A high order accurate difference scheme for complex flow fields

A high order accurate finite difference method for direct numerical simulation of coherent structure in the mixing layers is presented. The reason for oscillation production in numerical solutions is analyzed, It is caused by a nonuniform group velocity of wavepackets. A method of group velocity control for the improvement of the shock resolution is presented. In numerical simulation the fifth-order accurate upwind compact difference relation is used to approximate the derivatives in the convection terms of the compressible N-S equations, a sixth-order accurate symmetric compact difference relation is used to approximate the viscous terms, and a three-stage R-K method is used to advance in time. In order to improve the shock resolution the scheme is reconstructed with the method of diffusion analogy which is used to control the group velocity of wavepackets. (C) 1997 Academic Press.

Compact finite difference - Fourier spectral method for three-dimensional incompressible Navier-Stokes equations

A new compact finite difference-Fourier spectral hybrid method for solving the three dimensional incompressible Navier-Stokes equations is developed in the present paper. The fifth-order upwind compact finite difference schemes for the nonlinear convection terms in the physical space, and the sixth-order center compact schemes for the derivatives in spectral space are described, respectively. The fourth-order compact schemes in a single nine-point cell for solving the Helmholtz equations satisfied by the velocities and pressure in spectral space is derived and its preconditioned conjugate gradient iteration method is studied. The treatment of pressure boundary conditions and the three dimensional non-reflecting outflow boundary conditions are presented. Application to the vortex dislocation evolution in a three dimensional wake is also reported.

The plastic instability behaviour of laser-textured steel sheet

As the production of a new technique that can offer both good formability and high image clarity for texturing metal sheet, laser-textured sheet has attracted the attention of many manufacturers and users. Among the many subjects to be studied, plastic instability behaviour of the laser-textured sheet is one of most important to understand its ability in extending material ductility and to appropriately control this technique. Experimental investigations are carried out in this paper to study the macroscopic behaviour and microstructural mechanism of the laser-textured sheet, and comparison is made with the normal sheet taken from the same coil of metal sheet. It is demonstrated that, the difference in the behaviour of plastic instability obviously shows tendency to delay strain localization and the onset of thickness necking. Shear banding and internal void damage are spread to a much wider region in the sheet being laser-textured. The prestrained microcraters enforced on the surface of the textured sheet act as hardening spots, which are likely to share out deformation and inhibit the increasing rate of voiding, and eventually favouring the ductility of the material used.

Composite materials dynamic fracture studies by generalized Shmuely difference algorithm

The generalized Shmuely Difference Algorithm (GSDA) is presented here to analyze the dynamic fracture performance of orthogonal-anisotropic composite materials, such as glass fibre reinforced phenolplast. The difference recurrence Formulae and boundary condition difference extrapolation formulae are derived and programmed. The dynamic stress intensity factors (DSIF) of the isotropic and anisotropic centrally cracked plates are computed respectively using GSDA and compared with that published previously. GSDA is proved effective and reliable. Copyright (C) 1996 Elsevier Science Ltd.

A perturbational h4 exponential finite-difference scheme for the convective diffusion equation

A perturbational h4 compact exponential finite difference scheme with diagonally dominant coefficient matrix and upwind effect is developed for the convective diffusion equation. Perturbations of second order are exerted on the convective coefficients and source term of an h2 exponential finite difference scheme proposed in this paper based on a transformation to eliminate the upwind effect of the convective diffusion equation. Four numerical examples including one- to three-dimensional model equations of fluid flow and a problem of natural convective heat transfer are given to illustrate the excellent behavior of the present exponential schemes, the h4 accuracy of the perturbational scheme is verified using double precision arithmetic.

H4 exponential finite-difference scheme for convective diffusion-equations

Perturbations are applied to the convective coefficients and source term of a convection-diffusion equation so that second-order corrections may be applied to a second-order exponential scheme. The basic Structure of the equations in the resulting fourth-order scheme is identical to that for the second order. Furthermore, the calculations are quite simple as the second-order corrections may be obtained in a single pass using a second-order scheme. For one to three dimensions, the fourth-order exponential scheme is unconditionally stable. As examples, the method is applied to Burgers' and other fluid mechanics problems. Compared with schemes normally used, the accuracies are found to be good and the method is applicable to regions with large gradients.