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

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 $Ra=10^8$ 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.

arXiv comment12 pages, 5 figures

References in corpus (9)

• Large scale dynamics in turbulent Rayleigh-Benard convection
• Scaling in thermal convection: A unifying theory
• Boundary layer structure in turbulent thermal convection and its consequences for the required numerical resolution
• Radial boundary layer structure and Nusselt number in Rayleigh-Benard convection
• The unifying theory of scaling in thermal convection: The updated prefactors
• Prandtl and Rayleigh number dependence of heat transport in high Rayleigh number thermal convection
• AFiD-GPU: a versatile Navier-Stokes Solver for Wall-Bounded Turbulent Flows on GPU Clusters
• Resolving the fine-scale structure in turbulent Rayleigh-Benard convection
• Thermal Boundary Layer Equation for Turbulent Rayleigh-Benard Convection

Cited by in corpus (26)

• A FFT-based finite-difference solver for massively-parallel direct numerical simulations of turbulent flows
• Lattice Boltzmann simulations of three-dimensional thermal convective flows at high Rayleigh number
• Multiple states in turbulent large-aspect ratio thermal convection: What determines the number of convection rolls?
• Flow organization and heat transfer in turbulent wall sheared thermal convection
• Boundary Zonal Flow in Rotating Turbulent Rayleigh-Bénard Convection
• Elliptical Instability and Multi-Roll Flow Modes of the Large-scale Circulation in Confined Turbulent Rayleigh-Bénard Convection
• Correlation of internal flow structure with heat transfer efficiency in turbulent Rayleigh-Bénard convection
• Inclined turbulent thermal convection in liquid sodium
• The effect of Prandtl number on turbulent sheared thermal convection
• Boundary zonal flows in rapidly rotating turbulent thermal convection
• Large eddy simulations of turbulent thermal convection using renormalized viscosity and thermal diffusivity
• Wall-sheared thermal convection: heat transfer enhancement and turbulence relaminarization
• Large-eddy simulation of Rayleigh-Bénard convection at extreme Rayleigh numbers
• Particle transport and deposition in wall-sheared thermal turbulence
• Temporal modulation on mixed convection in turbulent channels
• Lyapunov Exponents of Two Stochastic Lorenz 63 Systems
• Oscillatory large-scale circulation in liquid-metal thermal convection and its structural unit
• Optimal heat transport in rotating Rayleigh-Bénard convection at large Rayleigh numbers
• Critical Prandtl number for Heat Transfer Enhancement in Rotating Convection
• Data-driven spectral turbulence modeling for Rayleigh-Bénard convection
• Performance of parallel-in-time integration for Rayleigh Bénard Convection
• Determining a priori a RANS model's applicable range via global epistemic uncertainty quantification
• Data-driven identification of the spatio-temporal structure of turbulent flows by streaming Dynamic Mode Decomposition
• Pseudo-spectral solver versus grid-based solver: A quantitative accuracy test using GMHD3D and PLUTO4.4
• Flow organization in laterally unconfined Rayleigh-Bénard turbulence
• Learning to traverse convective flows at moderate to high Rayleigh numbers