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Numerical Heat Transfer, Part B: Fundamentals
An International Journal of Computation and Methodology
Volume 52, 2007 - Issue 2
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Original Articles

Benchmark Solution for Time-Dependent Natural Convection Flows with an Accelerated Full-Multigrid Method

Nader Ben Cheikh Faculté des Sciences de Tunis, Département de Physique, Campus Universitaire, TunisiaCorrespondence[email protected]
,
Brahim Ben Beya Faculté des Sciences de Tunis, Département de Physique, Campus Universitaire, Tunisia
&
Taieb Lili Faculté des Sciences de Tunis, Département de Physique, Campus Universitaire, Tunisia
Pages 131-151 | Received 15 May 2006, Accepted 16 Feb 2007, Published online: 19 Jun 2007
 
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Abstract

A computational procedure is presented with an accelerated full-multigrid scheme for an efficient modeling of time-dependent buoyancy-driven flows. The smoother is the iterative red-and-black successive overrelaxation (RBSOR) scheme. In order to improve the convergence, an acceleration parameter, Γ, is implemented in the classical full-multigrid procedure. It is shown that an optimal value of Γ = 3.75 minimizes the number of iterations needed for convergence. Numerical results are presented and compared with available investigations for an 8:1 differentially heated enclosure and a square heated cavity. Solutions for Prandtl number Pr = 0.71, Rayleigh number Ra = 3.4 × 105 for the 8:1 heated enclosure, and 105 ≤ Ra ≤ 109 for the square cavity are presented and show excellent agreement.

Notes

a Estimated.

a Estimated.

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