梯度加权局部分析解差分格式及其应用

Gradient Weighted Locally Analytic Differencing Scheme and Its Application

提出了一种新的针对Navier－Stokes方程等含有梯度项的对流扩散方程的梯度加权局部分析解的有限差分（GWLAD）格式，且给出了通用的系数表达式。GW－LAD格式是基于积分型的有限体积法并且通过附加源项的方法来实现。能够适用于粘性和无粘性及不可压缩和可压缩的压力驱动流动。通过对叶栅流道中二维湍流流动的计算表明GWLAD格式与ED格式相比，具有较高的精度和很快的收敛速度并且能够得到更好的压力场和速度场。

For the convection and diffusion differential equations with gradient terms such as Navier-Stokes equations, a new gradient weighted locally analytic differencing(GWLAD)scheme is presented in this paper.The coefficients expressing formulas of this scheme are giyen out in common form. GWLAD scheme is obtained from finite volume method and implemented by means of additional source terms. This scheme can be applied to flow field computation of non-viscous or viscous flow, laminar or turbulent flow and compressible or incompressible flow.The results are compared with those obtained with exponential differencing (ED) scheme by turbulent flow field computation in cascade of axial fan.The GWLAD scheme is significantly more accurate at the same conditions. The pressure field obtained from GWLAD scheme is more rcasonable than that from ED scheme.