On the Use of Shock-Capturing Schemes for Large-Eddy Simulation

Abstract

Numerical simulations of freely decaying isotropic fluid turbulence were performed at various Mach numbers (from 0.2 to 1.0) using known shock-capturing Euler schemes (Jameson, TVD-MUSCL, ENO) often employed for aeronautical applications. The objective of these calculations was to evaluate the relevance of the use of such schemes in the large-eddy simulation (LES) context. The potential of the monotone integrated large-eddy simulation (MILES) approach was investigated by carrying out computations without viscous diffusion terms. Although some known physical trends were respected, it is found that the small scales of the simulated flow suffer from high numerical damping. In a quasi-incompressible case, this numerical dissipation is tentatively interpreted in terms of turbulent dissipation, yielding the evaluation of equivalent Taylor micro-scales. The Reynolds numbers based on these are found between 30 and 40, depending on the scheme and resolution (up to 1283). The numerical dissipation is also interpreted in terms of subgrid-scale dissipation in a LES context, yielding equivalent Smagorinsky “constants” which do not level off with time and which remain larger than the commonly accepted values of the classical Smagorinsky constant. On the grounds of tests with either the Smagorinsky or a dynamic model, the addition of explicit subgrid-scale (SGS) models to shock-capturing Euler codes is not recommended.