PERFORMANCE OF UNDER-RESOLVED 2-DIMENSIONAL INCOMPRESSIBLE-FLOW SIMULATIONS

A careful study of the behavior of a Godunov-projection method for the incompressible Navier-Stokes equations as a function of the resolution of the computational mesh is presented, By considering a representative example problem, it is demonstrated that a Godunov-projection method performs as well as an accurate centered finite difference method in cases where the smallest flow scales are well resolved. In underresolved cases, however, where centered methods compute solutions badly polluted with mesh-scale oscillations, the Godunov-projection method sometimes computes smooth, apparently physical solutions. Closer examination indicates that these underresolved Godunov solutions, although convergent when the grid is refined, contain spurious nonphysical vortices that are artifacts of the underresolution, These artifacts are not unique to Godunov methods, however, and are observed with other difference approximations as well. The implication of these results on the applicability of difference approximations to engineering flow problems in the underresolved case is discussed. (C) 1995 Academic Press, Inc.