Error estimation of prediction-correction legendre spectral approximation to incompressible fluid flow

1. IntroductionThere have been a lot of literatures concerning the existence, uniqueness, regularityof the solution of Navier-Stokes equation. Usually the primitive equation is considered,e.g.5 see 11,2]. Maily methods are used for its numerical simulation, e.g., see [2--7]. But wemeet several difficulties in calculation. For instance, if we use the finite difference method,then we have to evaluate the pressure at each time step. Some authors developed theartificial compressibility method or…     

谱逼近的某些新进展

本文综述谱逼近的某些新进展,非线怀计算不稳定性,数据的不连续性和解的奇异性会破坏谱方法的高精度,各种滤波方法,本质不振荡多项式插值,正交逼近的重构造方法和某些Ｈｉｌｂｅｒｔ空间中的Ｊａｃｏｂｉ逼近被应用,它们使得谱方法更有效。     

金纳米粒子组装体系的表面增强拉曼光谱特性研究——表面粒子密度与拉曼光谱强度的关系

利用纳米粒子组装制备了金基底———巯基苯胺自组装膜偶联层———金纳米粒子的“三明治”结构,研究了表面粒子密度与偶连层分子的拉曼光谱强度的关系。实验结果显示,该结构对偶连层分子的拉曼光谱有很好的增强效应,增强因子可达１０５。在表面粒子密度较低时,拉曼光谱强度与表面粒子密度曲线呈线形,随着表面粒子密度的增加,曲线出现负偏差并在粒子密度较高区域出现一个平台。     

不可忽视的系统误差

本文主要介绍了系统误差对实验结果的影响。     

Generalized monotone schemes, discrete paths of extrema, and discrete entropy conditions

Solutions of conservation laws satisfy the monotonicity property: the number of local extrema is a non-increasing function of time, and local maximum/minimum values decrease/increase monotonically in time. This paper investigates this property from a numerical standpoint. We introduce a class of fully discrete in space and time, high order accurate, difference schemes, called generalized monotone schemes. Convergence toward the entropy solution is proven via a new technique of proof, assuming that the initial data has a finite number of extremum values only, and the flux-function is strictly convex. We define discrete paths of extrema by tracking local extremum values in the approximate solution. In the course of the analysis we establish the pointwise convergence of the trace of the solution along a path of extremum. As a corollary, we obtain a proof of convergence for a MUSCL-type scheme that is second order accurate away from sonic points and extrema.

     

双曲型守恒律的一种高精度TVD差分格式

构造了一维双曲型守恒律方程的一个高精度高分辨率的守恒型TVD差分格式.其主要思想是:首先将计算区域划分为互不重叠的小单元,且每个小单元再根据希望的精度阶数分为细小单元;其次,根据流动方向将通量分裂为正、负通量,并通过小单元上的高阶插值逼近得到了细小单元边界上的正、负数值通量,为避免由高阶插值产生的数值振荡,进一步根据流向对其进行TVD校正;再利用高阶Runge KuttaTVD离散方法对时间进行离散,得到了高阶全离散方法.进一步推广到一维方程组情形.最后对一维欧拉方程组计算了几个算例.     

提高高聚物化学分析结果准确度的方法

从分析方法、分析过程、仪器与试剂、实验环境条件、试样组成的变动性、试样中被测组分分布的不均匀性等方面分析了高聚物材料化学分析结果的误差来源,提出了提高高聚物化学分析结果准确度的方法。     

A new alternating group explicit-implicit algorithm with high accuracy for dispersive equation

In this paper, a new alternating group explicit-implicit （nAGEI） scheme for dispersive equations with a periodic boundary condition is derived. This new unconditionally stable scheme has a fourth-order truncation error in space and a convergence ratio faster than some known alternating methods such as ASEI and AGE. Comparison in accuracy with the AGEI and AGE methods is presented in the numerical experiment.     

AN EVALUATION OF THE BOUNCE-BACK BOUNDARY CONDITION FOR LATTICE BOLTZMANN SIMULATIONS

The bounce-back boundary condition for lattice Boltzmann simulations is evaluated for flow about an infinite periodic array of cylinders. The solution is compared with results from a more accurate boundary condition formulation for the lattice Boltemann method and with finite difference solutions. The bounce-back boundary condition is used to simulate boundaries of cylinders with both circular and octagonal cross-sections. The convergences of the velocity and total drag associated with this method are slightly sublinear with grid spacing. Error is also a function of relaxation time, increasing exponentially for large relaxation times. However, the accuracy does not exhibit a trend with Reynolds number between 0·1 and 100. The square lattice Boltzmann grid conforms to the octagonal cylinder but only approximates the circular cylinder, and the resulting error associated with the octagonal cylinder is half the error of the circular cylinder. The bounce-back boundary condition is shown to yield accurate lattice Boltzmann simulations with reduced computational requirements for computational grids of 170×170 or finer, a relaxation time less than 1·5 and any Reynolds number from 0·1 to 100. For this range of parameters the root mean square error in velocity and the relative error in drag coefficient are less than 1 per cent for the octagonal cylinder and 2 per cent for the circular cylinder. © 1997 John Wiley & Sons, Ltd.     

A NEW HIGH-ORDER ACCURACY EXPLICIT DIFFERENCE SCHEME FOR SOLVING THREE-DIMENSIONAL PARABOLIC EQUATIONS

1.IntroductionInalotoffields,suchas'diffusion,seepageandheatconductionetc.,weoftenmeetproblemsofsolvingparabolicequations.Inthecaseofthree-dimension,themathematicalmodelissuchaninitialandboundaryvalueproblemasbelow:Thedifferenceschemesforsolvingtheproblemabove,whichhavehigh-orderaccuracyandcanbefiguredoutwithexplicitschemearesuchschemesasthoseinII]and[21.Theexplicitdifferenceschemeproposedinthispaperkeepsthehigh-orderaccuracy(it'hasthesameaccuracyasthosein[ifand[21),butitsexpressionismuchsimp…