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Finite element methods based on a new formulation for the non‐stationary incompressible Navier–Stokes equations
Author(s) -
Lin Ping,
Chen Xianqiao,
Ong Ming Tze
Publication year - 2004
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.794
Subject(s) - finite element method , pressure correction method , compressibility , navier–stokes equations , domain decomposition methods , incompressible flow , mathematics , flow (mathematics) , domain (mathematical analysis) , mathematical analysis , mathematical optimization , geometry , mechanics , engineering , physics , structural engineering
Abstract A new formulation of the Navier–Stokes equations is introduced to solve incompressible flow problems. When finite element methods are used under this formulation there is no need to worry whether Babuska–Brezzi condition is satisfied or not. Both velocity and pressure can be obtained separately and the pressure can be simply obtained by a substitution. Moreover, fully explicit time integration can be applied for easy implementation. Implementation issues are discussed and a couple of flow examples are simulated. Parallel implementation based on domain decomposition is incorporated as well. Copyright © 2004 John Wiley & Sons, Ltd.