A dynamic spatial gradient model for the subgrid closure in large-eddy simulation of turbulence

A dynamic spatial gradient model (DSGM) is proposed for the subgrid-scale (SGS) closure of large-eddy simulation (LES). The velocity gradients at neighboring LES grids are incorporated to improve the accuracy of the SGS stress. Compared to the previous machine-learning-based multi-point gradient models, the current model is free from the need of a priori knowledge. The model coefficients are dynamically determined by the least-square method using the Leonard stress. The a priori tests show that the correlation coefficients of the SGS stress for the DSGM framework are much larger than the traditional velocity gradient model over different tested filter widths from viscous to inertial scales. The analysis of the model coefficients in the a priori test suggests that the number of the model coefficients can be significantly reduced, leading to a simpler version of the model. A small-scale eddy viscosity (SSEV) model is introduced as an artificial viscosity to mimic the flux of kinetic energy to smaller scales which cannot be resolved at an LES grid. The velocity spectrum predicted by SSEV-based implicit LES is very close to that of direct numerical simulation (DNS) data. In the a posteriori tests, both the flow statistics and the instantaneous field are accurately recovered with the SSEV-enhanced DSGM model. Compared with the SSEV-based implicit LES, the dynamic Smagorinsky model, and the dynamic mixed model, the results predicted by the current model have overall closer agreements with the filtered DNS result, suggesting that the DSGM framework is well-suited for highly accurate LES of turbulence.