Abstract: Direct numerical simulation of aero-acoustics needs excellent numerical characteristics of spatial difference schemes such as dispersion relation and dissipation.The idea of compact finite difference scheme and Dispersion Relation Preserving (DRP) scheme is discussed first.Then,the dispersion characteristics and the dissipation characteristics of the two schemes are analyzed.The results show that either the solvable range of number of waves or the dissipation characteristics of the scheme combined with four-stage four-order Runge-Kutta method,the solvable range of the 6th-order compact scheme is larger than that of DRP scheme.However,the computational workload of the 6th-order compact scheme is far beyond DRP scheme.