For some current discrete schemes with extensive use in computational fluid dynamics, especially Roe’s, Osher’s, ENO, and WENO schemes, from the viewpoint of discontinuous decomposition wave, we analyzed the properties of the modified partial differential equation (PDE) and explored the relationships between group velocity and phase velocity. To investigate the influence of dispersion and dissipation on the discrete scheme’s characters, we also studied the mechanism of Roe’s, Osher’s, ENO, and WENO schemes. The results show that the common features of these discrete schemes lie in that, the Riemann discontinuity is approximated with waves by all these discrete schemes, and the difference among them lies in that, each of them uses a specific number and form of waves. The proper balance between the computational complexity and the accuracy forms the basis of each of these discrete schemes. A study on the common features of these schemes shows that a feasible discrete scheme should preserve the physical mechanism of the problem to be calculated and maintain such character during the computational processes. Finally, considering comprehensively the combination of the theory of partial differential equation and flowing properties, we gave some suggestions on the numerical scheme of Saint-Venant and Euler equations.