Energy dynamics modeling of commutator errors

For efficient large-eddy simulation of complex flow situations the use of non-uniform filter-widths is considered advantageous. It is, however, known that a non-uniform filter-width introduces additional SGS-terms, generally referred to as commutator-errors. The commutator-error can be associated with the creation and destruction of turbulent scales due to variations of the filter-width along Lagrangian flow-paths. A priori tests concerning the dynamics of kinetic energy have been carried out which confirm the validity of this idea. Consequently, a new model for the commutator-error has been developed. This model is tested on a turbulent temporal mixing layer at \mathrmRe=50.0 and \mathrmM=0.2 using a non-uniform filter-width in the non-homogeneous direction. This model, based on the energy dynamics of the commutator-error, is compared against more straight-forward formulations which represent the commutator-error in terms of the gradient and similarity model.