Title: Performance of Under-resolved Two-dimensional Incompressible Flow Simulations Ii Performance of Under-resolved Two-dimensional Incompressible Flow Simulations Ii 1

This paper presents a study of the behavior of several di erence approximations for the incompressible Navier-Stokes equations as a function of the computational mesh resolution. In particular, the under-resolved case is considered. The methods considered include a Godunov projection method, a primitive variable ENO method, an upwind vorticity stream-function method, centered di erence methods of both a pressurePoisson and vorticity stream-function formulation, and a pseudospectral method. It is demonstrated that all these methods produce spurious, non-physical vortices of the type described by Brown and Minion for a Godunov projection method [9] when the ow is su ciently under-resolved. The occurrence of these artifacts appears to be due to a nonlinear e ect in which the truncation error of the di erence method initiates a vortex instability in the computed ow. The implications of this study for adaptive mesh re nement strategies are also discussed. Subject Classi cation Index Numbers: 65M10, 76{8, 76D05