Exact integration in the boundary element method for two-dimensional elastostatic problems

This paper derives the exact integrations for the integrals in the boundary element analysis of two-dimensional elastostatics. For facilitation, the derivation is based on the simple forms of the fundamental functions by taking constant, discontinuous linear and discontinuous quadratic elements as examples. The efficiency and accuracy of the derived exact integrations are verified against five benchmark problems; the results indicate that the derived exact integrations significantly reduces the CPU time for forming the matrices of the boundary element analysis and solving the internal displacements.     

有限元数值试井解释技术在复杂断块油气藏评价中的应用

有限元数值模拟试井技术,可通过描述不同网格的瞬变压力对测试范围内各个小单元进行精细描述.综合运用解析试井、数值试井联带分析方法,将测试动态成果与地质静态成果有机结合、相互补充,可实现对复杂断块油气藏的精细描述,达到一口井搞清一个小型复杂断块油气藏的目的.     

An inverse solution methodology for estimating the diffusion coefficient of gases in Athabasca bitumen from pressure-decay data

An inverse solution methodology is developed for the estimation of diffusion coefficient of gases in highly viscous, oil-sands bitumens from isothermal, pressure-decay measurements. The approach involves modeling the rate of change in pressure using the diffusion equation for the liquid phase coupled with a mass balance equation for the gas phase. The inverse solution framework is utilized to arrive at two graphical techniques for estimating the diffusion coefficient. Both techniques involve the determination of the slope of a straight line resulting from plotting the experimental data in accordance with the developed model. An advantage of the proposed techniques is that the diffusion coefficient is estimated directly, i.e. without making it an adjustable parameter. The novelty of the proposed method is in its simplicity as well as its ability to isolate portions of the pressure-decay data affected by experimental fluctuations. The effect of the initial pressure on the predicted diffusion coefficient and pressure-decay profile was also investigated. The diffusion coefficients of CO₂, CH₄, C₂H₆ and N₂ in Athabasca bitumen at 50–90 °C and about 8 MPa were estimated and compared with literature values.     

地下水运动数值模拟过程中边界条件问题探讨

本文对地下水运动数值模拟过程中边界条件的涵义 和处理方法进行了分析和讨论。阐述了边界条件所包含的双重意义。指出随着人类活动影响 强度的日益增大，边界条件的处理要面临一些新的更为复杂的问题。在模型预报之前必须首 先对边界条件做出预报。边界条件的预报既要考虑自然因素的作用，同时也要考虑人类活动 (人工开采和人工补给)的影响及由于邻区水流条件变化而产生的耦合效应。之后，给出了两 个应用实例。     

Boundary knot method for 2D and 3D Helmholtz and convection–diffusion problems under complicated geometry

The boundary knot method (BKM) of very recent origin is an inherently meshless, integration‐free, boundary‐type, radial basis function collocation technique for the numerical discretization of general partial differential equation systems. Unlike the method of fundamental solutions, the use of non‐singular general solution in the BKM avoids the unnecessary requirement of constructing a controversial artificial boundary outside the physical domain. The purpose of this paper is to extend the BKM to solve 2D Helmholtz and convection–diffusion problems under rather complicated irregular geometry. The method is also first applied to 3D problems. Numerical experiments validate that the BKM can produce highly accurate solutions using a relatively small number of knots. For inhomogeneous cases, some inner knots are found necessary to guarantee accuracy and stability. The stability and convergence of the BKM are numerically illustrated and the completeness issue is also discussed. Copyright © 2003 John Wiley & Sons, Ltd.     

A fictitious domain decomposition method for the solution of partially axisymmetric acoustic scattering problems. Part 2: Neumann boundary conditions

We present a fictitious domain decomposition method for the fast solution of acoustic scattering problems characterized by a partially axisymmetric sound‐hard scatterer. We apply this method to the solution of a mock‐up submarine problem, and highlight its computational advantages and intrinsic parallelism. A key component of our method is an original idea for addressing a Neumann boundary condition in the general framework of a fictitious domain method. This idea is applicable to many other linear partial differential equations besides the Helmholtz equation. Copyright © 2003 John Wiley & Sons, Ltd.     

非均匀材料破坏过程数值模拟的边界元法研究

用格子模型和统计分布模拟非均匀材料性质的初始分布,针对二维非均匀材料格子模型建立了重复多子域边界元法求解方程。通过把各行子域集成为亚子域,然后对链状排列的亚子域应用域转移矩阵法进行求解。由于使用的域转移矩阵法对内存的要求仅略大于一个亚子域的求解,以及重复多子域法只需要进行一次系数矩阵积分,因而可以大大提高求解的规模和效率。在此基础上,对非均匀脆性材料在简单载荷作用下的破坏过程进行了数值模拟。采用重复多子域法和域转移矩阵法,可以得到子域内高精度的连续应力分布,为进一步研究非均匀材料裂纹萌生、扩展和破坏过程提供了基础。     

爆炸焊接边界效应的力学能量原理

在爆炸焊接工艺中,存在一种称为边界效应的物理现象。即在一般情况下,在爆炸焊接后的复合材料中,会出现雷管区不复、其余周边被打伤、打裂和变形严重等问题。这些问题严重地影响着这类材料的质量。该文从传统的和经典的力学及能量原理出发,探讨了边界效应产生的力学 能量原理,并且提出了预防的措施。     

一种简便的数据读入与文件管理子程序集

本文介绍了一种简便的数据读入子程序结构和微机用外部文件管理子程序结构,以及多种数据自动生成子程序结构。为开发微机用大型计算程序提供了一个子程序集。     

Bayesian and Dempster-Shafer fusion

The Kalman Filter is traditionally viewed as a prediction-correction filtering algorithm. In this work we show that it can be viewed as a Bayesian fusion algorithm and derive it using Bayesian arguments. We begin with an outline of Bayes theory, using it to discuss well-known quantities such as priors, likelihood and posteriors, and we provide the basic Bayesian fusion equation. We derive the Kalman Filter from this equation using a novel method to evaluate the Chapman-Kolmogorov prediction integral. We then use the theory to fuse data from multiple sensors. Vying with this approach is the Dempster-Shafer theory, which deals with measures of “belief”, and is based on the nonclassical idea of “mass” as opposed to probability. Although these two measures look very similar, there are some differences. We point them out through outlining the ideas of the Dempster-Shafer theory and presenting the basic Dempster-Shafer fusion equation. Finally we compare the two methods, and discuss the relative merits and demerits using an illustrative example.