Evaluating modulated gradient model in computing subgrid scale tensors

Accurate modeling of the sub-grid scales (SGS) is crucial in determining the accuracy of the large eddy simulations (LES) in turbulent flow analysis. In recent years, new branches of the sub-grid scales models called gradient-based models were developed in computing the sub-grid scales stresses and heat fluxes and used in large eddy simulations. In this work, the modulated gradient model (MGM) equations were implemented in the OpenFOAM package, and pimpleFoam solver was modified to improve the solution accuracy. The modulated gradient model is based on the Taylor-series expansion of the sub-grid scales stress and employs the local equilibrium hypothesis to evaluate the sub-grid scales kinetic energy. To assess the accuracy of the modulated gradient model as well as the improved pimpleFoam solver, turbulent channel flow at a frictional Reynolds number of 395 was simulated via the OpenFOAM package and results were compared with the direct numerical simulation (DNS) data as well as the numerical solution of the Smagorinsky, Dynamic Smagorinsky, Deardorff models. The results show that modulated gradient model evaluates first and second order turbulence parameters with a high-level of accuracy.