On reproducing the energy cascade when LES grids are too coarse to resolve energy-containing motions

The nonlinear advection terms in the momentum equation handle the energy cascade across scales through instability development. When the large-eddy simulations (LES) grids are too coarse to resolve energy-containing turbulent motions, regular advection schemes are unable to develop sufficient instabilities and the associated energy cascade from large to small scales. An example is the failure to reproduce the law-of-the-wall using wall-modeled LES, regardless of the choice of spatial discretization method. Near the surface, the insufficient energy cascade leads to underpredicted shear production of resolved Reynolds stress, which induces overpredicted nondimensional shear. This work proposes an approach to enhance instability development in the regions where energy-containing motions are underresolved by LES grids. The new advection scheme is inspired by the existing Weighted Essentially Non-Oscillatory (WENO) schemes that have been developed to reduce spurious oscillations generated in numerical simulations involving discontinuities or sharp gradients. As opposed to the WENO schemes, which suppress resolved momentum fluxes at locations associated with large first- and second-order spatial derivatives of velocities, the new advection scheme enhances resolved momentum fluxes in these regions. The new advection scheme has been found to be effective in reducing the overprediction of near-surface nondimensional shear in wall-modeled LES. Specifically, the new advection scheme increases the turbulent vortex stretching, enhances the energy cascade, amplifies the vertical velocity variance, increases the production of resolved Reynolds stress, and ultimately reduces the overprediction of near-surface shear. Compared to previous efforts, which have sought to reduce the overprediction of shear via modifications to the subgrid-scale model and/or wall model, the new advection scheme is an attractive alternative because it accounts for the nonlinearity, nonlocalness, and anisotropy of energy-containing motions.