On some pressure segregation methods of fractional-step type for the finite element approximation of incompressible flow problems

Ramon Codina, Santiago Badia

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32 Citations (Scopus)

Abstract

In this paper we treat several aspects related to time integration methods for the incompressible Navier-Stokes equations that allow to uncouple the calculation of the velocities and the pressure. The first family of schemes consists of classical fractional step methods, of which we discuss several possibilities for the pressure extrapolation and the time integration of first and second order. The second family consists of schemes based on an explicit treatment of the pressure in the momentum equation followed by a Poisson equation for the pressure. It turns out that this "staggered" treatment of the velocity and the pressure is stable. Finally, we present predictor-corrector methods based on the above schemes that aim to converge to the solution of the monolithic time integration method. Apart from presenting these schemes and check its numerical performance, we also present a complete set of stability results for the fractional step methods that are independent of the space stability of the velocity-pressure interpolation, that is, of the classical inf-sup condition.

Original languageEnglish
Pages (from-to)2900-2918
Number of pages19
JournalComputer Methods in Applied Mechanics and Engineering
Volume195
Issue number23-24
DOIs
Publication statusPublished - 15 Apr 2006
Externally publishedYes

Keywords

  • Fractional step methods
  • Incompressible Navier-Stokes equations

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