In this paper, a slip-wall model for large eddy simulation (LES) is improved and implemented in an immersed boundary method named the local domain-free discretization (DFD) method. Considering that the matching location may be in the viscous sublayer, the physics-based interpretation of a Robin-type wall closure is complemented. Then, the slip-wall wall model is improved, in which the slip length is redefined and the Robin boundary condition is imposed at the solid wall. The improved slip-wall model is implemented in the local DFD method to evaluated the tangential velocity at an exterior dependent node, and then the requirement on high resolution of boundary layers can be alleviated. The non-equilibrium effects are accounted for by adding an explicit correction to the wall shear stress. In order to validate the present wall-modeled LES/DFD method, a series of turbulent channel flows at various Reynolds numbers, the flow over periodic hills and the flows over a NACA 4412 airfoil at a high Reynolds number are simulated. The predicted results agree well with the referenced experimental data and numerical results. Especially, the results of the separated flow over the airfoil at a near-stall condition demonstrate the performance of the present wall-modeled LES/DFD method for complex flows.

中文翻译：

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改进的大涡模拟滑壁模型及其局部无域离散化方法的实现

本文对大涡模拟（LES）的滑壁模型进行了改进，并以浸入边界方法（称为局部无域离散（DFD）方法）实现。考虑到匹配位置可能在粘性子层中，补充了罗宾型壁封闭的基于物理的解释。然后，对滑移壁模型进行了改进，重新定义了滑移长度，并在实体壁上施加了Robin边界条件。改进的滑壁模型在局部DFD方法中实现，以评估外部相关节点处的切向速度，从而可以减轻对边界层高分辨率的要求。通过对壁剪应力添加显式修正来解释非平衡效应。为了验证当前的壁建模 LES/DFD 方法，模拟了一系列不同雷诺数下的湍流通道流、周期性山丘上的流以及高雷诺数下 NACA 4412 翼型上的流。预测结果与参考实验数据和数值结果非常吻合。特别是，在近失速条件下翼型上的分离流的结果证明了当前的壁模型 LES/DFD 方法对于复杂流的性能。