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

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.