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Discontinuous Galerkin methods for the Navier–Stokes equations using solenoidal approximations
Author(s) -
Montlaur A.,
FernandezMendez S.,
Peraire J.,
Huerta A.
Publication year - 2009
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.2161
Subject(s) - solenoidal vector field , mathematics , navier–stokes equations , piecewise , discontinuous galerkin method , galerkin method , computation , compressibility , divergence (linguistics) , pressure correction method , approximations of π , mathematical analysis , finite element method , computational fluid dynamics , geometry , vector field , physics , mechanics , algorithm , linguistics , philosophy , thermodynamics
Abstract An interior penalty method and a compact discontinuous Galerkin method are proposed and compared for the solution of the steady incompressible Navier–Stokes equations. Both compact formulations can be easily applied using high‐order piecewise divergence‐free approximations, leading to two uncoupled problems: one associated with velocity and hybrid pressure, and the other one only concerned with the computation of pressures in the elements interior. Numerical examples compare the efficiency and the accuracy of both proposed methods. Copyright © 2009 John Wiley & Sons, Ltd.