This work presents a new methodology in finite element to simulate, according to a controlled precision on an engineering value, steady turbulent flows. First, we developed a new implementation of Reynolds‐averaged Navier‐Stokes equations combined with $k-\omega$ SST turbulence model and automatic wall treatment. Then, to simulate these complex multiscale flows, spatial discretization is critical. It is still common for expert users to generate meshes manually since they can roughly anticipate the physics of the flow. However, this remains a difficult task, especially for a neophyte. A recent mesh adaptation methodology based on an adjoint sensitivity analysis allows generating automatically appropriate meshes for analysis of steady laminar flows. Here, we extended this work to turbulent flows. The presentation is limited to two‐dimensional (2D) to demonstrate the effectiveness of the approach without getting unnecessarily entangled in the implementation details. The methodology is validated on the classic 2D zero pressure gradient flat plate verification case at Re = 5 · 10⁶. Then, a more complex example is also presented: flow around multicomponent airfoil (30P30N, $\alpha =16.21^{\circ }$) at Re = 9 · 10⁶.

中文翻译：

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具有自动墙处理和基于伴随的网格自适应的k-ωSST的有限元实现

这项工作提出了一种新的有限元方法，可以根据工程值的受控精度来模拟稳定的湍流。首先，我们开发了结合了雷诺平均Navier-Stokes方程的新实现$ķ-\omega$SST湍流模型和自动墙面处理。然后，要模拟这些复杂的多尺度流，空间离散化至关重要。专家用户通常会手动生成网格，因为他们可以粗略地预测流的物理性质。但是，这仍然是一项艰巨的任务，特别是对于新手而言。基于伴随灵敏度分析的最新网格自适应方法允许自动生成适当的网格以分析稳定的层流。在这里，我们将这项工作扩展到湍流。该演示文稿仅限于二维（2D），以演示该方法的有效性，而不会不必要地纠缠于实现细节。该方法在Re的经典2D零压力梯度平板验证案例中得到了验证 = 5·10 ⁶。然后，还提供了一个更复杂的示例：围绕多组分机翼（30P30N，$\alpha =16。2{\mathrm{1个}}^{\circ }$）在Re  = 9·10 ⁶。