GLOBAL FINITE ELEMENT NONLINEAR GALERKIN METHOD FOR THE PENALIZED NAVIER-STOKES EQUATIONS GLOBAL FINITE ELEMENT NONLINEAR GALERKIN METHOD FOR THE PENALIZED NAVIER-STOKES EQUATIONS

1. IntroductionIn the numerical simulation of the Navier-Stokes equations one encounters three seriousdifficulties in the case of large Reynolds numbers f the treatment of the incomPressibility con-dition divu = 0, the treatment of the noIilinear terms and the large time integration. For thetreatment of the incoInPressibility condition, one use the penalty method in the case of finiteelemellts [1--2l and for the treatmen of the noulinar terms and the large tfor integration, oneuse the nonlin…     

Navier-Stokes方程的最佳有限元非线性Galerkin算法

1．引言对于Navier－Stokes方程有限元数值求解方面的研究已有很多的文章和专著,多数是采用有限元Galerkin算法,例见文献[1-4]．然而,由于Navier-Stokes方程在大雷诺数时有其强的非线性性和对时间土的长期依赖性,用计算机求解Navier－Stokes方程在速度和容量方面是难以承受的．为了克服这些困难,最近人们提出了有限元非线性Galerkin算法,见文献卜8］,然而这种算法只是在某一有限时刻之后具有好的收敛速度,在初始时刻的某一区间不能达到好的收敛速度．本文应用Taylor展开技术导出了数值求解二维非定常Navier－Stokes方程的最佳…     

FINITE ELEMENT NONLINEAR GALERKIN COUPLING METHOD FOR THE EXTERIOR STEADY NAVIER-STOKES PROBLEM

1.IntroductionNonlinearGalerkinmethodsaremultilevelschemesforthedissipativeevolutionpartialdifferentialequations.Theycorrespondtothesplittingsoftheunknownu:u=y z)wherethecomponentsareofdifferentorderofmagnitudewithrespecttoaparameterrelatedtothespati...     

NONLINEAR GALERKIN METHOD FOR NAVIER-STOKES EQUATIONS WITH STREAM-VORTICITY FORM

I Let D be a launder domain in Rz with Lipehitz continuous bodare I'. ac consider the stream-vortidty form of hmedependent Navier-stokes Muahons describing the 'flow Of a ~ incompreSSible nuid confined in Dwhere to and & are vorticity and stream function. BecaUSe the action (1) doeS not include the differentialten z, ~ tie ~ con&tion of' dab at In tthe Paper, we give a ho element n~ Galerkin ~, acs ~ is ~ an tab finite element spaceS X. and X* for the aPPmxhaation of the ~ ac v~ fUncti…     

A MIXED FINITE ELEMENT METHOD ON A STAGGERED MESH FOR NAVIER-STOKES EQUATIONS

In this paper, we introduce a mixed finite element method on a staggered mesh for the numerical solution of the steady state Navier-Stokes equations in which the two components of the velocity and the pressure are defined on three different meshes. This method is a conforming quadrilateral Q1 × Q1 - P0 element approximation for the Navier-Stokes equations. First-order error estimates are obtained for both the velocity and the pressure. Numerical examples are presented to illustrate the effectiveness of the proposed method.     

非定常线性化Navier-Stokes方程的子格粘性非协调有限元方法

本文结合子格粘性法的思想,空间采用非协调Crouzeix-Raviart元逼近,时间采用Crank-Nicolson差分离散,对非定常线性化Navier-Stokes方程建立了全离散的子格粘性非协调有限元格式.对稳定性和误差估计作出了详细的分析, 得出了最优的误差估计.最后, 通过数值算例进一步验证了该方法的稳定性和收敛性.     

非定常 N-S 方程的非线性 Galerkin 算法及其误差估计

本文给出了二维非定常N-S方程的三种数值格式,其中空间变量用谱非线性Galerkin算法进行离散,时间变量用有限差分离散,并研究了这些格式数值解的逼近精度．最后,给出了部分数值计算结果．     

MIXED FINITE ELEMENT METHODS FOR FRACTIONAL NAVIER-STOKES EQUATIONS

This paper gives the detailed numerical analysis of mixed finite element method for fractional Navier-Stokes equations.The proposed method is based on the mixed finite element method in space and a finite difference scheme in time.The stability analyses of semi-discretization scheme and fully discrete scheme are discussed in detail.Furthermore,We give the convergence analysis for both semidiscrete and flly discrete schemes and then prove that the numerical solution converges the exact one with order O(h2+k),where h and k:respectively denote the space step size and the time step size.Finally,numerical examples are presented to demonstrate the effectiveness of our numerical methods.     

管道Bingham流的Galerkin有限元法

1　引　言Galerkin有限元法从七十年代中期开始被广泛应用于求解抛物型方程的研究当中 ,其基本解法是对空间域采用有限元法 ,而对时间轴采用差分方法 ,并且对不同时刻的空间区域采用相同的网格 .但到至今为止 ,用此方法应用于变分不等式方面的研究工作甚少 ,本文就针对一类变分不等式— Bingham流问题应用此方法来进行分析、研究 ,给出其相应的近似解有限元计算格式 ,并在合理的正则性条件假设下 ,导出了近似解的 L2 模及能量模方面的误差估计式 .2　 Galerkin有限元格式设Ω为平面上的有界凸区域 ,边界为 Ω ,并适当光滑 .Wmp(Ω )为 S…     

Sobolev方程的CN全离散化有限元格式

首先给出Sobolev方程关于时间二阶精度的Crank-Nicolson(CN)时间半离散格式,然后直接从时间二阶精度的CN时间半离散格式出发,构造CN全离散化的有限元格式,并给出这种时间二阶精度的CN全离散化有限元解的误差估计.本文研究方法使得理论证明变得更简便, 也是处理Sobolev方程的一种新的尝试.     

不可压Navier-Stokes方程迎风格式及后验误差估计

1引言不可压Navier-Stokes方程作为流体力学的基本方程,其数值计算一直是科学与工程计算关心的问题．本文考虑定常问题: -ε△u (u·▽)u ▽p = f x∈Ω,▽·u=0 x∈Ω, (1) u =0 x∈(?)Ω．这里ε=1／Re是Reynolds数的倒数,u=(u1,u2,…,ud)为待求流速场,p是待求压力场,f=(f1,f2,…,fd)是给定的体力．Ωv(?) Rd(d=2,3)是有界区域,且具有分片Lipschitz连续边界(?)Ω．     

A TWO-GRID METHOD FOR THE STEADY PENALIZED NAVIER-STOKES EQUATIONS

A two-grid method for the steady penalized incompressible Navier-Stokes equations is presented. Convergence results are proved. If h = O(H^3-s) and ε = O(H^5-2s) (s = 0(n=2);s=1/2(n=3)are chosen, the convergence order of this two-grid method is the same as that of the usual finite element method. Numerical results show that this method is efficient and can save a lot of computation time.     

CHEBYSHEV SPECTRAL-FINITE ELEMENT METHOD FOR TWO-DIMENSIONAL UNSTEADY NAVIER-STOKES EQUATION

1. IntroductionSpectral method has been used successfu11y in computational fluid dynamics. FOr semi-periodic problems, we can use mixed FOurier-Chebyshev spectral method, FOurier spectral-finitedifference method and FOurier spectral-finite element method …     

FOURIER-LEGENDRE PSEUDOSPECTRAL METHOD FOR THE NAVIER-STOKES EQUATIONS

1. IntroductionThe mixed spectral and pseudospectral methods are successful to numerically solvethe semi-periodic problems of incompressible fluid flows (see [1--61). This paper is devoted to the FOurier--Legendre pseudospectral method for the two-dimensional unsteadyNavier--Stokes equations with semi-periodic boundary condition. This method is performed easily and has the same high accuracy as spectral method has.Let x = (x,,x,)" and fi ~ 11 x iZ where 11 ~ {xl/-- 1 < al < 1}, IZ ~ {xZ/--…     

二维Navier-Stokes方程同位有限体积法的稳定性改进

1 引言 考虑不可压缩粘性流体的二维Navier-Stokes方程,它由速度压力公式和连续性方程的耦合组成.     

A NEW NONCONFORMING MIXED FINITE ELEMENT SCHEME FOR THE STATIONARY NAVIER-STOKES EQUATIONS

In this article, a new stable nonconforming mixed finite element scheme is proposed for the stationary Navier-Stokes equations, in which a new low order CrouzeixRaviart type nonconforming rectangular element is taken for approximating space for the velocity and the piecewise constant element for the pressure. The optimal order error estimates for the approximation of both the velocity and the pressure in L2-norm are established, as well as one in broken H1-norm for the velocity. Numerical experiments are given which are consistent with our theoretical analysis.     

Navier-Stokes方程的非奇异解分支的谱Galerkin逼近

No error estimate of the spectral Galerkin approximation for the steady-state Navier-Stokes equations was given without assuming that the data of the externalforce field and the boundary conditions are small enough. In this paper, under the condition that the solutions of the Navier-Stokes equations are nonsingular,we proved the existence and convergence of the spectral Galerkin approximation solutions and gave the error estimate. At last, this approximation method wasapplied to simulate the spherical Couette flow.     

非定常Navier-Stokes方程加罚形式的两重网格算法

A two-grid method (TGM) for the fully discrete unsteady NavierStokes (N-S) equations in a penalty form is discussed. An error estimate is given,and a numerical test is also given to verify the correctness of theoretical analysis.     

ON THE STABILITY OF THE RESIDUAL-FREE BUBBLES FOR THE NAVIER-STOKES EQUATIONS

This paper considers the Calerkin finite element method for the incompressible Navier-Stokes equations in two dimensions, where the finite-dimensional spaces employed consist of piecewise polynomials enriched with residual-free bubble （RFB） functions. The stability features of the residual-free bubble functions for the linearized Navier-Stokes equations are analyzed in this work. It is shown that the enrichment of the velocity space by bubble functions stabilizes the numerical method for any value of the viscosity parameter for triangular elements and for values of the viscosity parameter in the vanishing limit case for quadrilateral elements.     

Navier-Stokes方程带Backtracking技巧的两重网格算法

1 引 言考虑二维不可压 Navier-Stokes方程: