Computational codes for direct numerical simulations of Rayleigh–Bénard (RB) convection are compared in terms of computational cost and quality of the solution. As a benchmark case, RB convection at Ra=108 and Pr=1 in a periodic domain, in cubic and cylindrical containers is considered. A dedicated second-order finite-difference code (AFID/RBFLOW) and a specialized fourth-order finite-volume code (GOLDFISH) are compared with a general purpose finite-volume approach (OPENFOAM) and a general purpose spectral-element code (NEK5000). Reassuringly, all codes provide predictions of the average heat transfer that converge to the same values. The computational costs, however, are found to differ considerably. The specialized codes AFID/RBFLOW and GOLDFISH are found to excel in efficiency, outperforming the general purpose flow solvers NEK5000 and OPENFOAM by an order of magnitude with an error on the Nusselt number Nu below 5%. However, we find that Nu alone is not sufficient to assess the quality of the numerical results: in fact, instantaneous snapshots of the temperature field from a near wall region obtained for deliberately under-resolved simulations using NEK5000 clearly indicate inadequate flow resolution even when Nu is converged. Overall, dedicated special purpose codes for RB convection are found to be more efficient than general purpose codes.
Bibliographical noteNOTICE: this is the author’s version of a work that was accepted for publication in Computers & Fluids. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made
to this work since it was submitted for publication. A definitive version was subsequently published in Computers & Fluids, 166, (2018) DOI: 10.1016/j.compfluid.2018.01.010
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- Direct Numerical Simulations
- Rayleigh-Bénard convection
- heat transfer