Temporal, spatial and thermal features of 3-D Rayleigh-Bénard convection by a least-squares finite element method

Li Q. Tang, Tate T.H. Tsang

Research output: Contribution to journalArticlepeer-review

34 Scopus citations

Abstract

Numerical solutions of 3-D time-dependent Rayleigh-Bénard convection are presented in this work. The temporal, spatial and thermal features of convective patterns are studied for four different geometric aspect ratios, 2:1:2, 4:1:4, 5:1:5 and 3.5:1:2.1 at supercritical Rayleigh numbers Ra = 8 × 103, 2.4 × 104 and Prandtl numbers Pr = 0.71, 2.5. Several physical phenomena, such as multicellular flow pattern, oscillatory transient solution, 'T-shaped' rolls at the ends of a rectangular box, and roll alignment, are observed in our simulations. The numerical technique is based on an implicit, fully coupled, and time-accurate method, which consists of the Crank-Nicolson scheme for time integration, Newton's method for the convective terms with extensive linearization steps, and a least-squares finite element method. A matrix-free algorithm of the Jacobi conjugate gradient method is implemented to solve the symmetric, positive definite linear system of equations.

Original languageEnglish
Pages (from-to)201-219
Number of pages19
JournalComputer Methods in Applied Mechanics and Engineering
Volume140
Issue number3-4
DOIs
StatePublished - Jan 30 1997

Bibliographical note

Funding Information:
The work was partially supportedb y the National ScienceF oundation (NSF/KY EPSCoR program) and the Center for Computational Sciences at the University of Kentucky. TTT is also partially supported by a grant from the U.S. Environmental Protection Agency. The authors appreciatet he reviewerst horough and thoughtfulc ommentsa nd suggestionsw hich helped us to improve this paper.

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • General Physics and Astronomy
  • Computer Science Applications

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