h-adaptive finite element solution of high Rayleigh number thermally driven cavity problem

D.A. Mayne, Asif Sohail Usmani, M. Crapper

Research output: Journal article publicationJournal articleAcademic researchpeer-review

72 Citations (Scopus)


An h-adaptive finite element code for solving coupled Navier-Stokes and energy equations is used to solve the thermally driven cavity problem. The buoyancy forces are represented using the Boussinesq approximation. The problem is characterised by very thin boundary layers at high values of Rayleigh number (> 106). However, steady state solutions are achievable with adequate discretisation. This is where the auto-adaptive finite element method provides a powerful means of achieving optimal solutions without having to pre-define a mesh, which may be either inadequate or too expensive. Steady state and transient results are given for six different Rayleigh numbers in the range 103 to 108 for a Prandtl number of 0.71. The use of h-adaptivity, based on a posteriori error estimation, is found to ensure a very accurate problem solution at a reasonable computational cost.
Original languageEnglish
Pages (from-to)598-615
Number of pages18
JournalInternational Journal of Numerical Methods for Heat and Fluid Flow
Issue number6
Publication statusPublished - 1 Jan 2000
Externally publishedYes

ASJC Scopus subject areas

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


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