Spatial computational modes in the centered finite-differencing schemes

The computational modes associated with a centered finite-differencing sche me in space are studied. The existence and impact of these computational mo des in a numerical solution are demonstrated with the use of theoretical an alyses and numerical experiments. The results show that the computational modes due to a spatial discretizati on can have a detrimental effect on the numerical solution in situations wh ere flows are evolved near shock (or having large spatial derivative). The numerical diffusion can reduce the impact of the computational modes, but c an also impose an adverse effect on the physical modes.