## 2.5. Large Eddy Simulation Theory

This section outlines the theoretical details of the LES model in ANSYS CFX. Additional information on setting up an LES simulation is available, as well as modeling advice. For details, see The Large Eddy Simulation Model (LES) in the CFX-Solver Modeling Guide.

The rationale behind the large-eddy simulation technique is a separation between large and small scales. The governing equations for LES are obtained by filtering the time-dependent Navier-Stokes equations in the physical space. The filtering process effectively filters out the eddies whose scales are smaller than the filter width or mesh spacing used in the computations. The resulting equations thus govern the dynamics of the large eddies.

A filtered variable is denoted in the following by an overbar and is defined by

| (2–159)

where is the fluid domain, and is the filter function that determines the scale of the resolved eddies.

The unresolved part of a quantity is defined by

| (2–160)

It should be noted that the filtered fluctuations are not zero:

| (2–161)

The discretization of the spatial domain into finite control volumes implicitly provides the filtering operation:

where is the control volume. The filter function implied here is then

| (2–162)

Filtering the Navier-Stokes equations leads to additional unknown quantities. The filtered momentum equation can be written in the following way:

where denotes the subgrid-scale stress. It includes the effect of the small scales and is defined by

| (2–163)

The large scale turbulent flow is solved directly and the influence of the small scales is taken into account by appropriate subgrid-scale (SGS) models. In ANSYS CFX an eddy viscosity approach is used that relates the subgrid-scale stresses to the large-scale strain rate tensor in the following way:

| (2–164)

Unlike in RANS modeling, where the eddy viscosity represents all turbulent scales, the subgrid-scale viscosity only represents the small scales.

It should be noted that the isotropic part of is not modeled, but added to the filtered static pressure.

Three models are available to provide the subgrid-scale (SGS) viscosity . You should use the wall-adapted local eddy-viscosity model by Nicoud and Ducros [200](LES WALE model) as a first choice. This is an algebraic model like the Smagorinsky model, but overcomes some known deficiencies of the Smagorinsky model: the WALE model produces almost no eddy-viscosity in wall-bounded laminar flows and is therefore capable to reproduce the laminar to turbulent transition. Furthermore, the WALE model has been designed to return the correct wall-asymptotic -variation of the SGS viscosity and needs no damping functions.

In addition to the WALE model, the Smagorinsky model [34] and the Dynamic Smagorinsky-Lilly model (Germano et al. [198], Lilly [199]) are available. The Dynamic Smagorinsky-Lilly model is based on the Germano-identity and uses information contained in the resolved turbulent velocity field to evaluate the model coefficient, in order to overcome the deficiencies of the Smagorinsky model. The model coefficient is no longer a constant value and adjusts automatically to the flow type. However this method needs explicit (secondary) filtering and is therefore more time consuming than an algebraic model.

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