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Stable and time‐dissipative finite element methods for the incompressible Navier–Stokes equations in advection dominated flows
Author(s) -
Simo J. C.,
Armero F.,
Taylor C. A.
Publication year - 1995
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620380904
Subject(s) - mathematics , incompressible flow , compressibility , navier–stokes equations , advection , pressure correction method , scalar (mathematics) , mathematical analysis , finite element method , convection–diffusion equation , dissipative system , physics , flow (mathematics) , mechanics , geometry , thermodynamics , quantum mechanics
Abstract This paper examines a new Galerkin method with scaled bubble functions which replicates the exact artificial diffusion methods in the case of 1‐D scalar advection–diffusion and that leads to non‐oscillatory solutions as the streamline upwinding algorithms for 2‐D scalar advection–diffusion and incompressible Navier–Stokes. This method retains the satisfaction of the Babuska–Brezzi condition and, thus, leads to optimal performance in the incompressible limit. This method, when, combined with the recently proposed linear unconditionally stable algorithms of Simo and Armero (1993), yields a method for solution of the incompressible Navier–Stokes equations ideal for either diffusive or advection‐dominated flows. Examples from scalar advection–diffusion and the solution of the incompressible Navier–Stokes equations are presented.