H-adaptive finite element solution of unsteady thermally driven cavity problem

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

Research output: Journal article publicationJournal articleAcademic researchpeer-review

11 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 for Rayleigh numbers at which no steady state exists (greater than 1.9 × 108). This problem is characterised by sharp thermal and flow boundary layers and highly advection dominated transport, which normally requires special algorithms, such as streamline upwinding, to achieve stable and smooth solutions. It will be shown that h-adaptivity provides a suitable solution to both of these problems (sharp gradients and advection dominated transport). Adaptivity is also very effective in resolving the flow physics, characterised by unsteady internal waves, are calculated for three Rayleigh numbers; 2 × 108, 3 × 108 and 4 × 108 using a Prandtl number of 0.71 and results are compared with other published results.
Original languageEnglish
Pages (from-to)172-194
Number of pages23
JournalInternational Journal of Numerical Methods for Heat and Fluid Flow
Issue number2
Publication statusPublished - 1 Jan 2001
Externally publishedYes


  • Finite element method
  • Natural convection

ASJC Scopus subject areas

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


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