Constant-coefficient spatial gradient models for the sub-grid scale closure in large-eddy simulation of turbulence

Constant-coefficient spatial gradient models (SGM) are proposed for the sub-grid scale (SGS) closure in large-eddy simulation (LES) of turbulence. The model coefficients are determined either by expanding the neighboring first-order gradients using the local higher-order gradient, or by directly discretizing the local higher-order gradients using first-order values among spatial stencil locations. The a priori tests show that the SGM model can have a correlation coefficient larger than 0.97, which is close to the machine-learning based model. In the a posteriori tests, the LESs with different SGS models are performed for the forced incompressible homogeneous isotropic turbulence (HIT) and weakly compressible turbulent mixing layer (TML). The performance of SGM model is comprehensively examined through the prediction of the flow statistics including the velocity spectrum, the probability density functions (PDFs) of the strain rate and velocity increments. The evolution of turbulent kinetic energy, the instantaneous structures of the vorticity field and the Q-criterion are also examined to evaluate the spatial temporal performances of the LES. The predictions of the SGM model are consistently more satisfying compared to the traditional models, including the dynamic Smagorinsky model (DSM), the dynamic mixed model (DMM) and implicit-LES (ILES) while its computational cost is similar to traditional models. For the weakly compressible TML, most LES perform better when the length scale of the initial perturbation field is larger than the filter width, providing a useful guidance for LES of turbulent mixing layers.