A Study of Large-eddy Simulation using Statistical and Machine Learning Techniques

The numerical solution of Navier-Stokes (N-S) equations has been found useful in various disciplines during its development, especially in recent years. However, a large-eddy simulation method has been developed to model the subgrid-scale dissipation rate by closing the Navier-Stokes equations. Because the instantaneous and time-averaged statistic characteristics of the subgrid-scale turbulent kinetic energy and dissipation have been studied by large eddy simulation. The purpose of this study is to check the statistical and machine learning of the subgrid-scale energy dissipation. As we know that the current turbulence theory states that the vortex stretching mechanism transports energy from large to small scales and leads to a high energy dissipation rate in a turbulent flow. Hence, a vortex-stretching-based subgrid-scale model is considered regarding the square of the velocity gradient to detect the playing role of the vortex stretching mechanism. The study in this article has shown a two-step process. Considering a posteriori statistic of the velocity gradient is analyzed through higher-order statistics and joint probability density function. Secondly, a machine learning approach is studied on the same data. The results of the vortex-stretching-based subgrid-scale model are then compared with the other two dynamic subgrid models, such as the localized dynamic kinetic energy equation model and the TKE-based Deardorff model. The results suggest that the vortex-stretching-based model can detect the significant subgrid-scale dissipation of small-scale motions and predict satisfactory turbulence statistics of the velocity gradient tensor.