Analysis and control of errors in the numerical simulation of turbulence

Turbulent flows are characterised by a continuum of length and time scales, a feature that introduces some unique problems in relation to the analysis and control of errors in numerical simulations of turbulent flows. In direct numerical simulation (DNS) one attempts to fully resolve the flow field. The primary sources of error in DNS are the aliasing error, which arises due to the evaluation of the nonlinear term on a discrete grid in physical space, and, the truncation error, due to the discretization of the derivative operator. In addition there are the time-stepping errors on account of the temporal discretization. In Large Eddy Simulation (LES) only the large scale flow is computed whereas the collective effect of the small scales are modeled. In that case, in addition to the above three types of errors, there are commutation errors arising out of the averaging process used to derive the LES equations and sub-grid modeling errors that arise because in the absence of a systematic method, the subgrid stress is evaluated using an ad hoc closure model. Methods for analyzing and quantifying these errors in turbulence simulations are discussed. In some instances the analysis points to suitable methods of error control.