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Consistent subgrid scale modelling for lattice Boltzmann methods

Published online by Cambridge University Press:  30 April 2012

Orestis Malaspinas  and
Pierre Sagaut
Orestis Malaspinas*
Affiliation:
Institut Jean le Rond d’Alembert, UMR 7190, Université Pierre et Marie Curie - Paris 6, 4 place Jussieu - case 162, F-75252, France
Pierre Sagaut
Affiliation:
Institut Jean le Rond d’Alembert, UMR 7190, Université Pierre et Marie Curie - Paris 6, 4 place Jussieu - case 162, F-75252, France
*
†Email address for correspondence: malaspinas@lmm.jussieu.fr
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Abstract

The lattice Boltzmann method has become a widely used tool for the numerical simulation of fluid flows and in particular of turbulent flows. In this frame the inclusion of subgrid scale closures is of crucial importance and is not completely understood from the theoretical point of view. Here, we propose a consistent way of introducing subgrid closures in the BGK Boltzmann equation for large eddy simulations of turbulent flows. Based on the Hermite expansion of the velocity distribution function, we construct a hierarchy of subgrid scale terms, which are similar to those obtained for the Navier–Stokes equations, and discuss their inclusion in the lattice Boltzmann method scheme. A link between our approach and the standard way on including eddy viscosity models in the lattice Boltzmann method is established. It is shown that the use of a single modified scalar relaxation time to account for subgrid viscosity effects is not consistent in the compressible case. Finally, we validate the approach in the weakly compressible case by simulating the time developing mixing layer and comparing with experimental results and direct numerical simulations.

JFM classification

Turbulent Flows: Turbulence modelling Turbulent Flows: Turbulence simulation
Type
Papers
Information
Journal of Fluid Mechanics , Volume 700 , 10 June 2012 , pp. 514 - 542
Copyright
Copyright © Cambridge University Press 2012

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