Large Eddy Simulations by approximate weak entropy solutions

Abstract

We propose to use weak (averaged) entropy solutions in lieu of LES models. This approach unites the theory for shock capturing schemes and turbulence modelling. To achieve this, we identify a number of conditions (albeit not sufficient) that a scheme should satisfy. Namely, a scheme should be: conservative, entropy dissipative, kinetic-energy preserving/diffusive, positivity preserving and have linearly stable (non anti-diffusive) continuity equation. We propose a finite-volume scheme with these properties and investigate its properties, and the properties of some related schemes, for the standard entropy-wave/shock interaction, a Kelvin-Helmoholtz instability, and a turbulent Rayleigh-Taylor problem.

These preliminary investigations suggest that the scheme is very robust, is competitive for turbulent problems and is far less prone to trip false turbulence. However, and as with any general purpose scheme, wildly under-resolved simulations can not be expected to be accurate. The advantage with the current scheme is that local averages converge which provides a possibility to estimate the accuracy of functionals of interest.