USE OF EXPLICIT FILTERING, SECOND-ORDER SCHEME AND SGS MODELS IN LES OF TURBULENT CHANNEL FLOW

Abstract. In large eddy simulations (LES) using low-order nite-dierence-type methods, the numerical error can be large in comparison to the eect of the sub-grid scale (SGS) model. In this paper, we study two approaches to explicit ltering which can reduce the numerical error involved. In the rst approach, the non-linear convection term of the Navier{Stokes equations is ltered explicitly, and in the second one, the small-scale shear stress is devided into sub-lter (SFS) and sub-grid (SGS) components, and ltering is provided via the model. The aims are to clarify the eect of SGS modelling in the rst approach and to compare the two approaches. For SGS and SFS modelling, the standard and dynamic Smagorinsky models and the scale-similarity model are applied. When the convection term is ltered explicitly, the eect of modelling on the simulation results reduces and dierences between the models are rather small. Filtering with a smooth three-dimensional lter has a strong eect on the ow statistics, and none of the models is able to compensate for this. Although the high frequencies are damped eciently, the total simulation error does not decrease. When ltering is provided only via modelling, improved results are obtained if both SGS and SFS modelling are applied. However in this approach, all terms in the equations do not have the same frequency content, and the high frequencies that are badly described by the discrete gird are not damped as eciently as when the convection term is explicitly ltered.