A systematic numerical study of three-dimensional natural convection of air in a differentially heated cubical cavity with Rayleigh number ($Ra$) up to $10^{10}$ is performed by using the recently developed coupled discrete unified gas-kinetic scheme. It is found that temperature and velocity boundary layers are developed adjacent to the isothermal walls, and become thinner as $Ra$ increases, while no apparent boundary layer appears near adiabatic walls. Also, the lateral adiabatic walls apparently suppress the convection in the cavity, however, the effect on overall heat transfer decreases with increasing $Ra$. Moreover, the detailed data of some specific important characteristic quantities is first presented for the cases of high $Ra$ (up to $10^{10}$) . An exponential scaling law between the Nusselt number and $Ra$ is also found for $Ra$ from $10^3$ to $10^{10}$ for the first time, which is also consistent with the available numerical and experimental data at several specific values of $Ra$.
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机译：通过使用最近开发的耦合离散统一气体动力学方案，对瑞利数（$ Ra $）高达$ 10 ^ {10} $的差热立方腔中空气的三维自然对流进行了系统的数值研究。发现温度和速度边界层在等温壁附近形成，并且随着$ Ra $的增加而变薄，而绝热壁附近没有明显的边界层出现。同样，绝热侧壁明显地抑制了空腔中的对流，但是，随着总热量的增加，对总传热的影响减小。此外，首先针对$ Ra $（最高$ 10 ^ {10} $）的情况提供一些特定的重要特征量的详细数据。还首次发现了从$ 10 ^ 3 $到$ 10 ^ {10} $的Nusselt数和$ Ra $之间的指数缩放定律，这也与在某些特定情况下可用的数值和实验数据一致$ Ra $的值。
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