Performance of Under-resolved Two-Dimensional Incompressible Flow Simulations, II

This paper presents a study of the behavior of several difference 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 difference methods of both a pressure–Poisson and vorticity stream-function formulation, and a pseudospectral method. It is demonstrated that all these methods produce spurious, nonphysical vortices of the type described by Brown and Minion for a Godunov projection method (J. Comput. Phys.121,1995) when the flow is sufficiently under-resolved. The occurrence of these artifacts appears to be due to a nonlinear effect in which the truncation error of the difference method initiates a vortex instability in the computed flow. The implications of this study for adaptive mesh refinement strategies are also discussed.