Toward DNS of the Ultimate Regime of Rayleigh-Bénard Convection

Stevens, R.J.A.M.; Lohse, D.; Verzicco, R.

doi:10.1007/978-3-030-42822-8_28

Publication 66 · Thermal convection

Toward DNS of the Ultimate Regime of Rayleigh-Bénard Convection

R.J.A.M. Stevens, D. Lohse, R. Verzicco, Direct and Large Eddy Simulation 12, ERCOFTAC Series 2019, volume 27, 215-224 (2020).

Main finding

Under the printed assumptions, the Cartesian and cylindrical formulas have a leading term linear in Ra; at fixed Gamma the cylindrical discretization uses asymptotically pi/2 times the Cartesian nodes. The displayed Ra=10^8, Pr=1 global heat-transfer data approach a common large-Gamma plateau for the two geometries.

Nusselt number against aspect ratio for Cartesian and cylindrical simulation domains — **How to read the figure.** Nusselt number against aspect ratio at Ra = 10^8 and Pr = 1, for periodic Cartesian and for cylindrical domains. Both approach the same plateau once the domain is wide enough, so geometry stops mattering for the global heat transport at large aspect ratio. That matters for cost: at fixed aspect ratio the cylindrical discretisation needs asymptotically pi/2 times as many nodes as the Cartesian one. Open the full-resolution figure. Figure 28.5. R.J.A.M. Stevens et al. (2020). No separate licence is stated here; consult the original publication and credited source before reuse.

Why this matters

Why simulating a more realistic or larger turbulent system can change both physics and cost.

Research context

This perspective combines published and preliminary data with mesh-count estimates. It frames slender cylindrical DNS as a feasible route toward a three-dimensional ultimate-regime transition; it does not itself demonstrate that transition.

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