求解不可压层流的一种全隐数值格式

A fully implicit numerical scheme for computing incompressible laminar flows

该文基于SMAC(simplified marker and cell)方法,发展了一种在任意曲线坐标系中求解不可压黏性层流的全隐数值格式。基本方程是以逆变速度为未知变量的动量方程和关于压力修正量的Poisson方程。所有方程离散在MAC交错网格系统中进行。根据构造的全隐数值格式自编程序对一可简化成二维层流的后台阶流场进行计算,通过与已有的实验结果和计算结果进行比较,确认目前的计算结果优于比较的计算结果,和实验结果也相当吻合。为进一步验证该数值格式的可靠性,扩展程序对三维后台阶层流进行计算,结果表明,三维计算结果比二维计算结果更加接近实验结果。

This paper presents a fully implicit numerical scheme based on the SMAC （simplified marker and cell） method in general curvilinear coordinates for computing incompressible viscous laminar flows. The fundamental equations are the momentum equations of contravariant velocities as unknown variables and the Poisson equation of the pressure correction. All the equations are discretized in the staggered MAC grid. Using the code written according to the fully numerical scheme, a simplified two-dimensional backward-facing step laminar flows are computed. The present numerical results are prior to the comparative one and in good agreement with the experimental results. To verify the reliability of the numerical scheme further, the three-dimensional backward-facing step laminar flows are computed by the code developed from the former one. It shows the three-dimensional numerical results are closer to the experimental results than the two-dimensional results.