A further study of numerical errors in large-eddy simulations

Numerical errors in large-eddy simulations (LES) arise from aliasing and discretization errors, and errors in the subfilter-scale (SFS) turbulence model. Using a direct numerical simulation (DNS) dataset of stably stratified shear flow to perform a priori tests, we compare the numerical error from several finite difference schemes to the magnitude of the SFS force. This is an extension of Ghosal’s analysis [J. Comput. Phys. 125 (1996) 187] to realistic flow fields. By evaluating different grid resolutions as well as different filter–grid ratios, we provide guidelines for LES: for a second-order finite difference scheme, a filter–grid ratio of at least four is desired; for a sixth-order Padé scheme, a filter–grid ratio of two is sufficient.