Number of nodes N (in a cylindrical cell of Γ = 0.5) and achievable flow Rayleigh number Ra versus the years for direct numerical simulations of RayleighBénard convection. Black squares for various data from the literature, blue bullets for simulations from our research group, big red bullet final goal for the ultimate regime simulation.

Number of nodes N (in a cylindrical cell of Γ = 0.5) and achievable flow Rayleigh number Ra versus the years for direct numerical simulations of RayleighBénard convection. Black squares for various data from the literature, blue bullets for simulations from our research group, big red bullet final goal for the ultimate regime simulation.

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In this contribution we have briefly introduced the problem of turbulent thermal convection with a particular look at its transition to the ultimate regime and the resolution requirements needed for the direct numerical simulation of this flow.

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Context 1
... a rectangular domain with Γ = 4 this Rayleigh number implies a mesh with N Car > 10 14 nodes that is clearly infeasible in the mid-term future. In a cylindrical cell of Γ = 0.5, however, it results N Cyl ≈ 10 12 nodes that could be achieved within the next five years (see figure 6). Indeed, we are already running simulations at Ra = 10 13 at Γ = 0.5 and even Ra = 10 14 at Γ = 0.25 with meshes of the order of 10 11 nodes (R. Stevens, Personal Communication) although we expect to tackle the ultimate regime only by the 'next generation' simulations. ...
Context 2
... a rectangular domain with Γ = 4 this Rayleigh number implies a mesh with N Car > 10 14 nodes that is clearly infeasible in the mid-term future. In a cylindrical cell of Γ = 0.5, however, it results N Cyl ≈ 10 12 nodes that could be achieved within the next five years (see figure 6). Indeed, we are already running simulations at Ra = 10 13 at Γ = 0.5 and even Ra = 10 14 at Γ = 0.25 with meshes of the order of 10 11 nodes (R. Stevens, Personal Communication) although we expect to tackle the ultimate regime only by the 'next generation' simulations. ...

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