高精度有限差分在湍流直接数值模拟中的应用

本文采用高精度有限差分法对矩形管道内充分发展湍流换热进行了直接数值模拟,湍流雷诺数Rer和普朗特数分别为400(Rem=6200)和0.71,压力泊松方程分别采用两种不同的离散格式(二阶和四阶中心差分离散).结果表明,同二阶中心差分格式相比,高精度有限差分可以在较少的网格下得到较好的结果;压力泊松方程采用四阶中心差分或二阶中心差分对计算结果的影响甚小,但采用二阶中心差分时,可以节省大量的计算时间.

THE APPLICATION OF HIGH RESOLUTION FINITE DIFFERENCE SCHEME IN DIRECT NUMERICAL SIMULATION OF TURBULENT FLOW

A direct numerical simulation of a fully developed turbulent flow and heat transfer in a square duct is studied based on high resolution finite difference scheme.The flow and temperature fields are obtained at a turbulent Reynolds number of 400 based on the mean friction velocity and the hydraulic diameter,and the Prandtl number(Pr)of 0.71.Two kinds of point-stencil method are used for the spatial derivatives of the pressure Poisson equation,i.e.the second-order and fourth- order central difference,respectively.The results show that satisfactory solutions can be obtained in the present DNS simulation with coarse grids compared with the method of second-order central difference.And the solutions from the two kinds of point-stencil method for pressure Poisson equation are consistent with the second-order central difference being more economical in saving computation time.