Robust dynamic adaptation of the Smagorinsky model based on a sub-grid activity sensor

Abstract

The present study deals with the application of a sub-grid activity sensor to an eddy viscosity type base model in the context of Large Eddy Simulation (LES). The coherent structure function is used to build this sensor in combination with explicit test filtering. The proposed sensor features two main advantages: First, it attenuates the sub-grid scale dissipation of the base model for transitional flows. Depending on local conditions, the sensor is essentially blending the eddy viscosity between zero and the value resulting from the standard Smagorinsky model. Second, the sensor rectifies the incorrect near-wall scaling of the standard Smagorinsky model. Application of the sensor requires no averaging (in the homogeneous direction) and is easy to implement, and the additional computational cost is insignificant. In order to assess the model, three different configurations have been examined: laminar-to-turbulent transition in the Taylor–Green vortex, wall-dominated channel flows, and a free planar jet flow including passive scalar mixing. Based on a posteriori LES, it has been found that the new sensor-enhanced Smagorinsky model often outperforms established eddy viscosity models from the literature, such as the standard Smagorinsky model and the sigma model, as well as the LES without the explicit sub-grid model.