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.

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