NUMERICAL STUDY OF HIGH-REYNOLDS-NUMBER FLOW PAST A BLUFF OBJECT

A semi-explicit finite difference scheme is proposed to study unsteady two-dimensional, incompressible flow past a bluff object at high Reynolds number. The bluff object comes from a class of elliptical cylinders in which the aspect ratio and the angle of attack are two controlled parameters. Associated with the streamfunction–vorticity formulation, the interior vorticity, streamfunction and wall vorticity are updated in turn for each time step. The streamfunction and wall vorticity are solved by means of a multigrid method and a projection method respectively. In regard to the vorticity transport equation, implicitness is merely associated with the diffusion operator, which can be made semi-explicit via approximate factorization. Low-diffusive upwinding is devised to handle the convection part. Numerical results are reported for Reynolds numbers up to 40,000. Comparisons with other numerical or physical experiments are included.     

亚、跨、超音速及不可压流动的数值分析方法的研究

为了对亚、跨、超音速及不可压无粘流动进行数值模拟,将LU－SGS方法与预处理方法结合,给出了PLU－SGS方法。方程离散基于有限体积法,采用高阶精度AUSMPW格式。方程求解采用了特征边界条件。通过典型算例的数值试验对比分析,表明PLU－SGS方法可以有效地对亚、跨、超音速及不可压流动进行数值模拟,并具有较高的计算精度和收敛速度。     

A stochastic theory for clustering of quenched-in vacancies—IV. Continuum model applied to the formation of stacking fault tetrahedra and vacancy loops

The continuum model for the growth of clusters developed in the previous paper (paper III) is applied to the formation of stacking fault tetrahedra in quenched gold and the formation of faulted vacancy loops in quenched aluminium. The results of the theory namely the distribution of the clusters as a function of their size and time, and the average size and the total density of the clusters as a function of time and the ageing temperature are shown to be in good agreement with the experimental results.     

Higher‐order bounded differencing schemes for compressible and incompressible flows

In recent years, three higher‐order (HO) bounded differencing schemes, namely AVLSMART, CUBISTA and HOAB that were derived by adopting the normalized variable formulation (NVF), have been proposed. In this paper, a comparative study is performed on these schemes to assess their numerical accuracy, computational cost as well as iterative convergence property. All the schemes are formulated on the basis of a new dual‐formulation in order to facilitate their implementations on unstructured meshes. Based on the proposed dual‐formulation, the net effective blending factor (NEBF) of a high‐resolution (HR) scheme can now be measured and its relevance on the accuracy and computational cost of a HR scheme is revealed on three test problems: (1) advection of a scalar step‐profile; (2) 2D transonic flow past a circular arc bump; and (3) 3D lid‐driven incompressible cavity flow. Both density‐based and pressure‐based methods are used for the computations of compressible and incompressible flow, respectively. Computed results show that all the schemes produce solutions which are nearly as accurate as the third‐order QUICK scheme; however, without the unphysical oscillations which are commonly inherited from the HO linear differencing scheme. Generally, it is shown that at higher value of NEBF, a HR scheme can attain better accuracy at the expense of computational cost. Copyright © 2006 John Wiley & Sons, Ltd.     

Pressure induced amorphization of AlPO4

AlPO₄ has been compressed to pressures of 16 GPa in a diamond anvil cell and its X-ray diffraction pattern studied by the energy-dispersive technique. The compound is observed to become amorphous at ∼ 12 GPa. This explains the loss of Raman spectrum of AlPO₄ reported by Jayaraman and coworkers (1987).     

A stochastic theory for clustering of quenched-in vacancies-V. Temperature dependence of cluster density

It is known that the density of vacancy loops in quenched aluminium and stacking fault tetrahedra in quenched gold show a saturation for low ageing temperatures. The physical mechanism leading to this effect is not well understood. In this paper we consider a simple model which allows us to obtain the temperature dependence of total density. The analysis shows that the plateau region arises due to the fact that the number of absorption sites of a cluster is larger than the number of emission sites. The temperature dependence of the average number of vacancies in a cluster and the single vacancy concentration in equilibrium with the clusters are discussed.     

Stochastic theory for clustering of quenched-in vacancies—1. General mathematical properties

The problem of clustering of quenched-in vacancies into various types of extended defects is considered. A master equation for the evolution of the concentration of clusters of various sizes is written down with general transition rates. It is shown that this model represents a continuous time non-stationary Markoff process. A particular choice of transition rates corresponding to the formation of vacancy loops and stacking fault tetrahedra is considered in some detail. It is shown that this choice of transition rates allows us to obtain the solution for the concentration of the single vacancy units, and hence yields some information on the nucleation time. Further, the transition matrix becomes stationary and doubly stochastic due to the short time constant of the concentration of single vacancy units. This in turn leads to an unphysical stationary state. Finally we show how the rate equations for the irradiated situation can be written down and derive the phenomenological rate equations that are conventionally used.