With the second order Euler-Taylor-Galerkin (ETG) finite element method, a large eddy simulation (LES) is used to simulate turbulent flows over a backward-facing step at Re=47 625. The simulation agrees well with Armaly's experiments.The influence of a ripplet on the turbulent flow is calculated. It is shown that large scale eddies and corresponding reattachment lengths change greatly with the ripplet height and its distance to the step. We argue that adding a ripplet could be a simple and effective passive control to the turbulent flow over a backward-facing step.

A semi-discrete method is proposed for finding the numerical solution of the boundary value problem(BVP) of Navier's equations on the polygon with a single edge-crack. After a suitable transformation of the coordinates, the BVP is reduced to a discontinuous coefficients problem on a semi-infinite strip, and the semi-discrete approximation of the problem is obtained, equivalent to a BVP of a system of O.D.E's with constant coefficients. Furthermore, the semi-discrete approximation of the BVP can be acquired by a direct method. It is worthwhile to note that, the semi-discrete approximation in the form of separable variables naturally possesses the singularity of the given problem. Finally numerical examples show the effectiveness of the method to calculate the approximation of the stress intensity factors.

In this paper, the effects of the fitting parameter △E₀ on the structural determinations in the EXAFS structural study of amorphous alloys have been discussed through the model calculations. The results show that the cancellation of the fitting parameter △E₀ can increase the reliability of the data analysis in the EXAFS structural study of amorphous alloys.

By Model Calculations, the effects of the scale factor approximation of the amplitude reduction factor on the structural parameters determinations of the crystalline and amorphous material, in the curve-fitting analysis of the EXAFS data have been.studied,and the methods of solving the problem have also been discussed.