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 ⌬ 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 ⌬ 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.

Explicit small-scale velocity simulation for high-Re turbulent flows

“…However, the explicit adding of the non-commutation terms into the filtered Navier-Stokes system not only would complicate the LES equations but also would require additional modeling of these new terms analogous to the modeling of the residual stresses. A challenging task of modeling of the non-commutation terms has been further addressed in works of van der Bos and Geurts [19,20].…”

Numerically induced high-pass dynamics in large-eddy simulation

“…The top-hat filter in ͑3͒ is called symmetric if a =−b Ͻ 0, but this definition also allows for general asymmetric or "skewed" filters 23,24 for which x is not the central point of the integration interval. We will show in Sec.…”

“…18 In case an upwind discretization method is adopted, the induced filter is skewed and contributes to both dispersive and dissipative aspects of the smaller resolved scales. 23,24 To quantify the induced filter of upwind methods in more detail, we first require the effect of a skewed top-hat filter on a Fourier mode e ıKx . This is readily obtained as…”

Computational error-analysis of a discontinuous Galerkin discretization applied to large-eddy simulation of homogeneous turbulence

“…In this paper only uniform grids are adopted. Hence, we may omit the so-called commutator error sub-filter terms in ( 12)-( 14) [6,37,30,38]. The various sub-filter terms can not be evaluated in terms of the filtered flow quantities alone.…”