Eliminating the residual velocity divergence of spectral methods in channel turbulence

The problem of residual velocity divergence exists in numerical simulations of channel flows which use spectral methods. The present contribution analyses the source of the residual velocity divergence, and introduce a new correction method by adding a new pressure correction substep and using ghost grids. The new method can completely eliminate the residual velocity divergence without breaking the non-slip condition. Numerical results show that the residual velocity divergence is well eliminated, while a-posteriori results are not becoming worse. We then conclude that the numerical simulations by using the present method are more close to the incompressible N-S equations, but the influence to a-posteriori statistical quantities is still worth to be investigated in the future.