Spatial Computational Modes in the Centered Finite-Differencing Schemes

Abstract

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