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Volume 3, Issue 3
Preconditioners for Incompressible Navier-Stokes Solvers

A. Segal, M. ur Rehman & C. Vuik

DOI: 10.4208/nmtma.2010.33.1

Numer. Math. Theor. Meth. Appl., 3 (2010), pp. 245-275.

Published online: 2010-03

[An open-access article; the PDF is free to any online user.]

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  • Abstract

In this paper we give an overview of the present state of fast solvers for the solution of the incompressible Navier-Stokes equations discretized by the finite element method and linearized by Newton or Picard's method. It is shown that block preconditioners form an excellent approach for the solution, however, if the grids are not to fine preconditioning, a Saddle point ILU matrix (SILU) may be an attractive alternative. The applicability of all methods to stabilized elements is investigated. In case of the stand-alone Stokes equations special preconditioners increase the efficiency considerably.

  • Keywords

Navier-Stokes equations, finite element method, block preconditioners, SIMPLE-type schemes, iterative methods, incompressible fluids.

  • AMS Subject Headings

65F10, 65N30, 76D05

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{NMTMA-3-245, author = {A. Segal, M. ur Rehman and C. Vuik}, title = {Preconditioners for Incompressible Navier-Stokes Solvers}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2010}, volume = {3}, number = {3}, pages = {245--275}, abstract = {

In this paper we give an overview of the present state of fast solvers for the solution of the incompressible Navier-Stokes equations discretized by the finite element method and linearized by Newton or Picard's method. It is shown that block preconditioners form an excellent approach for the solution, however, if the grids are not to fine preconditioning, a Saddle point ILU matrix (SILU) may be an attractive alternative. The applicability of all methods to stabilized elements is investigated. In case of the stand-alone Stokes equations special preconditioners increase the efficiency considerably.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2010.33.1}, url = {http://global-sci.org/intro/article_detail/nmtma/5999.html} }
TY - JOUR T1 - Preconditioners for Incompressible Navier-Stokes Solvers AU - A. Segal, M. ur Rehman & C. Vuik JO - Numerical Mathematics: Theory, Methods and Applications VL - 3 SP - 245 EP - 275 PY - 2010 DA - 2010/03 SN - 3 DO - http://doi.org/10.4208/nmtma.2010.33.1 UR - https://global-sci.org/intro/article_detail/nmtma/5999.html KW - Navier-Stokes equations, finite element method, block preconditioners, SIMPLE-type schemes, iterative methods, incompressible fluids. AB -

In this paper we give an overview of the present state of fast solvers for the solution of the incompressible Navier-Stokes equations discretized by the finite element method and linearized by Newton or Picard's method. It is shown that block preconditioners form an excellent approach for the solution, however, if the grids are not to fine preconditioning, a Saddle point ILU matrix (SILU) may be an attractive alternative. The applicability of all methods to stabilized elements is investigated. In case of the stand-alone Stokes equations special preconditioners increase the efficiency considerably.

A. Segal, M. ur Rehman and C. Vuik. (2010). Preconditioners for Incompressible Navier-Stokes Solvers. Numerical Mathematics: Theory, Methods and Applications. 3 (3). 245-275. doi:10.4208/nmtma.2010.33.1
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