粗颗粒高含沙两相紊流运动规律的实验研究

本文通过在矩形断面水平管道中的输沙试验,研究了粗颗粒二相高含沙水流的流速及含沙浓度分布。在主流区,流速分布遵从对数规律,卡门常数则为利查逊数及浓度的函数。底床附近,流速分布受到升力效应的影响。管道高含沙水流的悬沙浓度分布与明渠低含沙水流大不相同,利用扩散方程求出浓度分布公式,与实测结果符合得很好。     

气固两相弯管湍流场中圆柱状颗粒取向和沉积特性的研究北大核心CSCD

针对在Reynolds数Re=3000~50000、Stokes数S_(tk)=0.1~10、Dean数De=1400~2800的情况下,长径比β=2~12的圆柱状颗粒流经弯管湍流场时的取向与沉积特性进行了研究.圆柱状颗粒的运动采用细长体理论结合Newton第二定律进行描述,取向分布函数由Fokker-Planck方程给出,平均湍流场通过求解Reynolds平均运动方程结合Reynolds应力方程得到,作用在颗粒上的湍流脉动速度由动力学模拟扫掠模型描述.通过求解湍流场以及颗粒的运动方程和取向分布函数方程,得到并分析了沿流向不同截面和出口处颗粒的取向分布,讨论了各因素对颗粒沉积特性的影响.研究结果表明,随着S_(tk)和颗粒长径比β的增加、De和Re的减少,颗粒的主轴更趋向于流动方向.颗粒的沉积率随着De,Re,S_(tk)和颗粒长径比的增大而增加,所得结论对于工程实际应用具有参考价值.     

四阶R-K方法中一类新算法的分析

对常微分方程初值问题数值计算中的四阶R-K方法首次具体给出了一般格式中的参数所满足的方程,并提出了新的计算格式,这些新算法对某些初值问题其整体截断误差有明显的减少.这对常微分方程初值问题在社会、经济、生态等领域中的广泛应用将提供有益的新算法.     

变系数线性微分方程初值问题数值解的小波方法

通过利用小波尺度函数的正交性并结合配点法 ,本文给出了一种求解变系数线性微分方程初值问题数值解的小波算法 .在一定的假设条件下 ,对算法的收敛性进行了理论分析 .最后 ,我们还给出了一个具体的数值计算例子 .     

单位圆上一类高阶线性微分方程解的性质

结合微分方程理论和函数空间理论,研究了单位圆上一类特殊高阶线性微分方程解的性质,得到当方程系数满足某些条件时,其解属于某类函数空间的充分条件.     

Persistence of attractors for one-step discretization of ordinary differential equations

We consider numerical one-step approximations of ordinary differentialequations and present two results on the persistence of attractorsappearing in the numerical system. First, we show that the upperlimit of a sequence of numerical attractors for a sequence ofvanishing time-steps is an attractor for the approximated systemif and only if for all these time-steps the numerical one-stepschemes admit attracting sets which approximate this upper limitset and attract with a uniform rate. Second, we show that ifthese numerical attractors themselves attract with a uniformrate, then they converge to some set if and only if this setis an attractor for the approximated system. In this case, wecan also give an estimate for the rate of convergence dependingon the rate of attraction and on the order of the numericalscheme.     

Regularity for Almost Convex Viscosity Solutions of the Sigma-2 Equation

We establish interior regularity for almost convex viscosity solutions of thesigma-2 equation.     

一类滞后生态微分方程的初值问题

对一般的滞后系统，人们采用了将滞后变量ｘ（ｔ－１）用一个Ｈｅｒｍｉｔｅ插值多项式来处理，从而把滞后系统转化为常微分方程系统来求其数值解（见文［２］，［３］）．本文根据［２］中的表Ⅰ选用了一个带有五次Ｈｅｒｍｉｔｅ插值多项式的四阶Ｒｕｎｇｅ－Ｈｕｔａ法来求两个常见的滞后初值问题．     

Numerical Solution of Boundary Value Problems for Selfadjoint Differential Equations of 2nth Order

The paper is devoted to solving boundary value problems for self-adjoint linear differential equations of 2nth order in the case that the corresponding differential operator is self-adjoint and positive semidefinite. The method proposed consists in transforming the original problem to solving several initial value problems for certain systems of first order ODEs. Even if this approach may be used for quite general linear boundary value problems, the new algorithms described here exploit the special properties of the boundary value problems treated in the paper. As a consequence, we obtain algorithms that are much more effective than similar ones used in the general case. Moreover, it is shown that the algorithms studied here are numerically stable.     

Regularity of the solution for a final value problem for the Rayleigh‐Stokes equation

In this paper, we deal with the backward problem of determining initial condition for Rayleigh‐Stokes where the data are given at a fixed time. The problem has many applications in some non‐Newtonian fluids. We give some regularity properties of the solution to backward problem.     

On the complex oscillation theory of f ″ + A (z)f = 0 where A (z) is analytic in the unit disc

In this paper, we investigate the complex oscillation theory of the second order linear differential equation f ″ + A (z)f = 0, where the coefficient A (z) is an analytic function in the unit disc Δ = {z: |z | < 1} (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Novel numerical techniques based on Fokas transforms,for the solution of initial boundary value problems

The unified transform method of A. S. Fokas has led to important new developments, regarding the analysis and solution of various types of linear and nonlinear PDE problems. In this work we use these developments and obtain the solution of time-dependent problems in a straightforward manner and with such high accuracy that cannot be reached within reasonable time by use of the existing numerical methods. More specifically, an integral representation of the solution is obtained by use of the A. S. Fokas approach, which provides the value of the solution at any point, without requiring the solution of linear systems or any other calculation at intermediate time levels and without raising any stability problems. For instance, the solution of the initial boundary value problem with the non-homogeneous heat equation is obtained with accuracy 10⁻¹⁵, while the well-established Crank–Nicholson scheme requires 2048 time steps in order to reach a 10⁻⁸ accuracy.