Abstract: By comparing the energy spectrum and total kinetic energy, the effects of numerical errors (which arise from aliasing and discretization errors), subgrid-scale (SGS) models, and their interactions on direct numerical simulation (DNS)
and large eddy simulation (LES) are investigated. The decaying isotropic turbulence is chosen as the test case. To simulate complex geometries, both the spectral method and Padé compact difference schemes are studied. The truncated Navier-Stokes (TNS) equation model with Padé discrete filter is adopted as the SGS model. It is found that the discretization error plays a key role in DNS. Low order difference schemes may be unsuitable. However, for LES, it is found that the SGS model can represent the effect of small scales to
large scales and dump the numerical errors. Therefore, reasonable results can also be obtained with a low order discretization scheme.

Key words: numerical errors, truncated Navier-Stokes (TNS) model, Pad\'{e} compact difference scheme, discrete filter, large eddy simulation (LES)