Petrov‐Galerkin methods on multiply connected domains for the vorticity‐stream function formulation of the incompressible Navier‐Stokes equations

Tayfun E. Tezduyar, R. Glowinski, J. Liou

Research output: Contribution to journalArticle

48 Citations (Scopus)

Abstract

In this paper we present streamline‐upwind/Petrov‐Galerkin finite element procedures for two‐dimensional fluid dynamics computations based on the vorticity‐stream function formulation of the incompressible Navier‐Stokes equations. We address the difficulties associated with the convection term in the vorticity transport equation, lack of boundary condition for the vorticity at no‐slip boundaries, and determination of the value of the stream function at the internal boundaries for multiply connected domains. The proposed techniques, implemented within the framework of block‐iteration methods, have successfully been applied to various problems involving simply and multiply connected domains.

Original languageEnglish
Pages (from-to)1269-1290
Number of pages22
JournalInternational Journal for Numerical Methods in Fluids
Volume8
Issue number10
DOIs
Publication statusPublished - 1988
Externally publishedYes

Fingerprint

Incompressible Navier-Stokes
Multiply Connected Domain
Petrov-Galerkin Method
Vorticity
Navier-Stokes Equations
Petrov-Galerkin
Formulation
Stream Function
Fluid Dynamics
Fluid dynamics
Transport Equation
Convection
Boundary conditions
Finite Element
Internal
Term
Framework

Keywords

  • Multiply connected domains
  • Petrov‐Galerkin
  • Vorticity‐stream function

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Computer Science Applications
  • Applied Mathematics

Cite this

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AU - Glowinski, R.

AU - Liou, J.

PY - 1988

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AB - In this paper we present streamline‐upwind/Petrov‐Galerkin finite element procedures for two‐dimensional fluid dynamics computations based on the vorticity‐stream function formulation of the incompressible Navier‐Stokes equations. We address the difficulties associated with the convection term in the vorticity transport equation, lack of boundary condition for the vorticity at no‐slip boundaries, and determination of the value of the stream function at the internal boundaries for multiply connected domains. The proposed techniques, implemented within the framework of block‐iteration methods, have successfully been applied to various problems involving simply and multiply connected domains.

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KW - Petrov‐Galerkin

KW - Vorticity‐stream function

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