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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。
In this paper, a fully implicit numerical method for solving the time-averaged three-dimensional viscous incompressible turbulence R eyno lds in arbitrary curvilinear coordinate system is developed based on the SM AC method. The basic equation is the Reynolds-time averaged momentum equation and the elliptical pressure Po isson equation with the inversion speed as the variables, and closed the equations with the standard k-ε turbulence model. Pressure Po isson equations are iteratively iteratively solved using the T schebyscheff SLOR method. The Reynolds flow-momentum equations, the k-equations and the ε-equation convection terms are all discretized by the Chakravarthy-Orsher TVD scheme. This scheme not only helps to improve the numerical stability but also effectively eliminates the non-grid distortion Physical oscillation error. The self-programmed program was used to calculate the flow field in the back-stepped cavity. The calculated results agree well with the experimental results.