压力项处理方式对非定常流动投影方法时间精度的影响

Effect of treatment for pressure derivate terms on the temporal accuracy of the projection method for unsteady flow

针对三种典型的压力项处理方式,研究了投影方法的时间精度。结果显示三种压力项处理格式即P1-P3得到了一致高阶的速度精度,而压力精度为1阶。对于速度散度,P1格式的精度为1阶,P2与P3格式的精度为2阶。综合来看P2格式的误差最小。利用投影方法和P2格式进行了各向同性衰变湍流的三维直接数值模拟,计算得到的三维能谱与实验能谱相符合。得到的速度分量的概率密度函数符合高斯分布。当空间两点间隔较大时,速度分量增量的概率密度函数也服从高斯分布。

The temporal accuracy of the projection method is studied presently for three typical types of treatments for the pressure derivate terms （P1-P3）. The results show that high order temporal accuracy for the velocity is obtained, but the computed pressure has first-order temporal accuracy. The P1 scheme gives first-order accuracy for the velocity divergence. While both P2 and P3 schemes give second-order accuracy for this quantity. To sum up, the P2 scheme has less numerical errors. The direct numerical simulation of iso- tropic decaying turbulence is conducted by utilizing the projection method with the P2 scheme. The computed three-dimensional energy spectral conforms to the experimental data. The probability density functions for the velocity components obey a Gaussian distribution. For the increments of velocity components between two points with relatively large spatial distance, their probability density functions follow also a Gaussian distribution.