Underlying mechanism of numerical instability in Large-Eddy Simulation of turbulent flows

Ida, Masato; Taniguchi, Nobuyuki*

This paper extends our recent theoretical work concerning the feasibility of stable and accurate computation of turbulence using a large eddy simulation. In our previous paper, it was shown, based on a simple assumption regarding the instantaneous streamwise velocity, that the application of the Gaussian filter to the Navier-Stokes equations can result in the appearance of a numerically unstable term. In the present paper, based on assumptions regarding the statistically averaged velocity, we show that in several situations, the shears appearing in the statistically averaged velocity field numerically destabilize the fluctuation components because of the derivation of a numerically unstable term that represents negative diffusion in a fixed direction. This finding can explain the problematic numerical instability that has been encountered in large eddy simulations of wall-bounded flows. The present result suggests that if there is no failure in modeling, the resulting subgrid-scale model can still have unstable characteristics.