An efficient model for subgrid-scale velocity enrichment for large-eddy simulations of turbulent flows

In some applications of large-eddy simulation (LES), in addition to providing a closure model for the subgrid-scale stress tensor, it is necessary to also provide means to approximate the subgrid-scale velocity field. In this work, we derive a new model for the subgrid-scale velocity that can be used in such LES applications. The model consists in solving a linearized form of the momentum equation for the subgrid-scale velocity using a truncated Fourier-series approach. Solving within a structured grid of statistically homogeneous sub-domains enables the treatment of inhomogeneous problems. It is shown that the generated subgrid-scale velocity emulates key properties of turbulent flows, such as the right kinetic energy spectrum, realistic strain–rotation relations, and intermittency. The model is also shown to predict the correct inhomogeneous and anisotropic velocity statistics in unbounded flows. The computational costs of the model are still of the same order as the costs of the LES.