Numerical simulation with Gaussian low-pass filtered Navier-Stokes equations.

摘要

In this study, a low pass Gaussian type space-time filter is applied to the Navier-Stokes equations. Such an application will enhance the capabilities of simulating complex flows by eliminating the small scales of motion that cannot be resolved within the available computational grid. The derivation of filtered equations are presented both with and without separation of scales. The filtered Navier-Stokes equations contain terms which accurately represent the complex interaction between the resolved and subgrid scale components of the whole flow field. In addition, the significance of the filtering process from the numerical point of view is studied.;Using a two-dimensional general purpose Navier-Stokes equations solver which employs a consistent penalty formulation Galerkin finite element method, the filtered equations are applied to a recirculating, lid driven cavity test problem. A systematic investigation is performed to analyze the fundamental behavior and effectiveness of the filtered equations at moderate Reynolds numbers. Specifically, the Leonard/Clark approximation to the resolved-subgrid scale interaction terms and the subgrid scale closure models are thoroughly examined through numerical experiments.;The results of the study indicated that preparing the Navier-Stokes equations for the numerical simulations through space-time filtering enhances their solutions by providing more accurate momentum/energy transfer among the different scales of the flow. The increased stability properties together with the elimination of the extreme small scales from the flow field reduce the requirement for extensive grid refinement which consequently will increase the possibility to simulate more complex flows at higher Reynolds numbers with the available computer resources.