求解不可压三维湍流的隐式SMAC方法

Implicit SMAC method for incompressible three-dimensional turbulent flow

该文基于SM AC(s im p lified m arker and ce ll)方法,发展了一种在任意曲线坐标系中求解三维粘性不可压湍流R eyno lds时均方程的全隐式数值方法。基本方程是以逆变速度为变量的R eyno lds时均动量方程和椭圆型压力Po isson方程,并采用标准k-ε湍流模型封闭方程组。压力Po isson方程用T schebyscheff SLOR方法交替方向迭代求解。R eyno lds时均动量方程、k方程和ε方程对流项均采用Chakravarthy-O sher TVD格式离散,该格式不但有助于提高数值稳定性,而且能有效消除网格扭曲较大的地方产生的非物理振荡误差。用自编程序对后台阶方腔流场进行了计算,计算结果和实验结果吻合较好。

A completely implicit numerical method was developed based on the simplified marker and cell （SMAC） method to solve the three dimensional incompressible turbulence Reynolds-averaging equations in general curvilinear coordinates, The fundamental equations are the Reynolds averaged momentum equations with contravariant velocities as the variables and the elliptic pressure Poisson equation with the standard κ-ε turbulent model used to close the equations. The pressure Poisson equation is solved using Tschebyscheff SLOR method by alternating the computational directions. The Chakravarthy-Osher TVD scheme was used to model the convective terms of the Reynolds averaged momentum equations, and the k and ε equations to improve the numerical stability and suppress spurious oscillation errors where the grids are seriously skewed, Analyses of the flow over a backward facing step agree well with experimental data.