Numerically induced high-pass dynamics in large-eddy simulation

The numerical distortion of the smallest resolved-scale dynamics in large-eddy simulation may be understood in terms of the filter that is induced by the spatial discretization. At marginal subfilter resolution r=Delta/h, with filter width Delta and grid spacing h, the character of the large-eddy closure problem is strongly influenced by the numerical method. We show that additional high-pass contributions arise from the spatial discretization. The relative importance of, on the one hand, the turbulent stresses and, on the other hand, the numerically induced contributions, is quantified for general finite differencing methods. We derive and analyze the induced filters for several popular discretization methods, including higher order central and upwind methods. The application of these induced filters to small-scale turbulent flow structures gives rise to a characteristic amplitude reduction and phase shift. Their dynamic relevance is quantified in terms of the subfilter resolution. The numerical high-pass effects are found to be negligible if the subfilter resolution is large enough (r greater than or similar to 4). Conversely, the numerically induced effects are comparable to, or even larger than the turbulent stresses as r=1-2.