A posteriori study on modelling and numerical error in LES applying the Smagorinsky model

Summary. In this paper, numerical and modelling errors in large eddy simulation (LES) applying the standard Smagorinsky model and a second-order scheme are studied and compared a posteriori in a turbulent plane Poiseuille flow. The grid-independent solution of the LES equations is approached keeping the product of the model coefficient and the length scale constant as the grid is refined. The aim is to clarify the choice of the model parameters via the two error components, and to study the possibility to control the numerical error via the built-in filter of the model. The shape of the mean-velocity profile is mainly determined by the modelling error, while both modelling and numerical error affect the mean bulk velocity and the Reynolds stresses. As the model length scale is increased while keeping the grid resolution constant, the modelling error grows faster than the numerical error diminishes. Thus it is not reasonable to decrease the numerical error by increasing this parameter. The best choice of the model length scale is a compromise between the two errors, and in this case the modelling error is of the same size as the numerical error related to the second-order scheme.