ABSTRACT
As already mentioned in section 4.1, the numerical dissipation provided by the scheme used to discretize the differential terms in the governing equations can remove energy from the resolved scales, similar to a classical subgrid-scale model. This forms the basis of another type of LES methods that do not use an explicit subgrid-scale model but rather rely mostly on the numerical dissipation resulting from the discretization of the convective terms in the momentum equations. The governing equations before discretization are formally the unfiltered Navier-Stokes equations, like in DNS. The truncation error of the discretization (as discussed in section 4.2) is then used to model the effects of the unresolved scales, hence acting as an implicit SGS model. This type of methods is therefore generally referred to as implicit LES or ILES (e.g. see Boris et al., 1992, Adams et al., 2004). It should be noted, however, that not all dissipative discretization schemes are appropriate for ILES. The reason is that, as discussed in section 4.3, most schemes (e.g. classical upwind-biased schemes) remove substantial energy from the whole resolved wave-number range rather than removing energy only from the smallest resolved scales, and the amount of energy locally removed from the flow is not determined by the eddy content of the instantaneous flow fields but rather depends on the local grid spacing and numerical discretization.
