This numerical study based on high-order finite-difference schemes presents LES-NWR (Large Eddy Simulation with near-wall resolution) of turbulent channel flows up to $R{e}_{\tau }=5200$ using non-explicit approaches for which numerical dissipation is introduced via the discretisation of viscous terms of the Navier-Stokes equations. These models are cheaper than explicit LES models as no extra terms are needed in the equations to account for the contribution of the unresolved scales. The Approximate Deconvolution Method with Relaxation Term (ADM-RT) approach is also assessed and the present LES data are compared with reference Direct Numerical Simulations (DNS) data for first and second order moments as well as for the turbulent kinetic energy budget. Even if the viscous sublayer is not resolved, the proposed non-explicit LES approaches are in excellent agreement with the reference DNS data and to a certain extent with the ADM-RT model, for a fraction of the cost of the DNS. The proposed non-explicit models, for which the possibility to locally adjust the added numerical dissipation is investigated, are straightforward to implement and come with a negligible additional computational cost while the ADM-RT model is $30\%$ more expensive than the non-explicit models.The parameters of the models are defined before the simulations and no modifications of the parameters are needed when the Reynolds number and the mesh resolution are changed. It is shown that a modulation of the magnitude of the numerical dissipation in time and in space is not necessarily needed, at least for the mesh resolutions and Reynolds numbers considered in the present study. The main conclusion is that non-explicit models can replace advantageously explicit models when high-order finite-difference methods are used. They can generate accurate LES-NWR of turbulent channel flows over a wide range of Reynolds numbers at a fraction of a cost of DNS.

这项基于高阶有限差分格式的数值研究提出了湍流通道流动的 LES-NWR（具有近壁分辨率的大涡模拟） $\mathrm{电阻}{\mathrm{电子}}_{\tau }=5200$使用非显式方法，通过Navier-Stokes方程的粘性项的离散化引入数值耗散。这些模型比显式 LES 模型便宜，因为方程中不需要额外的项来说明未解析尺度的贡献。还评估了具有松弛项的近似解卷积方法 (ADM-RT) 方法，并将当前的 LES 数据与一阶和二阶矩以及湍流动能预算的参考直接数值模拟 (DNS) 数据进行比较。即使没有解决粘性子层，所提出的非显式 LES 方法与参考 DNS 数据非常一致，并且在一定程度上与 ADM-RT 模型非常一致，而成本仅为 DNS 的一小部分。建议的非显式模型，$30\%$比非显式模型更昂贵。模型的参数是在模拟之前定义的，当雷诺数和网格分辨率改变时不需要修改参数。结果表明，不一定需要对时间和空间中的数值耗散幅度进行调制，至少对于本研究中考虑的网格分辨率和雷诺数而言。主要结论是，当使用高阶有限差分方法时，非显式模型可以有利地替代显式模型。它们可以在很宽的雷诺数范围内生成湍流通道流的准确 LES-NWR，而成本只是 DNS 的一小部分。