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

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 isotropic 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.