A least‐squares finite element method for time‐dependent incompressible flows with thermal convection

Li Q. Tang, Tate T.H. Tsang

Research output: Contribution to journalArticlepeer-review

58 Scopus citations

Abstract

The time‐dependent Navier–Stokes equations and the energy balance equation for an incompressible, constant property fluid in the Boussinesq approximation are solved by a least‐squares finite element method based on a velocity–pressure–vorticity–temperature–heat‐flux (u–P–ω–T–q) formulation discretized by backward finite differencing in time. The discretization scheme leads to the minimization of the residual in the l2‐norm for each time step. Isoparametric bilinear quadrilateral elements and reduced integration are employed. Three examples, thermally driven cavity flow at Rayleigh numbers up to 106, lid‐driven cavity flow at Reynolds numbers up to 104 and flow over a square obstacle at Reynolds number 200, are presented to validate the method.

Original languageEnglish
Pages (from-to)271-289
Number of pages19
JournalInternational Journal for Numerical Methods in Fluids
Volume17
Issue number4
DOIs
StatePublished - Aug 30 1993

Keywords

  • Bqussinesq approximation
  • Incompressible flows
  • Least‐squares finite element method
  • Navier–Stokes equations
  • Time‐dependent

ASJC Scopus subject areas

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

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