Depth-averaged models are commonly employed for the simulation of environmental flows in river and coastal regions, as well as shallow flows within hydraulic structures. This paper presents a meshfree method for solving depth-averaged turbulence model, emphasizing the incorporation of wall functions. In order to assess the performance of the model, several flows are modelled and the numerical results are compared with experimental data and other numerical results. Comparative analyses against experimental data and existing numerical results provide a rigorous evaluation framework. The results show that the model's robustness and accuracy in capturing turbulent flow dynamics, particularly in contexts pertinent to river and coastal engineering. This study contributes to advancing computational techniques for hydraulic engineering applications, offering insights valuable for both research and practical implementation.