Smoothed particle hydrodynamics for modeling nutrient transport in shallow lakes

• A novel SWE–SPH NSMI model was developed for water quality and pollutant transport evaluation. • Applications in 1D and 2D benchmark studies captured key seasonal dynamics through temperature effect. • Xuanwu Lake case study showed errors < 3.5 % in water level and < 9 % in total nitrogen/total phosphorus. This study aimed to investigate the spatiotemporal characteristics of water quality in shallow lakes and simulate complex pollutant transport by developing the Nutrient Simulation Modules I (NSMI) based on the SWE-SPH (Shallow Water Equation, SWE; Smoothed Particle Hydrodynamics, SPH) method. This study innovatively extends the SWE-SPH method to water environment modeling by coupling it with a modularly designed NSMI water quality model. This design facilitates the customization according to different research and engineering requirements and supports the integration of additional water environment processes, therefore enabling more efficient multi-physics simulations. The accuracy and stability of the model were validated through a one-dimensional (1D) steady flow, two-dimensional (2D) idealized bathymetry, and a water diversion project in Xuanwu Lake. In 1D validations, the NSMI simulations of Carbonaceous Biochemical Oxygen Demand and Dissolved Oxygen closely aligned with both the Streeter-Phelps (SP) model and analytical solutions. Furthermore, in the Bohai Bay case, the predictions of the NSMI model in organic nitrogen and phosphorus concentration changes aligned well under varying temperature conditions. For the Xuanwu Lake application, the simulation relative error of the NSMI model for water level was <3.5 %, while the total nitrogen and phosphorus errors were 6.46 % and 8.96 %, respectively. The comprehensive error analysis indicates that the SWE-SPH NSMI model is highly accurate and adaptable for water quality simulation. The findings confirm its suitability for application in shallow lake ecosystems, offering valuable insights for the lake water environmental engineering.