共查询到20条相似文献,搜索用时 187 毫秒
1.
Yann Brenier Roberto Natalini Marjolaine Puel 《Proceedings of the American Mathematical Society》2004,132(4):1021-1028
We consider a hyperbolic singular perturbation of the incompressible Navier Stokes equations in two space dimensions. The approximating system under consideration arises as a diffusive rescaled version of a standard relaxation approximation for the incompressible Euler equations. The aim of this work is to give a rigorous justification of its asymptotic limit toward the Navier Stokes equations using the modulated energy method.
2.
AGLOBALALGORITHMINTHENUMERICALRESOLUTIONOFTHEVISCOUS/INVISCIDCOUPLEDPROBLEMXUCHUANJUMADAY,Y.ManuscriptreceivedOctober17,19... 相似文献
3.
Caidi Zhao 《Mathematical Methods in the Applied Sciences》2013,36(7):840-856
This paper studies the approximation of the non‐Newtonian fluid equations by the artificial compressibility method. We first introduce a family of perturbed compressible non‐Newtonian fluid equations (depending on a positive parameter ε) that approximates the incompressible equations as ε → 0+. Then, we prove the unique existence and convergence of solutions for the compressible equations to the solutions of the incompressible equations. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
4.
Grégoire Loeper 《偏微分方程通讯》2013,38(8):1141-1167
ABSTRACT This paper studies the pressureless Euler–Poisson system and its fully nonlinear counterpart, the Euler–Monge–Ampère system, where the fully nonlinear Monge–Ampère equation substitutes for the linear Poisson equation. While the first is a model of plasma physics, the second is derived as a geometric approximation to the Euler incompressible equations. Using energy estimates, convergence of both systems to the Euler incompressible equations is proved. 相似文献
5.
On Error Estimates of the Projection Methods for the Navier-Stokes Equations: Second-order Schemes 总被引:4,自引:0,他引:4
Jie Shen. 《Mathematics of Computation》1996,65(215):1039-1065
We present in this paper a rigorous error analysis of several projection schemes for the approximation of the unsteady incompressible Navier-Stokes equations. The error analysis is accomplished by interpreting the respective projection schemes as second-order time discretizations of a perturbed system which approximates the Navier-Stokes equations. Numerical results in agreement with the error analysis are also presented.
6.
G.N. Milstein & M.V. Tretyakov 《高等学校计算数学学报(英文版)》2021,14(1):1-30
We consider a time discretization of incompressible Navier-Stokes equations with spatial periodic boundary conditions and additive noise in the vorticity-velocity formulation. The approximation is based on freezing the velocity on time
subintervals resulting in a linear stochastic parabolic equation for vorticity. At each
time step, the velocity is expressed via vorticity using a formula corresponding to
the Biot-Savart-type law. We prove the first mean-square convergence order of the
vorticity approximation. 相似文献
7.
Approximation of the unsteady Brinkman‐Forchheimer equations by the pressure stabilization method
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Mohammed Louaked Nour Seloula Saber Trabelsi 《Numerical Methods for Partial Differential Equations》2017,33(6):1949-1965
In this work, we propose and analyze the pressure stabilization method for the unsteady incompressible Brinkman‐Forchheimer equations. We present a time discretization scheme which can be used with any consistent finite element space approximation. Second‐order error estimate is proven. Some numerical results are also given.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1949–1965, 2017 相似文献
8.
In this paper, the authors consider the zero-viscosity limit of the three dimensional incompressible steady Navier-Stokes equations in a half space R+×R2. The result shows that the solution of three dimensional incompressible steady Navier-Stokes equations converges to the solution of three dimensional incompressible steady Euler equations in Sobolev space as the viscosity coefficient going to zero. The method is based on a new weighted energy estimates and Nash-Moser itera... 相似文献
9.
本文对周期边界条件Navier-Stokes方程,证明了其Fourier非线性Galerkin逼近解的存在唯一性,同时给出了逼近解的误差估计. 相似文献
10.
Dongho CHAE 《数学年刊B辑(英文版)》2009,30(5):513-526
The author reviews briefly some of the recent results on the blow-up problem for the incompressible Euler equations on R^N and also presents Liouville type theorems for the incompressible and compressible fluid equations. 相似文献
11.
We present in this paper an error analysis of a fractional-step method for the approximation of the unsteady incompressible Navier-Stokes equations. Under mild regularity assumptions on the continuous solution, we obtain second-order error estimates in the time step size, both for velocity and pressure. Numerical results in agreement with the error analysis are also presented. 相似文献
12.
Yinnian He 《计算数学(英文版)》2004,22(1):21-32
In this article we consider a two-level finite element Galerkin method using mixed finite elements for the two-dimensional nonstationary incompressible Navier-Stokes equations. The method yields a $H^1$-optimal velocity approximation and a $L_2$-optimal pressure approximation. The two-level finite element Galerkin method involves solving one small, nonlinear Navier-Stokes problem on the coarse mesh with mesh size $H$, one linear Stokes problem on the fine mesh with mesh size $h << H$. The algorithm we study produces an approximate solution with the optimal, asymptotic in $h$, accuracy. 相似文献
13.
This study proposes Haar wavelet (HW) approximation method for solving magnetohydrodynamic flow equations in a rectangular duct in presence of transverse external oblique magnetic field. The method is based on approximating the truncated double Haar wavelets series. Numerical solution of velocity and induced magnetic field is obtained for steady-state, fully developed, incompressible flow for a conducting fluid inside the duct. The calculations show that the accuracy of the Haar wavelet solutions is quite good even in the case of a small number of grid points. The HW approximation method may be used in a wide variety of high-order linear partial differential equations. Application of the HW approximation method showed that it is reliable, simple, fast, least computation at costs and flexible. 相似文献
14.
S. Faure 《Numerical Methods for Partial Differential Equations》2005,21(2):242-271
The aim of this article is to describe a colocated finite volume approximation of the incompressible Navier‐Stokes equation and study its stability. One of the advantages of colocated finite volume space discretizations over staggered space discretizations is that all the variables share the same location; hence, the possibility to more easily use complex geometries and hierarchical decompositions of the unknowns. The time discretization used in the scheme studied here is a projection method. First, we give the full discretization of the incompressible Navier‐Stokes equations, then, we state the stability result and prove it following the methods of Marion and Temam. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005 相似文献
15.
This paper studies the approximation of solutions for the incompressible convective Brinkman–Forchheimer (CBF) equations via the artificial compressibility method. We first introduce a family of perturbed compressible CBF equations that approximate the incompressible CBF equations. Then, we prove the existence and convergence of solutions for the compressible CBF equations to the solutions of the incompressible CBF equations. 相似文献
16.
Wei-zhu Bao 《计算数学(英文版)》1998,16(3):239-256
1.IntroductionManyproblemsarisinginfluidmechanicsaregiveninanunboundeddomain,suchasfluidflowaroundobstacles.Whencomputingthenumericalsolutionsoftheseproblems,oneoftenintroducesartificialboundariesandsetsupaxtificialboundaryconditionsonthem.Thentheoriginal… 相似文献
17.
Peter Constantin 《Journal of the American Mathematical Society》2001,14(2):263-278
We study a formulation of the incompressible Euler equations in terms of the inverse Lagrangian map. In this formulation the equations become a first order advective nonlinear system of partial differential equations.
18.
This paper is concerned with a shape sensitivity analysis of a viscous incompressible fluid driven by Stokes equations. The structures of continuous shape gradients with respect to the shape of the variable domain for some given cost functionals are established by introducing the Piola transformation and then deriving the state derivative and its associated adjoint state. Finally we give the finite element approximation of the problem and a gradient type algorithm is effectively used for our problem. 相似文献
19.
The Cahn-Hilliard equation with irregular potentials and dynamic boundary conditions is considered.The existence of the global attractor is proved and the long time behavior of the trajectories,namely,the convergence to steady states,is studied. 相似文献
20.
Sang Dong Kim Chang‐Ock Lee Thomas A. Manteuffel Stephen F. McCormick Oliver Rhrle 《Numerical Linear Algebra with Applications》2006,13(7):523-542
Following earlier work for Stokes equations, a least squares functional is developed for two‐ and three‐dimensional Oseen equations. By introducing a velocity flux variable and associated curl and trace equations, ellipticity is established in an appropriate product norm. The form of Oseen equations examined here is obtained by linearizing the incompressible Navier–Stokes equations. An algorithm is presented for approximately solving steady‐state, incompressible Navier–Stokes equations with a nested iteration‐Newton‐FOSLS‐AMG iterative scheme, which involves solving a sequence of Oseen equations. Some numerical results for Kovasznay flow are provided. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献