SUMMARYWhen low-order ÿnite-di erence methods are applied in large eddy simulation (LES), the magnitude of the numerical error may be larger than that of the subgrid-scale (SGS) term. In this paper, the e ect of explicit ÿltering on the numerical error related to the spatial discretization of the convection term and the exact SGS term is studied a priori in the turbulent fully developed channel ow. As the ÿlter width is increased the grid resolution is kept constant. Also ÿltering in the inhomogeneous wall-normal direction is discussed. The main conclusions are related to two approaches to explicit ÿltering. In the traditional approach, the whole velocity ÿeld is ÿltered explicitly while in the alternative approach, only the non-linear convection term of the Navier-Stokes equations is ÿltered explicitly. Based on the results presented in the paper it seems that the ÿrst approach leads to an unphysical situation. However, the later approach works in the desired way, and the numerical error becomes clearly smaller than the SGS term. The main di erence between the two approaches seems to be the interpretation of the resolved non-linear term in the ÿltered Navier-Stokes equations.
SUMMARYBased on a priori tests, in large eddy simulation (LES) of turbulent fluid flow, the numerical error related to low-order finite-difference-type methods can be large in comparison with the effect of subgrid-scale (SGS) model. Explicit filtering has been suggested to reduce the error, and it has shown promising results in a priori studies and in some simulations with fourth-order method. In this paper, the effect of explicit filtering on the total simulation error is studied together with a second-order scheme, where the numerical error should be even larger. The fully developed turbulent channel flow between two parallel walls is used as a test case. Rather simple SGS models are applied, because these models are most likely used in practical applications of LES. Explicit filtering is here applied to the non-linear convection term of the Navier-Stokes equations, four three-dimensional filter functions are applied, and the effect of filtering is separated from the effect of SGS modelling. It is shown that the effect of filtering is rather large and smooth filters introduce an additional error component that increases the total simulation error. Finally, filtering via subfilter-scale modelling is applied, and it is shown that this approach performs better. However, the large-frequency components of the resolved flow field are not as effectively damped as when the non-linear convection term is filtered.
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