This paper presents a Weakly Compressible Smoothed Particle Hydrodynamics (WCSPH) method solving the two-equation Reynolds-Averaged Navier-Stokes (RANS) model {for the turbulent wall-bounded flows with or without flow separation. The inconsistency between the Lagrangian nature of the SPH and RANS model, primarily caused by intense shearing and near-wall discontinuities, is firstly revealed and addressed by the improved mainstream and near-wall treatments, respectively.}The mainstream treatments, including Adaptive Riemann-eddy Dissipation (ARD) and { de-noised} transport velocity formulation, address dissipation incompatibility, turbulent kinetic energy disturbance and over-prediction issues. The near-wall treatments, such as the particle-based wall model realization, weighted near-wall compensation scheme, {and constant wall-normal spacing strategy}, improve the accuracy and stability of the adopted wall model, where the wall dummy particles are still used for future coupling of solid dynamics. Besides, to perform rigorous convergence tests, {a level-set-based Boundary-Offset Technique (BOT)} is developed to {ensure consistent wall-normal distance} across different resolutions. Several benchmark wall-bounded turbulent flow cases are simulated, including straight, mildly curved, strongly curved, Half Converging-Diverging (HCD) channels, and a fish-pass. The present method yields smoothed and reasonably accurate results, and, to the best of our knowledge, achieves for the first time satisfactory convergence of both velocity and turbulent kinetic energy in SPH-RANS simulations. The proposed method bridges particle-based and mesh-based RANS models, providing adaptability for other turbulence models and potential for turbulent fluid-structure interaction (FSI) simulations.

翻译：本文提出了一种弱可压缩光滑粒子流体动力学（WCSPH）方法，用于求解带或不带流动分离的湍流壁面流动的两方程雷诺平均纳维-斯托克斯（RANS）模型。首先揭示了SPH的拉格朗日特性与RANS模型之间的不一致性（主要由剧烈剪切和近壁面不连续性引起），并分别通过改进的主流区处理和近壁面处理加以解决。主流区处理方法，包括自适应黎曼-涡耗散（ARD）和去噪传输速度公式，解决了耗散不相容、湍动能扰动和过度预测问题。近壁面处理方法，如基于粒子的壁面模型实现、加权近壁补偿方案和恒定壁面法向间距策略，提高了所采用壁面模型的精度和稳定性，其中壁面虚拟粒子仍保留用于未来固体动力学的耦合。此外，为进行严格的收敛性测试，开发了一种基于水平集的边界偏移技术（BOT），以确保在不同分辨率下保持一致的壁面法向距离。模拟了多个基准壁面湍流流动案例，包括直通道、轻度弯曲通道、强烈弯曲通道、半收敛-扩张（HCD）通道以及鱼道。本方法获得了平滑且合理准确的结果，并且据我们所知，首次在SPH-RANS模拟中实现了速度和湍动能均令人满意的收敛性。所提出的方法架起了基于粒子和基于网格的RANS模型之间的桥梁，为其他湍流模型提供了适应性，并具备用于湍流流固耦合（FSI）模拟的潜力。