Comparison of computational codes for direct numerical simulations of turbulent Rayleigh-B\'enard convection

TL;DR

This study compares various computational codes for simulating turbulent Rayleigh-Bénard convection, highlighting differences in efficiency and resolution quality, and emphasizing the importance of detailed flow diagnostics beyond heat transfer metrics.

Contribution

It provides a systematic comparison of specialized and general-purpose numerical codes for RB convection, demonstrating the superior efficiency of dedicated codes and the limitations of using Nusselt number alone for solution quality assessment.

Findings

Specialized codes outperform general-purpose codes by an order of magnitude.

Nusselt number convergence does not guarantee flow resolution accuracy.

Under-resolved simulations can produce accurate heat transfer predictions but miss flow details.

Abstract

Computational codes for direct numerical simulations of Rayleigh-B\'enard (RB) convection are compared in terms of computational cost and quality of the solution. As a benchmark case, RB convection at $Ra=10^8$ 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.