Numerical modelling of viscous non-Newtonian effects in lubricating systems

Modern lubricants often exhibit shear-thinning due to the presence of high molecular weight polymers as additives. Therefore the influence of such non-Newtonian effects on the performances of lubricating systems must be predicted. The corresponding fluid film flow is governed by a non-linear partial differential equation, which generalizes the classical Reynolds equation. Having prescribed adequate boundary conditions, this equation is solved by a finite element method with optimal control. The problem of the square slider bearing lubricated by the Rabinowitsch fluid is solved in order to test the accuracy of the numerical scheme. The pressure and velocity fields are given and compared with the corresponding ones obtained for the Newtonian fluid.     

Studies on Fast Algorithm for the Scattering of a Large Array of Waveguide-Fed Wide-Slot Antennas in Millimeter Wave Region

We present an effective numerical technique to characterize the scattering of wide-slot antennas fed by waveguides with arbitrary terminations in terms of the method of moment (MoM) and the mixed potential integral equation (MPIE). In particular, the precorrected-fast Fourier transform (P-FFT) eliminates the need to generate and store the usual square impedance matrix andthus leads to speed up the matrix-vector multiplication in the resultant system. This property makes the Rao-Wilton-Glisson (RWG) functions to be useful in simulating electrically large-scale problems. In addition, the scattering from the finite ground surfaces is accounted for in the total scattered field by using the method of equivalent edge currents. The numerical results are presented and compared with both the traditional method of moment results obtained using the entire-domain basis functions and the experimental results, to demonstrate the proposed method to be a good candidate for study on the scattering of arbitrary wide-slot large array.     

Visualization of shock-wave formation processes during shock reflection at obstacles with multiple steps

According to standard textbooks on compressible fluid dynamics, a shock wave is formed by an accumulation of compression waves. However, the process by which an accumulated compression wave grows into a shock wave has never been visualized. In the present paper, the authors tried to visualize this process using a model wedge with multiple steps. This model is useful for generating a series of compression waves and can simulate a compression process that occurs in a shock tube. By estimating the triple-point trajectory angle, we demonstrated visually that an accumulated compression wave grows into a shock wave. Further reflection experiments over a rough-surface wedge confirmed the tendency for the triple point trajectory angle to reach the asymptotic value _s in the end.This work was first presented at the Symposium on Shock Waves, Japan 2002     

The method of lines applied to nonlinear nonlocal functional differential equations

This paper discusses nonlinear functional differential equation in a real reflexive Banach space with nonlocal history condition. By using the method of lines, the existence and uniqueness of a strong solution are established. Finally, some applications of the abstract results are presented.     

SPH分析中的齿轮建模方法研究

对利用光滑粒子动力学(SPH-Smoothed Particle Hydrodynanlics)方法进行轮齿动态力学数值分析中的齿轮建模方法进行了研究.确定了齿轮齿根过渡曲线以及其他部分的参数方程,并根据所确定的参数方程建立了三维齿轮离散粒子模型的数学模型.编制了划分齿轮整体及局部离散粒子的SPH前处理程序.并对划分后齿轮离散粒子与齿轮理论轮廓之间进行了误差分析.分析结果表明,利用此办法可正确划分齿轮的SPH离散化粒子,是一种较好的前处理方法.     

DPSIR = A Problem Structuring Method? An exploration from the “Imagine” approach

The Drivers, Pressures, State, Impact and Response or DPSIR framework has been with us for over a decade now and it is widely used as a means to assess and measure and, eventually provide a guide to managing the environment. With its repertoire of diagnostic and analytical components the DPSIR can be argued to be a Problem Structuring Method or PSM. Criticisms of the framework abound but it has a resilience which is noteworthy. Some argue that DPSIR, by its nature, is a narrowly formulated, engineering device, incompatible with the multiple perspectives which human interaction in global ecology requires. Is there a value in DPSIR being more flexible in expression and experience of users? In this article it is shown how the DPSIR framework was applied within a multi-methodology approach called Imagine in a number of coastal management projects around the Mediterranean and in other contexts. The article argues that DPSIR, whilst admittedly limited in its scope and approach can, if applied in a participatory and systemic multi-methodology, combine with other tools and help to create outcomes of value to local populations.     

Notes on a paper considering nonlinear equations

In abstract of the paper [A. Rafiq, A note on “A family of methods for solving nonlinear equations”, Appl. Math. Comput. 195 (2008) 819-821] we can find the following sentences. We cite: Ujevi? et al. introduced a family of methods for solving nonlinear equations. However the main Algorithm 1 put forward by Ujevi? et al. (p. 7) is wrong. This is the main aim of this note. We also point out some major bugs in the results of Ujevi? et al. - the end of the citation. Here it is shown that all of the mentioned assertions are not true. In other words, the Algorithm 1 is correct (up to an obvious misprint, which is not mentioned in the above paper) and there are no major bugs in the paper by Ujevi? et al. In fact, these observations, which will be given in this note, show that the main aim of the paper by Rafiq is wrong.     

A superlinearly convergent norm-relaxed SQP method of strongly sub-feasible directions for constrained optimization without strict complementarity

In this paper, a kind of optimization problems with nonlinear inequality constraints is discussed. Combined the ideas of norm-relaxed SQP method and strongly sub-feasible direction method as well as a pivoting operation, a new fast algorithm with arbitrary initial point for the discussed problem is presented. At each iteration of the algorithm, an improved direction is obtained by solving only one direction finding subproblem which possesses small scale and always has an optimal solution, and to avoid the Maratos effect, another correction direction is yielded by a simple explicit formula. Since the line search technique can automatically combine the initialization and optimization processes, after finite iterations, the iteration points always get into the feasible set. The proposed algorithm is proved to be globally convergent and superlinearly convergent under mild conditions without the strict complementarity. Finally, some numerical tests are reported.     

混合边界条件下的三维定常 旋转Navier-Stokes方程的原始变量有限元计算

本文利用原始变量有限元法求解混合边界条件下的三维定常旋转Navier-Stokes方程,证明了离散问题解的存在唯一性,得到了有限元解的最优误差估计.给出了求解原始变量有限元逼近解的简单迭代算法,并证明了算法的收敛性.针对三维情况下计算资源的限制,采用压缩的行存储格式存储刚度矩阵的非零元素,并利用不完全的LU分解作预处理的GMRES方法求解线性方程组.最后分析了简单迭代和牛顿迭代的优劣对比,数值算例表明在同样精度下简单迭代更节约计算时间.     

An efficient algorithm for solving the incompressible fluid flow equations

The present paper reports on a modified pressure implicit predictor corrector type scheme for solving the flow governing equations, in which a consistent formulation is combined with a multi-grid solver for the pressure correction. In addition a parabolic sublayer (PSL) approach for the treatment of the flow in the vicinity of solid walls is critically evaluated in terms of accuracy and computational efficiency. The lid-driven cavity flow is chosen as the test case and results are presented for Reynolds numbers ranging from 100 to 1000. Predictions with the proposed scheme indicate substantial computational savings and fairly good agreement when compared with previous work. The PSL approach reduces the computing time, but with increasing Reynolds numbers the accuracy of the solutions tends to deteriorate.