The discrete element (roughness) method developed a few decades ago is revisited using the double-averaging technique applied to the Navier-Stokes equation. A $k-\omega$-based DANS turbulence model is thus derived to be able to account for roughness effects. Several closure relations are proposed to model all terms induced by the use of the double averaging. The momentum and energy equations are considered in their simplified forms adapted to a 1D channel code in accordance with the DNS results used for the validation. To reconcile the discrete element (roughness) method with the double-averaged Navier-Stokes equations the notion of representative elementary roughness is introduced. A large validation dataset coming from various DNS configurations is then used to assess the predictions of the proposed DANS model. Yet not fully complete, especially regarding the dispersive terms due to a lack of data, the performed validation already proves the overall excellent behaviour of the DANS model and demonstrates the relevance of the present methodology based on the representative elementary roughness.

使用应用于 Navier-Stokes 方程的双平均技术重新审视了几十年前开发的离散元素（粗糙度）方法。一种$克-\omega$基于 DANS 的湍流模型由此推导出来能够解释粗糙度影响。提出了几种闭合关系来模拟由使用双重平均引起的所有项。根据用于验证的 DNS 结果，动量和能量方程以适应一维通道代码的简化形式被考虑。为了使离散元（粗糙度）方法与双平均 Navier-Stokes 方程相协调，引入了代表性基本粗糙度的概念。然后使用来自各种 DNS 配置的大型验证数据集来评估提议的 DANS 模型的预测。但并不完全完整，尤其是由于缺乏数据而导致的离散项，