Dynamics of Commutator-Errors in LES with Non-Uniform Filter-Width

Abstract

In large-eddy simulation only the large scales in a turbulent flow are calculated explicitly and the small scales are effectively removed by the application of a filter with filter-width ∆. For LES of flows in complex geometries it is generally assumed that a non-uniform filter-width ∆(x) is advantageous. Application of non-uniform filters introduces additional sub-grid scale terms, referred to as commutator-errors. The commutator-error corresponds to filter-width variations along a flow-path and expresses differences in the local capturing of small scale flow-features. Therefore, a high correlation is expected between the specific filter-width non-uniformities and the production/dissipation of kinetic energy. This is confirmed by novel a priori analysis of turbulent mixing. In particular, commutator-errors arising from symmetric or non-symmetric filters are shown to differ considerably in dynamic implications.