Rayleigh-Bénard对流的高Rayleigh数变分多尺度大涡模拟
High Rayleigh number variational multiscale large eddy simulations of Rayleigh-Bénard Convection
摘要：
采用变分多尺度（VMS）方法，建立了瑞利-贝纳德对流的基于残差的VMS大涡模拟（LES）模式。由此产生的模型是一个混合模型，其中包括VMS模型和涡粘性模型。本文采用壁面自适应局部涡粘模型（WALE）作为涡粘模型。在有限元程序Drekar中实现了新的LES模型。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$Pr = 7$进行。考虑了两个领域：纵横比为2的二维区域，其中流体被限制在两个平行板之间，以及纵横比为$1/4$的三维圆柱体。从VMS结果的努塞尔数进行了比较，对三维直接数值模拟和实验。在所有情况下，VMS的结果与现有文献吻合良好。
英文摘要：
The variational multiscale (VMS) formulation is used to develop residual-based VMS large eddy simulation (LES) models for Rayleigh-Bénard 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.
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