The variational multiscale (VMS) formulation is used to develop residual-based VMS large eddy simulation (LES) models for Rayleigh-Benard convection. The resulting model is a mixed model that incorporates the VMS model and an eddy viscosity model. The Wall-Adapting Local Eddy-viscosity (WALE) model is used as the eddy viscosity model in this work. The new LES models were implemented in the finite element code Drekar. Simulations are performed using continuous, piecewise linear finite elements. The simulations ranged from $Ra = 10^6$ to $Ra = 10^{14}$ and were conducted at $Pr = 1$ and $Pr = 7$. Two domains were considered: a two-dimensional domain of aspect ratio 2 with a fluid confined between two parallel plates and a three-dimensional cylinder of aspect ratio $1/4$. The Nusselt number from the VMS results is compared against three dimensional direct numerical simulations and experiments. In all cases, the VMS results are in good agreement with existing literature.

中文翻译：

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瑞利-贝纳德对流的高瑞利数变分多尺度大涡模拟

变分多尺度 (VMS) 公式用于为 Rayleigh-Benard 对流开发基于残差的 VMS 大涡模拟 (LES) 模型。得到的模型是一个混合模型，它结合了 VMS 模型和涡流粘度模型。Wall-Adapting Local Eddy-viscosity (WALE) 模型在这项工作中用作涡流粘度模型。新的 LES 模型在有限元代码 Drekar 中实现。使用连续的分段线性有限元进行模拟。模拟范围从 $Ra = 10^6$ 到 $Ra = 10^{14}$，并在 $Pr = 1$ 和 $Pr = 7$ 下进行。考虑了两个域：纵横比为 2 的二维域，流体限制在两个平行板之间，纵横比为 1/4 的三维圆柱体。来自 VMS 结果的 Nusselt 数与三维直接数值模拟和实验进行了比较。在所有情况下，VMS 结果与现有文献非常吻合。