A minimum-relaxation model for large-eddy simulation

Abstract

This paper is about a relaxation model for large-eddy simulation of turbulent flow that truncates the small scales of motion for which numerical resolution is not available by making sure that they do not get energy from the larger, resolved, eddies. The resolved scales are defined with the help of a box filter. The relaxation parameter is determined in such a way that the production of too small, box-fitting, scales is counteracted by the modeled dissipation. This dissipation-production balance is worked out with the help of Poincaré’s inequality, which results in a relaxation model that depends on the invariants of the velocity gradient. This model is discretized and equipped with a Schumann filter. It is successfully tested for isotropic turbulence as well as for turbulent channel flow.