Low and moderate Reynolds number transient flow simulations using space filtered Navier-Stokes equations

In this study, low and moderate Reynolds number flow problems in the laminar range are solved numerically with grids that do not resolve all the significant scales of motion. Spatial averaging or filtering of the Navier-Stokes equations and Taylor series approximations to the filtered advective terms are used in order to account for the effects of the unresolved or subgrid scales on the resolved scales. Numerical experiments with a transient 2-D lid driven cavity flow problem, using a penalty method Galerkin finite element code, show that this approach enhances the momentum transfer properties of the numerical solution, eliminates 2Δx type oscillations, and enables the use of coarser grids. The significance and order of the terms that describe the interaction between the resolved and the subgrid scales is studied and the success of the series approximations to these terms is demonstrated. © 1994 John Wiley & Sons, Inc.