Numerical comparison of CBS and SGS as stabilization techniques for the incompressible Navier–Stokes equations
- 20 March 2006
- journal article
- research article
- Published by Wiley in International Journal for Numerical Methods in Engineering
- Vol. 66 (10) , 1672-1689
- https://doi.org/10.1002/nme.1697
Abstract
In this work, we present numerical comparisons of some stabilization methods for the incompressible Navier–Stokes. The first is the characteristic‐based split (CBS). It combines the characteristic Galerkin method to deal with convection‐dominated flows with a classical splitting technique, which in some cases allows us to use equal velocity–pressure interpolations. The other two approaches are particular cases of the subgrid scale (SGS) method. The first, obtained after an algebraic approximation of the subgrid scales, is very similar to the popular Galerkin/least‐squares (GLS) method, whereas in the second, the subscales are assumed to be orthogonal to the finite element space. It is shown that all these formulations display similar stabilization mechanisms, provided the stabilization parameter of the SGS methods is identified with the time step of the CBS approach. This paper provides the numerical experiments for the comparison of formulations made by Codina and Zienkiewicz in a previous article. Copyright © 2006 John Wiley & Sons, Ltd.Keywords
This publication has 20 references indexed in Scilit:
- Stabilized finite element approximation of transient incompressible flows using orthogonal subscalesComputer Methods in Applied Mechanics and Engineering, 2002
- CBS versus GLS stabilization of the incompressible Navier–Stokes equations and the role of the time step as stabilization parameterCommunications in Numerical Methods in Engineering, 2001
- A stabilized finite element method for generalized stationary incompressible flowsComputer Methods in Applied Mechanics and Engineering, 2001
- The characteristic-based-split procedure: an efficient and accurate algorithm for fluid problemsInternational Journal for Numerical Methods in Fluids, 1999
- A general algorithm for compressible and incompressible flows. Part III: The semi-implicit formInternational Journal for Numerical Methods in Fluids, 1998
- Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methodsComputer Methods in Applied Mechanics and Engineering, 1995
- A general algorithm for compressible and incompressible flow—Part I. the split, characteristic‐based schemeInternational Journal for Numerical Methods in Fluids, 1995
- Convergence analyses of Galerkin least-squares methods for symmetric advective-diffusive forms of the Stokes and incompressible Navier-Stokes equationsComputer Methods in Applied Mechanics and Engineering, 1993
- A new finite element formulation for computational fluid dynamics: IX. Fourier analysis of space-time Galerkin/least-squares algorithmsComputer Methods in Applied Mechanics and Engineering, 1991
- A new finite element formulation for computational fluid dynamics: VIII. The galerkin/least-squares method for advective-diffusive equationsComputer Methods in Applied Mechanics and Engineering, 1989