Numerical stability analysis of the Gaussian filtered Navier-Stokes equations

Ida, Masato; Taniguchi, Nobuyuki*

The numerical stability of the Gaussian filtered Navier-Stokes equations is studied theoretically. Our recent theoretical results showed that for a large filter width, the linear shears in the time-averaged velocity fields numerically destabilize the fluctuation components because a numerically unstable term is derived by the Gaussian filtering operation. In this report we extend that numerical stability analysis based on an exact expansion series for the subgrid-scale stress terms and a numerical stability analysis of arbitrary-order spatial derivatives. The present investigation shows that numerically unstable terms can appear in many situations.