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A stabilized finite element method for incompressible viscous flows using a finite increment calculus formulation

✍ Scribed by Eugenio Oñate

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
182 KB
Volume
182
Category
Article
ISSN
0045-7825

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✦ Synopsis

A stabilized ®nite element formulation for incompressible viscous ¯ows is derived. The starting point are the modi®ed Navier± Stokes equations incorporating naturally the necessary stabilization terms via a ®nite increment calculus (FIC) procedure. Application of the standard ®nite element Galerkin method to the modi®ed dierential equations leads to a stabilized discrete system of equations overcoming the numerical instabilities emanating from the advective terms and those due to the lack of compatibility between approximate velocity and pressure ®elds. The FIC method also provides a natural explanation for the stabilization terms appearing in all equations for both the Navier±Stokes and the simpler Stokes equations. Transient solution schemes with enhanced stabilization properties are also proposed. Finally a procedure for computing the stabilization parameters is presented.

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