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

✍ Scribed by Michael L. Minion; David L. Brown

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 882 KB
• Volume: 138
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1006/jcph.1997.5843

✦ Synopsis

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 streamfunction 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.