We performed simulations of Rayleigh-Benárd convection (RBC) for very high $\mathrm{Ra}$ number, ${10}^9,{10}^{12},{10}^{13},{10}^{14}$ and ${10}^{16}$, thus beyond the reach of classical LES, by using an elliptic-relaxation hybrid RANS-LES (ER-HRL) model paired with a compound wall treatment that allows much coarser mesh resolution in the near wall region. The standard switching criterion used in the hybrid RANS-LES modeling based on wall distance is modified and linked to the local turbulence properties in order to sustain the modeled turbulence production in the RBC configuration. The proposed hybrid model successfully predicts the main integral and mean flow features at $\mathrm{Ra}={10}^9$ for which experimental and LES data exists. The Nusselt number obtained is closely following the power law correlation based on $0.307$ exponent up to $\mathrm{Ra}={10}^{13}$. For higher $\mathrm{Ra}$ number, the Nusselt number displays a $\mathrm{Ra}$-scaling behaviour that is consistent with the so-called ultimate regime, where $\mathrm{Nu}\approx {\mathrm{Ra}}^{1/2}$. Furthermore, unlike LES, the ER-HRL model provides generally good results even when using a very coarse mesh at high $\mathrm{Ra}$ number. The instantaneous three-dimensional fields reveal interesting features of the Rayleigh-Benárd convection at very high Ra number such as a strong correlation between instantaneous pressure and temperature fields, a major similarity of the flow structures in the near-wall region to those present in the impinging jet, existence of the superstructures and their tendency to cluster and localise with increasing $\mathrm{Ra}$ number. The simulations are performed with an in–house unstructured finite-volume code T-Flows, using second-order-accuracy discretisation schemes for space and time.

我们对瑞利-贝纳德对流（RBC）进行了非常高的模拟 $\mathrm{镭}$ 数字， ${10}^9，{10}^{12}，{10}^{13}，{10}^{14}$ 和 ${10}^{16}$，因此，通过使用椭圆松弛混合RANS-LES（ER-HRL）模型与复合墙面处理配对使用，可以超出近邻区域的网格分辨率，从而超出了经典LES的范围。修改了基于壁距的混合RANS-LES建模中使用的标准转换标准，并将其链接到局部湍流特性，以便在RBC配置中维持建模的湍流产生。提出的混合模型成功地预测了主要积分和平均流量特征$\mathrm{镭}={10}^9$存在实验数据和LES数据。所获得的Nusselt数严格遵循基于以下公式的幂定律相关性$0.307$ 指数高达 $\mathrm{镭}={10}^{13}$。为了更高$\mathrm{镭}$ 数字，Nusselt数字显示一个 $\mathrm{镭}$与所谓的最终制度相一致的按比例缩放行为，其中 $\mathrm{怒江}\approx {\mathrm{镭}}^{\mathrm{1个}/\mathrm{2个}}$。此外，与LES不同，ER-HRL模型即使在高密度下使用非常粗糙的网格时也能提供良好的结果$\mathrm{镭}$数字。瞬时三维场揭示了在非常高的Ra值下Rayleigh-Benárd对流的有趣特征，例如瞬时压力和温度场之间的强相关性，近壁区域中流动结构的主要相似性。撞击射流，上部结构的存在及其聚集和局部化的趋势$\mathrm{镭}$数字。使用内部非结构化有限体积代码T-Flows进行仿真，并使用针对空间和时间的二阶精度离散化方案。