Comparison of computational codes for direct numerical simulations of turbulent Rayleigh–Bénard convection

Gijs L. Kooij; Mikhail A. Botchev; Edo M. A.  Frederix; Bernard J. Geurts; Susanne Horn; Detlef Lohse; Erwin P. van der Poel; Olga Shishkina; Richard J. A. M. Stevens; Roberto Verzicco

doi:10.1016/j.compfluid.2018.01.010

Comparison of computational codes for direct numerical simulations of turbulent Rayleigh–Bénard convection

Gijs L. Kooij, Mikhail A. Botchev, Edo M. A. Frederix, Bernard J. Geurts, Susanne Horn, Detlef Lohse, Erwin P. van der Poel, Olga Shishkina, Richard J. A. M. Stevens, Roberto Verzicco

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Abstract

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.

Original language	English
Pages (from-to)	1-8
Number of pages	8
Journal	Computers & Fluids
Volume	166
Early online date	31 Jan 2018
DOIs	https://doi.org/10.1016/j.compfluid.2018.01.010
Publication status	Published - 30 Apr 2018
Externally published	Yes

Bibliographical note

NOTICE: 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

© 2018, Elsevier. Licensed under the Creative Commons Attribution- NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/

Keywords

Direct Numerical Simulations
Rayleigh-Bénard convection
heat transfer

Access to Document

10.1016/j.compfluid.2018.01.010

Post-PrintAccepted author manuscript, 3.43 MBLicence: CC BY-NC-ND

Cite this

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title = "Comparison of computational codes for direct numerical simulations of turbulent Rayleigh–B{\'e}nard convection",

abstract = "Computational codes for direct numerical simulations of Rayleigh–B{\'e}nard (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.",

keywords = "Direct Numerical Simulations, Rayleigh-B{\'e}nard convection, heat transfer",

author = "Kooij, {Gijs L.} and Botchev, {Mikhail A.} and Frederix, {Edo M. A.} and Geurts, {Bernard J.} and Susanne Horn and Detlef Lohse and {van der Poel}, {Erwin P.} and Olga Shishkina and Stevens, {Richard J. A. M.} and Roberto Verzicco",

note = "NOTICE: this is the author{\textquoteright}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 {\textcopyright} 2018, Elsevier. Licensed under the Creative Commons Attribution- NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/",

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AU - Kooij, Gijs L.

AU - Botchev, Mikhail A.

AU - Frederix, Edo M. A.

AU - Geurts, Bernard J.

AU - Horn, Susanne

AU - Lohse, Detlef

AU - van der Poel, Erwin P.

AU - Shishkina, Olga

AU - Stevens, Richard J. A. M.

AU - Verzicco, Roberto

N1 - NOTICE: 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 © 2018, Elsevier. Licensed under the Creative Commons Attribution- NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/

PY - 2018/4/30

Y1 - 2018/4/30

N2 - 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.

AB - 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.

KW - Direct Numerical Simulations

KW - Rayleigh-Bénard convection

KW - heat transfer

U2 - 10.1016/j.compfluid.2018.01.010

DO - 10.1016/j.compfluid.2018.01.010

M3 - Article

SN - 0045-7930

VL - 166

SP - 1

EP - 8

JO - Computers & Fluids

JF - Computers & Fluids

ER -

Comparison of computational codes for direct numerical simulations of turbulent Rayleigh–Bénard convection

Abstract

Bibliographical note

Keywords

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