This article analyses the simulation methodology for wall-modeled large-eddy simulations using solvers based on the spectral-element method (SEM). To that end, algebraic wall modeling is implemented in the popular SEM solver Nek5000. It is combined with explicit subgrid-scale (SGS) modeling, which is shown to perform better than the high-frequency filtering traditionally used with the SEM. In particular, the Vreman model exhibits a good balance in terms stabilizing the simulations, yet retaining good resolution of the turbulent scales. Some difficulties associated with SEM simulations on relatively coarse grids are also revealed: jumps in derivatives across element boundaries, lack of convergence for weakly formulated boundary conditions, and the necessity for the SGS model as a damper for high-frequency modes. In spite of these, state-of-the-art accuracy is achieved for turbulent channel flow and flat-plate turbulent boundary layer flow cases, proving the SEM to be a an excellent numerical framework for massively-parallel high-order WMLES.

翻译：本文分析了基于谱元法求解器的壁面建模大涡模拟的模拟方法。为此，在流行的谱元法求解器Nek5000中实现了代数壁面建模。该方法与显式亚格子尺度建模相结合，研究表明其性能优于传统与谱元法结合使用的高频滤波。特别地，Vreman模型在稳定模拟的同时保留了湍流尺度的良好分辨率，表现出良好的平衡性。研究还揭示了在相对粗糙网格上进行谱元法模拟时的一些困难：单元边界处导数的跳跃、弱形式边界条件缺乏收敛性，以及亚格子尺度模型作为高频模态阻尼器的必要性。尽管如此，在湍流槽道流和平板湍流边界层流案例中仍实现了最先进的精度，证明谱元法是用于大规模并行高阶壁面建模大涡模拟的卓越数值框架。