共查询到20条相似文献，搜索用时 78 毫秒
1.
Axia Wang Yichen Ma Zhiming Gao 《Numerical Methods for Partial Differential Equations》2010,26(6):1642-1659
This article is concerned with a numerical simulation of shape optimization of the Oseen flow around a solid body. The shape gradient for shape optimization problem in a viscous incompressible flow is computed by the velocity method. The flow is governed by the Oseen equations with mixed boundary conditions containing the pressure. The structure of continuous shape gradient of the cost functional is derived by using the differentiability of a minimax formulation involving a Lagrange functional with a function space parametrization technique. A gradient type algorithm is applied to the shape optimization problem. Numerical examples show that our theory is useful for practical purpose and the proposed algorithm is feasible. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010 相似文献
2.
Jiří Neustupa 《Mathematical Methods in the Applied Sciences》2009,32(6):653-683
We assume that Ωt is a domain in ?3, arbitrarily (but continuously) varying for 0?t?T. We impose no conditions on smoothness or shape of Ωt. We prove the global in time existence of a weak solution of the Navier–Stokes equation with Dirichlet's homogeneous or inhomogeneous boundary condition in Q[0, T) := {( x , t);0?t?T, x ∈Ωt}. The solution satisfies the energy‐type inequality and is weakly continuous in dependence of time in a certain sense. As particular examples, we consider flows around rotating bodies and around a body striking a rigid wall. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
3.
We establish the moment estimates for a class of global weak solutions to the Navier–Stokes equations in the half‐space. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
4.
We consider the planar rotation-symmetric motion by inertia of a viscous incompressible fluid in a ring with free boundary. We reduce the corresponding initial-boundary value problem for the Navier–Stokes equations to some problem for a coupled system of one parabolic equation and two ordinary differential equations. We suppose that the coefficient of the derivatives of the sought functions with respect to time (the quasistationary parameter) is small; so the system is singularly perturbed. In this article we construct an asymptotic expansion for a solution to the rotating ring problem in a small quasistationary parameter and obtain a smallness estimate for the difference between the exact and approximate solutions. 相似文献
5.
In this paper, we study the existence and regularity of solutions to the Stokes and Oseen equations with nonhomogeneous Dirichlet boundary conditions with low regularity. We consider boundary conditions for which the normal component is not equal to zero. We rewrite the Stokes and the Oseen equations in the form of a system of two equations. The first one is an evolution equation satisfied by Pu, the projection of the solution on the Stokes space – the space of divergence free vector fields with a normal trace equal to zero – and the second one is a quasi-stationary elliptic equation satisfied by (I−P)u, the projection of the solution on the orthogonal complement of the Stokes space. We establish optimal regularity results for Pu and (I−P)u. We also study the existence of weak solutions to the three-dimensional instationary Navier–Stokes equations for more regular data, but without any smallness assumption on the initial and boundary conditions. 相似文献
6.
Yong Zhou 《Mathematical Methods in the Applied Sciences》2007,30(10):1223-1229
In this paper we derive a decay rate of the L2‐norm of the solution to the 3‐D Navier–Stokes equations. Although the result which is proved by Fourier splitting method is well known, our method is new, concise and direct. Moreover, it turns out that the new method established here has a wide application on other equations. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
7.
This paper studies the Cauchy problem of the 3D Navier–Stokes equations with nonlinear damping term | u | β?1u (β ≥ 1). For β ≥ 3, we derive a decay rate of the L2‐norm of the solutions. Then, the large time behavior is given by comparing the equation with the classic 3D Navier–Stokes equations. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
8.
We prove, on one hand, that for a convenient body force with values
in the distribution space (H
-1(D))
d
, where D is the geometric
domain of the fluid, there exist a velocity u and a pressure p
solution of the stochastic Navier–Stokes equation in dimension
2, 3 or 4.
On the other hand, we prove that, for a body force with values in the
dual space V of the divergence free subspace V of (H
1
0(D))
d
,
in general it is not possible to solve the stochastic Navier–Stokes
equations.
More precisely, although such body forces have been considered, there
is no topological space in which Navier–Stokes equations could be
meaningful for them. 相似文献
9.
Z.Z. Ganji D.D. Ganji Ammar D. Ganji M. Rostamian 《Numerical Methods for Partial Differential Equations》2010,26(1):117-124
In this letter, we implement a relatively new analytical technique, the homotopy perturbation method (HPM), for solving linear partial differential equations of fractional order arising in fluid mechanics. The fractional derivatives are described in Caputo derivatives. This method can be used as an alternative to obtain analytic and approximate solutions of different types of fractional differential equations applied in engineering mathematics. The corresponding solutions of the integer order equations are found to follow as special cases of those of fractional order equations. Some numerical examples are presented to illustrate the efficiency and reliability of HPM. He's HPM, which does not need small parameter is implemented for solving the differential equations. In this method, a homotopy is introduced to be constructed for the equation. The initial approximations can be freely chosen with possible unknown constants that can be determined by imposing the boundary and initial conditions. It is predicted that HPM can be found widely applicable in engineering. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010 相似文献
10.
This paper presents a numerical method for shape optimization of a body immersed in an incompressible viscous flow governed by Stokes–Oseen equations. The purpose of this work is to optimize the shape that minimizes a given cost functional. Based on the continuous adjoint method, the shape gradient of the cost functional is derived by involving a Lagrangian functional with the function space parametrization technique. Then, a gradient‐type algorithm is applied to the shape optimization problem. The numerical examples indicate the proposed algorithm is feasible and effective in low Reynolds number flow. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
11.
In this paper, we consider a two-grid method for resolving the nonlinearity in finite element approximations of the equilibrium Navier–Stokes equations. We prove the convergence rate of the approximation obtained by this method. The two-grid method involves solving one small, nonlinear coarse mesh system and two linear problems on the fine mesh which have the same stiffness matrix with only different right-hand side. The algorithm we study produces an approximate solution with the optimal asymptotic in h and accuracy for any Reynolds number. Numerical example is given to show the convergence of the method. 相似文献
12.
We investigate the properties of a class of variational solutions to the equations of fluid dynamics when radiation effects are taken into account. The main aim is to prove weak sequential stability of the solution set under certain hypotheses imposed on the pressure, viscosity, and heat conductivity. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
13.
14.
Luigi C. Berselli 《Mathematical Methods in the Applied Sciences》1999,22(13):1079-1085
In this paper we find sufficient conditions, involving only the pressure, that ensure the regularity of weak solutions to the Navier–Stokes equations. Conditions involving only the pressure were previously obtained in [7,4]. Following a remark in this last reference we improve, in particular, Kaniel's result [7]. Our condition can be seen at the light of the heuristic idea that the pressure behaves similarly to the modulus squared of the velocity. Copyright © 1999 John Wiley & Sons, Ltd. 相似文献
15.
In this per, we consider a special class of initial data for the three‐dimensional incompressible Navier–Stokes equations with gravity. We show that, under such conditions, the incompressible Navier‐Stokes equations with gravity are globally well posed, and the velocity minus gravity term has finite energy. The important features of the initial data is that the velocity fields minus gravity term are almost parallel to the corresponding vorticity fields in a very large space domain. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
16.
P. Braz e Silva M. A. Rojas‐Medar E. J. Villamizar‐Roa 《Mathematical Methods in the Applied Sciences》2010,33(3):358-372
We show the existence of strong solutions for the nonhomogeneous Navier–Stokes equations in three‐dimensional domains with boundary uniformly of class C3. Under suitable assumptions, uniqueness is also proved. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
17.
The conforming spectral element methods are applied to solve the linearized Navier–Stokes equations by the help of stabilization techniques like those applied for finite elements. The stability and convergence analysis is carried out and essential numerical results are presented demonstrating the high accuracy of the method as well as its robustness. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 115–141, 1998 相似文献
18.
We study Dirichlet boundary optimal control problems for 2D Boussinesq equations. The existence of the solution of the optimization problem is proved and an optimality system of partial differential equations is derived from which optimal controls and states may be determined. Then, we present some computational methods to get the solution of the optimality system. The iterative algorithms are given explicitly. We also prove the convergence of the gradient algorithm. 相似文献
19.
Manuel Núñez 《Mathematical Methods in the Applied Sciences》2010,33(3):323-331
A number of bounds upon the pressure are known to guarantee regularity of the solutions of the Navier–Stokes equations. Since the pressure is the potential whose source is the product of the velocity and its gradient, it is worth to consider bounds depending on the quotient of the pressure and some quantity measuring the size of this source. Estimates involving the ratio pressure–velocity are known. Our result includes the velocity gradient: if the ratio remains bounded for some r<1, so does the velocity and therefore it retains its regularity. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
20.
In this article, we represent a new numerical method for solving the nonstationary Navier–Stokes equations in an unbounded domain. The technique consists of coupling the boundary integral and the finite element method. The variational formulation and the well-posedness of the coupling method are obtained. The convergence and optimal error estimates for the approximate solution are provided. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 549–565, 1998 相似文献