Subgrid Scale Turbulence Models

Large Eddy Simulation requires closure of the filtered Navier-Stokes equations by modeling the subgrid scale stress tensor.

A subgrid scale model provides a formula for the subgrid scale viscosity, $μ_{t}$ , in the Boussinesq approximation of the subgrid scale stress tensor (see Eqn. (253)). Currently, three subgrid scale models are available in Simcenter STAR-CCM+:

Smagorinsky Subgrid Scale

The Smagorinsky Subgrid Scale model ([355]) is the original and most basic subgrid scale model, upon which many more advanced models are based. This model uses a mixing length hypothesis to model the subgrid scale stresses.

One shortcoming of the Smagorinsky Subgrid Scale model is that it contains a model coefficient $C_{s}$ that is not universal and depends on the local flow conditions. Additionally, a damping function is needed for proper results in wall-bounded flows. The Van Driest damping function is a non-local operation, requiring the use of a KD-tree data structure to communicate wall information to the interior. In simulations with very complex geometries, this KD-tree must be broadcast to each parallel node, resulting in a memory and communication overhead. An update policy can be used to improve the communication overhead, but not the memory overhead. Therefore, this model should be avoided for large-scale computations on complex geometries. It is, however, useful for reference simulations, since it is the original algebraic subgrid scale model formulation.

Dynamic Smagorinsky Subgrid Scale

The Dynamic Smagorinsky Subgrid Scale model ([352], [353]) has the same basic form as the Smagorinsky model, however instead of using a single user-defined

C_{s}

coefficient, the model computes a local time-varying coefficient by test-filtering the flow field at a length scale greater than the grid length scale. This dynamic variation of the constant gives the model its name, and allows it to compute the correct result for wall-bounded flows without the use of damping functions.

WALE Subgrid Scale

The WALE (Wall-Adapting Local-Eddy Viscosity) Subgrid Scale model ([354]) is a more modern subgrid scale model that uses a novel form of the velocity gradient tensor in its formulation.

Similar to the Smagorinsky Subgrid Scale model, it suffers from the limitation that the model coefficient

C_{w}

is not universal. But validations using Simcenter STAR-CCM+ have shown that the WALE model is seemingly less sensitive to the value of this coefficient than the Smagorinsky model. Another advantage of the WALE model is that it does not require any form of near-wall damping—it automatically gives accurate scaling at walls.