Optimal Spectral-Galerkin Methods Using Generalized Jacobi Polynomials

We extend the definition of the classical Jacobi polynomials withindexes α, β>−1 to allow α and/or β to be negative integers. We show that the generalized Jacobi polynomials, with indexes corresponding to the number of boundary conditions in a given partial differential equation, are the natural basis functions for the spectral approximation of this partial differential equation. Moreover, the use of generalized Jacobi polynomials leads to much simplified analysis, more precise error estimates and well conditioned algorithms.Mathematics subject classification 1991. 65N35, 65N22, 65F05, 35J05     

Methods of Verifying Continuous Automatic Belt Weighers: State and Prospects

The basic methods of verifying continuous automatic belt weighers are described. A comparative analysis of these methods on the basis of experimental studies is made and ways of implementing the results in industry are recommended.     

A comparison of transformation methods for evaluating two‐dimensional weakly singular integrals

Accurate numerical evaluation of integrals arising in the boundary element method is fundamental to achieving useful results via this solution technique. In this paper, a number of techniques are considered to evaluate the weakly singular integrals which arise in the solution of Laplace's equation in three dimensions and Poisson's equation in two dimensions. Both are two‐dimensional weakly singular integrals and are evaluated using (in a product fashion) methods which have recently been used for evaluating one‐dimensional weakly singular integrals arising in the boundary element method. The methods used are based on various polynomial transformations of conventional Gaussian quadrature points where the transformation polynomial has zero Jacobian at the singular point. Methods which split the region of integration into sub‐regions are considered as well as non‐splitting methods. In particular, the newly introduced and highly accurate generalized composite subtraction of singularity and non‐linear transformation approach (GSSNT) is applied to various two‐dimensional weakly singular integrals. A study of the different methods reveals complex relationships between transformation orders, position of the singular point, integration kernel and basis function. It is concluded that the GSSNT method gives the best overall results for the two‐dimensional weakly singular integrals studied. Copyright © 2002 John Wiley & Sons, Ltd.     

储层泥浆侵入深度预测方法研究

泥浆侵入半径的确定尚缺乏严格的验证标准.以油水两相渗流理论和离子扩散方程为基础,结合储集层特点,研究了不同储层参数下泥浆滤液对地层的侵入特性.数值模拟侵入时间选取10 d和20 d.数值模拟结果表明,侵入半径在渗透率不变的情况下随孔隙度的增大而减小,在孔隙度不变的情况下随渗透率的增大而增大;当渗透率和孔隙度都发生变化时,泥浆侵入半径一般随孔隙度的增加呈幂函数增加.依据这种关系对测井资料约束处理,得到的泥浆侵入半径较客观地反映了地层的真实情况.     

循环伏安法在润滑油检测中的应用

介绍了循环伏安法的产生背景、原理。应用该技术可以快速、方便地对润滑油中抗氧剂、总酸（碱）值进行测定，并且可以对不同厂家润滑油的抗氧剂包进行区别。该技术还可以有效地评价润滑油的使用寿命和设备工作状况。     

燃气管网动态仿真的研究及应用

研究和了解燃气在管道中的流动，是进行燃气管网系统优化和提高管网输运系统安全性的前提和基础。以流体力学三大守恒方程为基础，建立了等温和非等温条件下的燃气管网稳态和动态仿真理论模型。以有限差分法为基础，得到了上述模型的求解方法，并加入了耗散项，提高了求解方法的稳定性。通过增加初始点和延长出口点的方法，简化了模型的求解。通过在北京六环天然气管网中的初步应用，分别得到了与实际值综合相对误差为1.21％和2.62％的压力和流量仿真值，从而验证了模型及求解方法的可靠性。     

波动方程数值模拟的隐式差分法

在有限差分波动方程数值模拟中,通常采用高阶差分方法来提高空间导数的数值逼近精度,以实现降低数值频散,提高数值模拟精度的目的。首先对差分频散进行了理论分析;然后讨论了估计一阶空间导数的隐式差分格式,并与通常采用的高阶精度显式差分格式进行了对比分析,结果表明,隐式差分格式能够在更宽的波数范围使差分频散控制在可接受的水平,如8阶精度的显式差分格式所适应的波数带宽约为O．55kmax,而隐式差分格式所适应的波数带宽约为0．7kmax;最后通过模型试算,对隐式差分格式的有效性进行了验证。模拟结果表明,用隐式差分格式在一定程度上降低了差分频散,提高了模拟精度。     

软件集成测试技术研究

首先分析了集成测试的原理和特点，并指出了集成测试的重要性。然后结合传统软件与面向对象软件开发的方法和技术，详细介绍了传统软件的集成测试方法和策略，并深入分析了面向对象软件集成测试的原理和方法。     

一种估算单桩经济直径的方法

在滩海油田开发过程中,经常需要设立立管桩,在环境荷载的作用下,立管桩顶部会发生位移,较大的位移对立管及栈桥的安全很不利,因此需要合理确定单桩的直径。埕岛油田在确定单桩直径时引入了经济直径的概念,文章对经济直径的原理进行了分析,给出了桩顶位移和桩径经济指数计算公式,并举例进行了计算,得出了桩径与桩顶位移及桩径经济指数的关系曲线, 进而求得经济桩径的取值范围。文章还对该方法的优缺点进行了分析。     

A multigrid accelerated hybrid unstructured mesh method for 3D compressible turbulent flow

 A cell vertex finite volume method for the solution of steady compressible turbulent flow problems on unstructured hybrid meshes of tetrahedra, prisms, pyramids and hexahedra is described. These hybrid meshes are constructed by firstly discretising the computational domain using tetrahedral elements and then by merging certain tetrahedra. A one equation turbulence model is employed and the solution of the steady flow equations is obtained by explicit relaxation. The solution process is accelerated by the addition of a multigrid method, in which the coarse meshes are generated by agglomeration, and by parallelisation. The approach is shown to be effective for the simulation of a number of 3D flows of current practical interest. Sponsored by The Research Council of Norway, project number 125676/410 Dedicated to the memory of Prof. Mike Crisfield, a respected colleague