9.3 Large Eddy Simulation (LES)
283
The arguments on which the dynamic model is based are not restricted
to the Smagorinsky model. One could, instead, use the mixed Smagorinskyscale-similarity model. The mixed model has been used by Zang et al. (1993)
and Shah and Ferziger (1995) with considerable success.
Finally, we note that other versions of the dynamic procedure have been
devised to overcome the difficulties with the simplest form of the model.
One of the better of these is the Lagrangian dynamic model of Meneveau
et a1 (1996). In this model, the terms in the numerator and denominator of
the expression for the model parameter terms of thk dynamic procedure are
averaged along flow trajectories. This is done by solving partial differential
equations for these quantities.
The boundary conditions and numerical methods used for LES are very
similar to those used in DNS. The most important difference is that, when
LES is applied to flows in complex geometries, some numerical methods (for
example, spectral methods) become difficult to apply. In these cases, one is
forced to use finite difference, finite volume, or finite element methods. In
principle, any method described earlier in this book could be used, but it is
important to bear in mind that structures that challenge the resolution of the
grid may exist almost anywhere in the flow. For this reason, it is important
to employ methods of the highest accuracy possible.
In LES, it is possible to use wall functions of the kind used in RANS
modeling (see next section). This approach has been shown to work well for
attached flows (see Piomelli et al., 1989) but, despite considerable effort, it
is not yet known whether this approach can be made to work for separated
flows.
It is also important to note that, because LES and DNS require large
amounts of computer time, the programs used to make these kinds of simulations are usually special-purpose codes i.e., they are written for a specific
geometry and contain special programming elements designed to obtain the
highest performance on a particular machine. For this reason, the discretization methods employed in DNS and LES are often particular to the problem
being solved.
We should also note that, because the unsteadiness that is inherent to
turbulence often affects a flow in profound ways, it is not uncommon to find
significant differences in the predictions of the two methods. This introduces
the possibility of using a crude form of LES as a tool for determining the
gross features of a flow. Indeed, a few industrial applications of this kind
have been made.
9.3.3 Deconvolution Models
The most recent approach to SGS modeling is based on the deconvolution
concept. These models attempt to estimate the unfiltered velocity from the
filtered one. They then use this estimated velocity t o compute the subgrid
Reynolds stress from its definition (9.9). These models share with the dynamic
283
The arguments on which the dynamic model is based are not restricted
to the Smagorinsky model. One could, instead, use the mixed Smagorinskyscale-similarity model. The mixed model has been used by Zang et al. (1993)
and Shah and Ferziger (1995) with considerable success.
Finally, we note that other versions of the dynamic procedure have been
devised to overcome the difficulties with the simplest form of the model.
One of the better of these is the Lagrangian dynamic model of Meneveau
et a1 (1996). In this model, the terms in the numerator and denominator of
the expression for the model parameter terms of thk dynamic procedure are
averaged along flow trajectories. This is done by solving partial differential
equations for these quantities.
The boundary conditions and numerical methods used for LES are very
similar to those used in DNS. The most important difference is that, when
LES is applied to flows in complex geometries, some numerical methods (for
example, spectral methods) become difficult to apply. In these cases, one is
forced to use finite difference, finite volume, or finite element methods. In
principle, any method described earlier in this book could be used, but it is
important to bear in mind that structures that challenge the resolution of the
grid may exist almost anywhere in the flow. For this reason, it is important
to employ methods of the highest accuracy possible.
In LES, it is possible to use wall functions of the kind used in RANS
modeling (see next section). This approach has been shown to work well for
attached flows (see Piomelli et al., 1989) but, despite considerable effort, it
is not yet known whether this approach can be made to work for separated
flows.
It is also important to note that, because LES and DNS require large
amounts of computer time, the programs used to make these kinds of simulations are usually special-purpose codes i.e., they are written for a specific
geometry and contain special programming elements designed to obtain the
highest performance on a particular machine. For this reason, the discretization methods employed in DNS and LES are often particular to the problem
being solved.
We should also note that, because the unsteadiness that is inherent to
turbulence often affects a flow in profound ways, it is not uncommon to find
significant differences in the predictions of the two methods. This introduces
the possibility of using a crude form of LES as a tool for determining the
gross features of a flow. Indeed, a few industrial applications of this kind
have been made.
9.3.3 Deconvolution Models
The most recent approach to SGS modeling is based on the deconvolution
concept. These models attempt to estimate the unfiltered velocity from the
filtered one. They then use this estimated velocity t o compute the subgrid
Reynolds stress from its definition (9.9). These models share with the dynamic