A direct quantification of numerical dissipation towards improved large eddy simulations

Abstract

In implicit large eddy simulations (ILES), it becomes increasingly clear that numerical errors are essential to simulation accuracy. Nevertheless, whether the numerical dissipation in a CFD solver can be regarded as a means of turbulence modeling cannot be known $a$ $priori$. In the present work, we propose a general method to quantify the numerical dissipation rate for arbitrary flow solvers. Unlike previous approaches in which the numerical dissipation is estimated from the perspective of kinetic energy transfer, our method focuses on direct comparisons with the SGS dissipation from explicit models. The new method is both self-contained and self-consistent, which can be applied to any numerical solver through a simple post-processing step in the physical space. We show that for two common techniques to introduce numerical dissipation (through numerical schemes and solution filtering), the quantification results help to determine if a simulation can be considered as a legitimate ILES run and provide direct guidance for designing better models. When the numerical dissipation is already significant, an improved ILES filtering approach is proposed, which reduces the native numerical dissipation and works better for low order codes. The methods are general and work well for different Reynolds numbers, grid resolutions, and numerical schemes.