Improvement on stability and convergence of A. D. I. schemes

IntroductionAlternatingdirectionimplicit(A.D.I.)schemeswhichwasdiscoveredin1950',hasbecomeoneofthemostimportantmethodsintheapproximationofthesolutionsofparabolicpartialdifferentialequationsinmulti-dimensionalspace.Someofresultsaboutstabilityandconvergencearetooweakandincomplete,we'lltrytoimprovetheminthispaper.Considerinitial-boundaryvalueproblemintwospacevariablesLetΩhbeauniformrectangularmeshofO.h>0isthespacestepinxandydireehon*ProjectsupPOI'tedbytheNahonalNaturalScienceFoundahonofChi…     

求解热传导方程的一类新的加权差分格式

本文提出了数值求解热传导方程的一类新的Ｏ（ｋ,ｈ２）加权差分格式,并利用Ｆｏｕｒｉｅｒ方法讨论了格式的稳定性,证明了当１／（１＋ｅε）≤θ≤１时,格式是无条件稳定的,而当０≤θ＜１／（１＋ｅε）时,只有０＜ｒ≤ｆ（θ,ε）,格式才稳定,其中ｆ（θ,ε）对任何固定的θ是正实数ε的严格单调增函数．最后通过数值算例检验了文中格式的高稳定性．     

冲击接触问题增广 Lagrangian 双共轭梯度法

为避免动力接触问题罚函数法由于满足表面接触条件所带来的数值解的振荡,及常规Ｌａｇｒａｎｇｉｎａ乘子法与显式积分算法不相容的缺陷,本文发展了一个既与显式积分算法相容,又可自然地用于隐式自法的增广Ｌａｇｒａｎｇｉａｎ双共轭梯度算法。增广Ｌａｇｒａｎｇｉａｎ双共轭梯度算法既可精确地满足接触约束条件,又可避免数值解的振荡;在改善数值迭代的收敛性的同时又提高了计算效率。     

QUICK与多种差分方案的比较和计算

本文用QUICK和多种差分方案计算了四个流动与换热问题．计算结果表明。对于强制流动问题,QUICK用较粗网格就能得到其他差分方案用较细网格才能得到的结果。对稳态自然对流,QUICK与其他差分方案的计算结果相近,但QUICK方案能预测出所计算的低Pr数流体自然对流的物理振荡,而其他几种方案不能．     

On Baire Measurable Homomorphisms of Quotients of the Additive Group of the Reals

The quotient ℝ/G of the additive group of the reals modulo a countable subgroup G does not admit nontrivial Baire measurable automorphisms.     

人工选择耗散法抑制数值振荡

通过在差分方程上加一耗散项,根据其系数的选取得到只对短波起作用,而对长波没有影响的人工选择耗散法。数值算例表明该方法具有良好的激波捕获能力和可移植性。得到均匀非对称网格上的人工选择耗散法,并把人工选择耗散法推广到二维问题。     

Exponential spline interpolation in characteristic based scheme for solving the advective–diffusion equation

This paper demonstrates the use of shape‐preserving exponential spline interpolation in a characteristic based numerical scheme for the solution of the linear advective–diffusion equation. The results from this scheme are compared with results from a number of numerical schemes in current use using test problems in one and two dimensions. These test cases are used to assess the merits of using shape‐preserving interpolation in a characteristic based scheme. The evaluation of the schemes is based on accuracy, efficiency, and complexity. The use of the shape‐preserving interpolation in a characteristic based scheme is accurate, captures discontinuities, does not introduce spurious oscillations, and preserves the monotonicity and positivity properties of the exact solution. However, fitting exponential spline interpolants to the nodal concentrations is computationally expensive. Exponential spline interpolants were also fitted to the integral of the concentration profile. The integral of the concentration profile is a smoother function than the concentration profile. It requires less computational effort to fit an exponential spline interpolant to the integral than the nodal concentrations. By differentiating the interpolant, the nodal concentrations are obtained. This results in a more efficient and more accurate numerical scheme. Copyright © 2000 John Wiley & Sons, Ltd.     

Revised patterns of reactivity scheme. VII. Revised patterns scheme and its relationship to carbon‐13 NMR spectra

The electron density on a carbon atom determines the ¹³C chemical shift observed in the NMR spectrum. In a vinyl monomer, the same electron density must contribute strongly to polar effects involved in the addition of a radical to that monomer and possibly in the addition (to a double bond) of a radical terminated by a unit derived from that monomer. It is shown that the expected correlation exists when the polar effects in polymerization reactions are represented by the parameters of the revised patterns scheme. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 4336–4342, 2000     

转动惯量平行轴定理验证实验的改进方案

本文介绍了一种刚体转动惯量平行轴定理验证实验的改进方案.该方案通过调节对称放置在承物台上的两个钢柱到仪器转轴的距离来改变系统的转动惯量,使得总转动惯量可以在较大的范围内改变,并且始终保持了系统质量的对称性分布,从而有效地减小了实验的相对误差,提高了实验结果的可信度.     

再谈相干态在算符编序中的应用

利用广义Weyl对应导出了相干态密度算符的S-编序表示.通过此表示并结合S-编序内的算符积分技术,导出了若干量子玻色算符的S-编序形式(包含了正规编序、Weyl编序和反正规编序).此方法进一步推广了相干态在算符编序中的应用.