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

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

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48 Citations (Scopus)


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
Issue number10
Publication statusPublished - 1988 Oct



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

ASJC Scopus subject areas

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

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