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X. Y. Hu
Lehrstuhl fur Aerodynamik, Technische Universitat Munchen 85748 Garching, Germany

Nikolaus A. Adams
Chair of Aerodynamics and Fluid Mechanics, Department of Mechanical Engineering, Technical University of Munich, 85748 Garching bei München, Germany


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, numerical 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 model of the adaptive central-upwind weighted-essentially-non-oscillatory scheme (WENO-CU6) (Hu, XY, Wang, Q. & Adams, NA, 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 quasi-isentropic compressible turbulence the the pseudo-sound regime of the dilatational kinetic-energy spectrum and the non-Gaussian probability-density function of the longitudinal velocity derivative are reproduced.