非交错网格上不可压流动中的近似投影方法

对于压力增量形式的投影方法,在非交错网格上,仅仅采用近似投影过程,通常不足以抑制压力场的数值振荡.本文通过选取合适的投影变量,构造了一种可以在非交错网格上避免压力振荡的新方法.该方法在不增加计算量的前提下,让前一时刻的压力参与投影过程,有效地割断了前一时刻中可能存在的压力数值振荡向下一时刻传递的途径,避免了数值振荡的积累,提高了数值方法的稳定性.此外,我们在投影变量中考虑了"几何网格雷诺数"的影响,拓宽了本方法的适用范围.数值试验验证了本文提出的近似投影方法是可行的.

Approximate projection methods for incompressible flow on nonstaggerd grids

On staggered grids, the approximate projection procedure for incremental projection methods is not sufficient to avoid the oscillation of pressure. In this paper, a new technique to prevent the pressure from oscillating is obtained bychanging the form of velocity on the face and introducing a corrected factor. The advantages are: the previous pressure is smoothed without additional computation, which cuts effectively the way of possible oscillation in pressure from the previous to the next. The possible oscillation in pressure will be restricted to the present time and not be accumulated, and the stability of numerical methods will be enforced. In addition, since grid and viscous enclosed the corrected factor, the approximate projection method with the new technique will be wider in application. Finally, the numerical tests verify the method well.