Development of subgrid-scale model for LES of Burgers turbulence with large filter size

Abstract

A neural network (NN) with one hidden layer is implemented to establish a relationship between the resolved-scale flow field and the subgrid-scale (SGS) stress for large eddy simulation (LES) of the Burgers equation. Five sets of input are considered for the neural network by combining the velocity gradient and the filter size. The training datasets are obtained by filtering the direct numerical simulation (DNS) results of the Burgers equation with random forcing function. The number of modes is sufficiently large ( N =  65 536) to resolve extremely small scales of motion. In the a priori test, a correlation coefficient over 0.93 is achieved for the SGS stress between the NN models and the filtered DNS data. The results of the a posteriori test reveal that the obtained solutions are stable for all NN models without applying any stabilization techniques. However, not all NN models have a reasonable performance when embedded in the LES code. The applicability of the NN models to the Burgers equation with higher and lower viscosity is also investigated, and it is indicated that the most reliable NN models obtained in this paper can be applied to a set of parameters which are different from those used in training. The results of the SGS models constructed using the neural network are also compared with the existing models, and it is shown that the best obtained NN models outperform the Smagorinsky model and the gradient model, and are comparable to the dynamic Smagorinsky model. However, the NN models have an advantage over the dynamic Smagorinsky model in numerical cost.