Large Eddy Simulation (LES)

Large Eddy Simulation (LES) is an inherently transient technique in which the large scales of the turbulence are directly resolved everywhere in the flow domain, and the small-scale motions are modeled.

One justification for the LES technique is that by modeling “less” of the turbulence, and explicitly solving for more of it, the error in the turbulence modeling assumptions is not as consequential. Furthermore, it is hypothesized that the smaller eddies are self-similar and thus lend themselves to simpler and more universal models. The downside of the approach is the computational expense, which, although less than direct numerical simulation, is still nonetheless excessive.

In contrast to the RANS equations, the equations that are solved for LES are obtained by a spatial filtering rather than an averaging process. Each solution variable $\varphi$ is decomposed into a filtered value $\tilde{\varphi }$ and a sub-filtered, or sub-grid, value $\varphi \prime$:

where $\varphi$ represents velocity components, pressure, energy, or species concentration.

Inserting the decomposed solution variables into the Navier-Stokes equations results in equations for the filtered quantities. The filtered equations are rearranged into a form that looks identical to the unsteady RANS equations. However, the turbulent stress tensor now represents the subgrid scale stresses. These stresses result from the interaction between the larger, resolved eddies and the smaller, unresolved eddies and are modeled using the Boussinesq approximation as follows:

where:

• $\mathbf{\text{S}}$ is the mean strain rate tensor given by Eqn. (1130) and computed from the resolved velocity field.
• $\tilde{v}$ is the filtered velocity.

The subgrid scale turbulent viscosity ${\mu }_t$ must be described by a Subgrid Scale Model that accounts for the effects of small eddies on the resolved flow.

Mean-flow quantities must be obtained by gathering statistics either over a long physical time, and/or from a homogeneous spatial coordinate. Field function monitors are provided in Simcenter STAR-CCM+ to monitor the field statistics.