WIAS Preprint No. 1509, (2010)

Stable computing with an enhanced physics based scheme for the 3D Navier--Stokes equations



Authors

  • Case, Michael
  • Ervin, Vincent
  • Linke, Alexander
    ORCID: 0000-0002-0165-2698
  • Rebholz, Leo
  • Wilson, Nicholas

2010 Mathematics Subject Classification

  • 76D05 65M60

2008 Physics and Astronomy Classification Scheme

  • 47.11.Fg

Keywords

  • incompressible Navier-Stokes equations, finite element methods, grad-div stabilization, helicity conservation

Abstract

We study extensions of an earlier developed energy and helicity preserving scheme for the 3D Navier-Stokes equations and apply them to a more general class of problems. The scheme is studied together with stabilizations of grad-div type in order to mitigate the effect of the Bernoulli pressure error on the velocity error. We prove stability, convergence, discuss conservation properties, and present numerical experiments that demonstrate the advantages of the scheme.

Appeared in

  • Int. J. Numer. Anal. Model., 8 (2011) pp. 118--136.

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