Scale separation for implicit large eddy simulation

With implicit large eddy simulation (ILES) the truncation error of the discretization scheme acts as subgrid-scale (SGS) model for the computation of turbulent flows. Although ILES is comparably simple, numerically robust and easy to implement, a considerable challenge is the design of numerical discretization schemes resulting in a physically consistent SGS model. In this work, we consider the implicit SGS modeling capacity of the adaptive central-upwind weighted-essentially-non-oscillatory scheme (WENO-CU6) [X.Y. Hu, Q. Wang, N.A. Adams, An adaptive central-upwind weighted essentially non-oscillatory scheme, J. Comput. Phys. 229 (2010) 8952–8965] by incorporating a physically-motivated scale-separation formulation. Scale separation is accomplished by a simple modification of the WENO weights. The resulting modified scheme maintains the shock-capturing capabilities of the original WENO-CU6 scheme while it is also able to reproduce the Kolmogorov range of the kinetic-energy spectrum for turbulence at the limit of infinite Reynolds number independently of grid resolution. For isentropic compressible turbulence the pseudo-sound regime of the dilatational kinetic-energy spectrum and the non-Gaussian probability-density function of the longitudinal velocity derivative are reproduced.