Lagrangian dynamics of commutator errors in large-eddy simulation

Abstract

In large-eddy simulations of turbulent flow only the flow structures with length scales larger than the local filter width Δ are explicitly resolved. We analyze the dynamic effect associated with spatial variations in the filter width. With the introduction of such a nonuniform filter width a number of additional closure terms emerges, generally referred to as commutator errors. The dynamic effect of the commutator errors is shown to correspond to the apparent local creation or destruction of turbulent flow scales, depending on, respectively, a decrease or an increase in Δ along the flow path. This Lagrangian context suggests significant correlation between the material derivative of the filter width and the production or dissipation of kinetic energy due to the commutator error. This is confirmed by novel a priori analysis of turbulent mixing. An explicit Lagrangian model for the commutator error in the momentum equations is proposed. Additionally, the dynamic effect of a skewed filter on the commutator error is investigated. It is shown that skewed filters induce both dissipative and dispersive behaviors, which are explicitly retained in the new Lagrangian model.