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Low and moderate Reynolds number transient flow simulations using space filtered Navier‐Stokes equations
Author(s) -
Cantekin M. E.,
Westerink J. J.,
Luettich R. A.
Publication year - 1994
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.1690100407
Subject(s) - mathematics , reynolds number , laminar flow , navier–stokes equations , series (stratigraphy) , flow (mathematics) , galerkin method , mathematical analysis , finite element method , statistical physics , mechanics , physics , geometry , turbulence , compressibility , paleontology , biology , thermodynamics
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 2Δ x 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.