A new numerical method-basic function method is proposed. This method can directly discrete differential operators on unstructured grids. By using the expansion of basic function to approach the exact function,the central and upwind schemes of derivative are constructed. By using the polynomial as basic function,applying the technique of flux splitting method and the combination of central and upwind schemes,the non-physical fluctuation near the shock wave is suppressed. The first-order basic function scheme of polynomial type for solving inviscid compressible flow numerically is constructed in this paper. Several numerical results of many typical examples for one-,two-and three-dimensional inviscid compressible steady flow illustrate that it is a new scheme with high accuracy and high resolution for shock wave. Especially,combining with the adaptive remeshing technique,the satisfactory results can be obtained by these schemes.
WU WangYi & XIE WenJun State Key Laboratory for Turbulence and Complex System,Department of Mechanics and Aerospace Engineering,College of En-gineering,Peking University,Beijing 100871,China
Two-dimensional Navier-Stokes equations and energy equation governing incompressible laminar flow past a bundle of cylinders were numerically solved by using the finite element method. The velocity correction method was used for time advancement, and spatial discretization was carried out with the Galerkin weighted residual method. Viscous flows past the cylinder banks arranged in in-line cylinder bundles and staggered cylinder bundles, coupled with heat transfer, were investigated for pitch-diameter ratios of 1.5 and 2.0 and the Reynolds numbers from 50 to 500. Flow structures and heat transfer behavior were discussed. The results obtained agree well with available numerical data.
In the framework of the finite element method (FEM), a prediction method for the heating rate and the skin friction on a body surface is presented by using the energy and momentum conservation equations respectively. Meanwhile, a brief analysis is made of the role the weighted functions play in the present work.
In the present paper, a new dynamic subgrid-scale (SGS) model of turbulent stress and heat flux for stratified shear flow is proposed. Based on our calculated results of stratified channel flow, the dynamic subgrid-scale model developed in this paper is shown to be effective for large eddy simulation (LES) of stratified turbulent shear flows. The new SGS model is then applied to the LES of the stratified turbulent channel flow to investigate the coupled shear and buoyancy effects on the behavior of turbulent statistics, turbulent heat transfer and flow structures at different Richardson numbers.
