Advanced large-eddy simulation for lattice Boltzmann methods: The approximate deconvolution model

The aim of this paper is to extend the approximate deconvolution model for large-eddy simulations to the lattice Boltzmann method. This approach allows to directly act on the velocity distribution function and is based on the intrinsic nonlinearities of the lattice Boltzmann methods. It is not a straightforward extrapolation of classical eddy-viscosity models developed within the Navier-Stokes framework, which exhibits a convective quadratic nonlinearity in the incompressible flow case. A simple implementation is presented, which relies on the implementation of an ad hoc linear filter in any basic lattice Boltzmann solver. The new model is validated on the turbulent, time developing mixing layer, and a very satisfactory agreement is found with existing direct numerical simulations results. The equivalent Navier-Stokes-type macroscopic model is also discussed. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3650422]