Reliability of LES in Complex Applications

Abstract

The accuracy of large-eddy simulations is limited, among others, by the quality of the subgrid parameterisation and the numerical contamination of the smaller retained flow-structures. We review the effects of discretisation and modelling errors from two different perspectives. First, we review a database-approach to assess the total simulation error and its numerical and modelling contributions. The interaction between the different sources of error in the kinetic energy is shown to lead to their partial cancellation. An ‘optimal refinement strategy’ for given subgrid model, given discretisation method and given flow conditions is identified, leading to minimal total simulation error at given computational cost. We provide full detail for homogeneous decaying turbulence in a ‘Smagorinsky fluid’. The optimal refinement strategy is compared with the error-reduction that arises from grid-refinement of the dynamic eddy-viscosity model. Dynamic modelling yields significant error reduction upon grid refinement. However, at coarse resolutions high error-levels remain. To address this deficiency in eddy-viscosity modelling, we then consider a new successive inverse polynomial interpolation procedure with which the optimal Smagorinsky constant may be efficiently approximated at any given resolution. The computational overhead of this optimisation procedure is well justified in view of the achieved reduction of the error-level relative to the ’no-model’ and dynamic model predictions.