Development of a dynamic subgrid-scale model for large eddy simulations with two transport equations.

A new SGS model for LES using two transportation equations for the turbulent kinetic energy production k_sgs and the specific dissipation rate ω_sgs is presented. The new SGS model aims at more accurately predicting the physics of highly transient turbulent flow relatively with low-order numerical schemes. This new model, which is called “k-ω SGS model”, employs an additional transport equation for ω_sgs besides one for k_sgs. Thus their transient histories can be traced and updated to calculate the eddy viscosity. In this new SGS model, some new treatments for the turbulent production and dissipation terms in the two transport equations are utilized. One of treatments is to apply the similar mechanism of the WALE SGS model to consider the anisotropy of the SGS eddy viscosity near the wall using the velocity gradient tensor and then to dynamically determine it in the transport equations. Thanks to this aspect, it can detect not only strain rate, but also rotation rate. Moreover, a new formula for the SGS eddy viscosity is adopted to consider both the contributions of the turbulent kinetic energy and dissipation to it, and the SGS stress tensor is determined by them. Accordingly, for example, the new two-equation SGS model is able to result in more accurate Reynolds normal and shear stresses for wall-bounded turbulent flows such as lid-driven cavity and square cylinder flows compared with other models even though it would need to be further validated for turbulent flows occurring over more complex geometries in the near future.