A Nonlinear Multigrid Method for the Three-Dimensional Incompressible Navier-Stokes Equations

D. Drikakis, O.P. Iliev, D.P. Vassileva

Research output: Contribution to journalArticle

65 Citations (Scopus)

Abstract

A nonlinear multigrid method is developed for solving the three-dimensional Navier–Stokes equations in conjunction with the artificial compressibility formulation. The method is based on the full multigrid (FMG)—full approximation storage (FAS)—algorithm and is realized via an “unsteady-type” procedure, according to which the equations are not solved exactly on the coarsest grid, but some pseudo-time iterations are performed on the finer grids and some on the coarsest grid. The multigrid method is implemented in conjunction with a third-order upwind characteristics-based scheme for the discretization of the convection terms, and the fourth-order Runge–Kutta scheme for time integration. The performance of the method is investigated for three-dimensional flows in straight and curved channels as well as flow in a cubic cavity. The multigrid acceleration is assessed in contrast to the single-grid and mesh-sequencing algorithms. The effects of various multigrid components on the convergence acceleration, such as prolongation operators, as well as pre- and postrelaxation iterations, are also investigated.
LanguageEnglish
Pages301-321
Number of pages21
JournalJournal of Computational Physics
Volume146
Issue number1
DOIs
Publication statusPublished - 10 Oct 1998

Fingerprint

multigrid methods
Navier-Stokes equation
Navier Stokes equations
grids
Channel flow
Compressibility
iteration
prolongation
three dimensional flow
sequencing
compressibility
mesh
convection
formulations
operators
cavities
approximation
Convection

Keywords

  • Navier–Stokes equations
  • multigrid
  • upwind schemes
  • artificial compressibility

Cite this

Drikakis, D. ; Iliev, O.P. ; Vassileva, D.P. / A Nonlinear Multigrid Method for the Three-Dimensional Incompressible Navier-Stokes Equations. In: Journal of Computational Physics. 1998 ; Vol. 146, No. 1. pp. 301-321.
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A Nonlinear Multigrid Method for the Three-Dimensional Incompressible Navier-Stokes Equations. / Drikakis, D.; Iliev, O.P.; Vassileva, D.P.

In: Journal of Computational Physics, Vol. 146, No. 1, 10.10.1998, p. 301-321.

Research output: Contribution to journalArticle

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