Large Eddy Simulation for Incompressible Flows. An Introduction

Abstract

Large Eddy Simulation (LES) is an approach to compute turbulent flows based on resolving the unsteady large-scale motion of the fluid while the impact of the small-scale turbulence on the large scales is accounted for by a sub-grid scale model. This model distinguishes LES from any other method and reduces the computational demands compared with a Direct Numerical Simulation. On the other hand, the cost typically is still at least an order of magnitude larger than for steady Reynolds-averaged computations. The LES approach is attractive when statistical turbulence models fail, when insight into the vortical dynamics or unsteady forces on a body is desired, or when additional features are involved such as large-scale mixing, particle transport, sound generation etc. In recent years the rapid increase of computer power has made LES accessible to a broader scientific community, and this is reflected in an abundance of papers on the method and its applications. Still, however, some fundamental aspects of LES are not conclusively settled, a fact residing in the intricate coupling between mathematical, physical, numerical and algorithmic issues. In this situation it is of great importance to gain an overview of the available approaches and techniques.Pierre Sagaut, in the style of a French encyclopedist, gives a very complete and exhaustive treatment of the different kinds of sub-grid scale models which have been developed so far. After discussing the separation into resolved and unresolved scales and its application to the Navier-Stokes equations, more than 140 pages are directly devoted to the description of sub-grid scale models. They are classified according to different criteria, which helps the reader to find his or her way through the arsenal of reasonings. The theoretical framework for which these models have mostly been developed is isotropic turbulence. The required notions from classical turbulence theory are summarized together with notions from EDQNM theory in two concise and helpful appendices. Further sections deal with numerical and implementational issues, boundary conditions and validation practice. A final section assembles a few key applications, cumulating in a condensed list of some general experiences gained so far.The book very wisely concentrates on issues particular to LES, which to a large extent is sub-grid scale modelling. Classical issues of CFD, such as numerical discretization schemes, solution procedures etc, or post-processing are not addressed. Limiting himself to incompressible, non-reactive flows, the author succeeds in describing the fundamental issues in great detail, thus laying the foundations for the understanding of more complex situations. The presentation is essentially theoretical and the reader should have some prior knowledge of turbulence theory and Fourier transforms. The text itself is well written and generally very clear. A pedagogical effort is made in several places, e.g. when an overview over a group of models is given before these are described in ...

Numerical simulation of a weak breaking tidal bore

“…A dual grid, or underlying grid (Rudman, 1998), is used to gain an improved accuracy for the interface description, the mesh grid size being divided by two in each direction for the interface tracking. The turbulent viscosity is calculated with the Mixed Scale model (Sagaut, 1998). The numerical model has proved its accuracy for coastal applications (Lubin et al, 2006) and has been benchmarked through numerous test-cases including mesh refinement analysis (Lubin, 2004).…”

High-resolution data assimilation through stochastic subgrid tensor and parameter estimation from 4DEnVar

“…However, its construction is quite different. It is not based on Boussinesq's eddy viscosity assumption nor on any structural turbulence models (Sagaut, 2006) but arises from stochastic calculus rules. It expresses the mixing process exerted by the fast oscillating velocity component.…”

Large-eddy simulation of turbulent flows in a heated streamwise rotating channel

“…The time-and plane-averaged deviatoric part of the 'true' (or exact) Reynolds stresses (denoted using − u ′e i u ′e j ) obtained from a DNS approach can be estimated from LES using the resolved turbulent and SGS stresses [69,70] . (2.11)), viz.…”