Numerical stability and error analysis for the incompressible Navier-Stokes equations

Serge Prudhomme*, J. T. Oden

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

This paper describes a strategy to control errors in finite element approximations of the time-dependent incompressible Navier-Stokes equations. The approach involves estimating the errors due to the discretization in space, using information from the residuals in the momentum and continuity equations. Following a numerical stability analysis of channel flows past a cylinder, it is concluded that the errors due to the residual in the continuity equation should be carefully controlled since it appears to be the source of unphysical perturbations artificially created by the spatial discretization. The performance of the adaptive strategy is then tested for lid-driven oblique cavity flows.

Original languageEnglish (US)
Pages (from-to)779-787
Number of pages9
JournalCommunications in Numerical Methods in Engineering
Volume18
Issue number11
DOIs
StatePublished - Nov 1 2002

Keywords

  • A posteriori error estimation
  • Incompressible Navier-Stokes equations
  • Mesh adaptivity
  • Numerical stability
  • Reliability
  • Residuals

ASJC Scopus subject areas

  • Software
  • Modeling and Simulation
  • Engineering(all)
  • Computational Theory and Mathematics
  • Applied Mathematics

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