共查询到18条相似文献,搜索用时 62 毫秒
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对流扩散问题的交替方向差分-流线扩散格式 总被引:1,自引:0,他引:1
1.引 言 差分-流线扩散法(Finite Difference-Streamline Diffusion Method,简称FDSD方法)于1998年由文[1]提出并对线性对流占优扩散问题给出分析,随后文[2],[3]就非线性问题的FDSD格式及FDSD预测-校正格式,分别作出了分析,文[4]讨论了FDSD方法的后验估计及自适应技术,[5],[6]则分别讨论了FDSD方法的某些重要应用.与基于时-空有限元的传统流线扩散法相比,FDSD方法的计算工作量已有成数量级的减少,且较易于推广到非线性问题,然而,对于高维问题,在每一时间层,仍然需要求解一大型线性或非线性方程组,工作量仍然很大.参照J.Douglas与T.Dupont关于抛物问题交替方向 相似文献
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非线性对流扩散问题的差分-流线扩散法 总被引:20,自引:0,他引:20
1.引言流线扩散法(简称SD方法)是由Huzhes和Brooks在1980年前后提出的一种数值求解对流占优扩散问题的新型有限元算法.随后,Johnson和N8vert将SD方法推广到发展型对流扩散问题([1],[2],[3]).熟知,对于对流扩散问题,标准有限元法虽具有高阶精度,但常产生数值振荡;古典人工粘性Galerkin法更具有较好的稳定性,但仅具有一阶精度.而(SD方法兼具良好的数值稳定性和高阶精度,因此得到了越来越多的重视,对于发展型对流扩散问题,传统的SD方法均采用时空有限元.这样做,虽然可使时间和空间方向上的精度很好的协调起… 相似文献
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1 引 言流线扩散法 (Stream line- Diffusion method,简称 SD方法 )是由 Hughes和 Brooks在文献 [1]中提出 ,并由 Johnson等人 (文献 [2 ]- [4])发展起来的求解对流占优扩散问题 (包括双曲型问题 )的一种有效的数值方法 .SD方法兼具有良好的数值稳定性和高阶收敛精度已广泛地应用于计算流体等诸多问题 .然而 ,传统的 SD方法均采用时空有限元求解发展型问题 .这样 ,虽可使时间和空间方向上的精度很好的协调起来 ,却增大了实际计算的复杂程度 ;对非线性问题也不便进行线性化处理 .孙澈等人在文献 [5 ]中对对流扩散问题提出了仅对空间… 相似文献
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讨论了对流扩散问题C rank-N ico lson差分流线扩散格式,利用插值后处理技术提高了特殊网格下该格式在双线性元空间解的精度,从而按Lα(L2(Ω))模达到最优. 相似文献
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一维对流扩散方程CRANK—NICOLSON特征差分格式 总被引:10,自引:0,他引:10
本文针对一维线性和非线性对流扩散方程提出一种Crank-Nicolson类型的特征差分格式,给出了该格式形成的线性代数方程组可解的一个充条件,证明了该格式按离散L^2模是收敛的,且其收敛阶为O(△t^ h^2). 相似文献
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In this paper, two kinds of Finite Volume-Streamline Diffusion Finite Element methods (FV-SD) for steady convection dominated-diffusion problem are presented and the stability and error estimation for the numerical schemes considered are established in the norm stronger than L^2-norm. The theocratical analysis and numerical example show that the schemes constructed in this paper are keeping the basic properties of Streamline Diffusion (SD) method and they are more economical in computing scale than SD scheme, and also, they have same accuracy as FV-Galerkin FE method and better stability than it. 相似文献
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THE FINITE DIFFERENCE STREAMLINE DIFFUSION METHODS FOR TIME-DEPENDENT CONVECTION-DIFFUSION EQUATIONS 总被引:1,自引:0,他引:1
In this paper, two finite difference streamline diffusion (FDSD) schemes for solving two-dimensional time-dependent convection-diffusion equations are constructed. Stability and optimal order error estimati-ions for considered schemes are derived in the norm stronger than L~2-norm. 相似文献
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本文研究了一类含源项非定常奇异摄动对流扩散问题.利用Crank-Nicolson差分格式下的移动网格方法,获得了求解该类问题的数值实验结果,改进了均匀网格下求解的结果. 相似文献
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对流扩散方程的经济差分格式 总被引:21,自引:0,他引:21
1.引言 对流扩散方程是一类基本的运动方程,它可描述质量、热量的输运过程以及反应扩散过程等众多物理现象.寻找稳定、快速实用的数值方法,有着重要的理论和实际意义.标准的差分方法或有限元方法对它常常失效,根本原因在于“对流项”的存在.[1]提出了解对流扩散方程的特征线修正技术,这一方法考虑沿着特征线(流动方向)的离散,利用了对流扩散问题的物理力学性质,可以有效地克服数值振荡,保证数值解的稳定,尤其对“对流占优”的问题,这一方法有突出的优越性.这方面已有大量的理论和应用研究成果[2,3,7].对大规模… 相似文献
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由同顺 《高等学校计算数学学报》2004,26(4):289-297
Using FCT idea,the non-oscillation MMOCAA(The modified method of characteristics with adjusted advection) finite difference scheme satisfing the discrete maximum principle for convection-dominated diffusion equation in 2D is constructed.The scheme is free from oscillation,with which the problem is solved by the MMOCAA difference method based on 2-order Lag-range interpolation proposed by Jim.Douglas, Jr.(Numer.Math.,1999,83:353-369.). The error analysis of the new scheme and numerical example are given in the paper.The numerical example shows that the scheme has smaller numerical viscosity than the MMOCAA difference method based on bilineax Lagrange interpolation. 相似文献
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The Alternating Segment Crank-Nicolson scheme for one-dimensional diffusion equation has been developed in [ 1 ], and the Alternating Block Crank-Nicolson method for two-dimensional problem in [2]. The methods have the advantages of parallel computing, stability and good accuracy. Tn this paper for the two-dimensional diffusion equation, the net region is divided into bands, a special kind of block. This method is called the alternating Band Crank-Nicolson method. 相似文献
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Abdellatif Agouzal 《计算数学(英文版)》2000,18(6):639-644
1. IlltroductionThe finite element approximation of the convection--diffusin equations has been investigated using several different approaches (see e.g. [3] [4] and the references therein).Previous analysis in primal formulation of these problems was done for two types ofapproximation schemes: one which produces a continuous piecewise polynomial approximation and one which produces a piecewise polynomial approximation which arecontinuous for certain number of moments accross interelement edge… 相似文献
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赵卫东 《高校应用数学学报(英文版)》1999,14(3)
The thermistor problem is an initial-boundary value problem of coupled nonlinear differential equations.The nonlinear PDEs consist of a heat equation with the Joule heating as a source and a current conservation equation with temperature-dependent electrical conductivity.This problem has important applications in industry.In this paper,A new finite difference scheme is proposed on nonuniform rectangular partition for the thermistor problem.In the theoretical analyses,the second-order error estimates are obtained for electrical potential in discrete L2 and H1 norms,and for the temperature in L2 norm.In order to get these second-order error estimates,the Joule heating source is used in a changed equivalent form. 相似文献
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本文把三层修正特征线法,MMOCAA 差分方法及WENO 插值相结合,提出了求解对流扩散方程的三层WENO-MMOCAA 差分格式.此格式关于时间具有二阶精度,关于空间具有二阶以上精度且可避免基于二次以上Lagrange 插值的三层MMOCAA 差分方法在解的大梯度附近所产生的振荡.本文使用新的分析方法,给出了格式的误差估计.本文的数值算例表明新格式可消除振荡. 相似文献