Smoothed Particle Hydrodynamics Simulation of Flow and Contaminant Transport over Terrain and Stream

Accumulation of contaminants on urban impervious surfaces poses a threat of contaminating downstream water bodies during rainfall-runoff events. Conventional grid approaches are used to model the transport and spread of these components individually. Whereas available watershed models either predominantly centralize on runoff processes or provide simplified river channel sections. Smoothed Particle Hydrodynamics (SPH) is introduced as a meshless method to demonstrate and model the complexity of precipitation, surface runoff, contaminant transport and channel flow. With the representation of fluid and contaminant as particles, the spatial and temporal variation of contaminants can be easily tracked and traced notably of infinitesimal amount which represents a difficult feat in Eulerian grid-based method. The ability of the proposed SPH model to capture variations of contaminants can benefit existing hydrological models which approximate washed-off contaminants only as summation onto nodes. Weakly Compressible SPH (WCSPH) represents the form adopted for fluid motion with the consideration of turbulence effects. The Lagrangian nature of WCSPH allows advection transport of contaminants to be accurately represented. Concentration field of contaminants is influenced by diffusion transport mechanism which is formulated by SPH approximation. The functionality of SPH diffusion formulation is demonstrated under verification cases of one- and multiple- dimensions, with a focus on still water cases. The effects of kernel functions and smoothing length factors are studied on the convergence of SPH diffusion formulation with analytical solutions. It is indicated that smoothing length factor not exceeding unity showed increasing convergence. The verified SPH model is applied in model and real topography setting with elevation data extracted from Advanced Spaceborne Thermal Emission and Reflection Radiometer Global Digital Elevation Model (ASTER GDEM). Boundary particles allow fine depiction of terrain surface and features as well as river channel geometry. The application highlights the capability of SPH in describing the transport path of contaminants over basic and complex topography under advection-dominated, advection-diffusion and diffusion-dominated conditions.