似文献
19.
New solutions of the Falkner-Skan equation are presented which display jet-like behaviour. Within non-uniform flow the parameter range over which the new solutions exist is bounded by a singular limit. The limit is shown to be closely related to the well-known plane jet similarity solution. 相似文献
20.
We investigate the instability and stability of some steady-states of a three-dimensional nonhomogeneous incompressible viscous flow driven by gravity in a bounded domain Ω of class C2. When the steady density is heavier with increasing height (i.e., the Rayleigh–Taylor steady-state), we show that the steady-state is linear unstable (i.e., the linear solution grows in time in H2) by constructing a (standard) energy functional and exploiting the modified variational method. Then, by introducing a new energy functional and using a careful bootstrap argument, we further show that the steady-state is nonlinear unstable in the sense of Hadamard. When the steady density is lighter with increasing height, we show, with the help of a restricted condition imposed on steady density, that the steady-state is linearly globally stable and nonlinearly asymptotically stable in the sense of Hadamard. 相似文献