A pure-compact scheme for the streamfunction formulation of Navier-Stokes equations

Matania Ben-Artzi, Jean Pierre Croisille, Dalia Fishelov*, Shlomo Trachtenberg

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

73 Scopus citations

Abstract

A pure-streamfunction formulation is introduced for the numerical simulation of the two-dimensional incompressible Navier-Stokes equations. The idea is to replace the vorticity in the vorticity-streamfunction evolution equation by the Laplacian of the streamfunction. The resulting formulation includes the streamfunction only, thus no inter-function relations need to be invoked. A compact numerical scheme, which interpolates streamfunction values as well as its first order derivatives, is presented and analyzed. A number of numerical experiments are presented, including driven and double driven cavities, where the Reynolds numbers are sufficiently large, leading to symmetry breaking of asymptotic solutions.

Original languageEnglish
Pages (from-to)640-664
Number of pages25
JournalJournal of Computational Physics
Volume205
Issue number2
DOIs
StatePublished - 20 May 2005

Keywords

  • Asymptotic behavior
  • Compact schemes
  • Driven cavity
  • Navier-Stokes equations
  • Numerical algorithm
  • Streamfunction formulation
  • Symmetry breaking
  • Vorticity

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