Research papersModeling rainfall-runoff processes using smoothed particle hydrodynamics with mass-varied particles

- Mass-varied particle is used in smoothed particle hydrodynamics for the first time.
- The smoothing length updating formula is modified according to new assumptions.
- The SPH-SWE method is successfully extended to model rainfall-runoff processes.

In this study, a novel treatment of adopting mass-varied particles in smoothed particle hydrodynamics (SPH) is proposed to solve the shallow water equations (SWEs) and model the rainfall-runoff process. Since SWEs have depth-averaged or cross-section-averaged features, there is no sufficient dimension to add rainfall particles. Thus, SPH-SWE methods have focused on modeling discharge flows in open channels or floodplains without rainfall. With the proposed treatment, the application of SPH-SWEs can be extended to rainfall-runoff processes in watersheds. First, the numerical procedures associated with using mass-varied particles in SPH-SWEs are introduced and derived. Then, numerical validations are conducted for three benchmark problems, including uniform rainfall over a 1D flat sloping channel, nonuniform rain falling over a 1D three-slope channel with different rainfall durations, and uniform rainfall over a 2D plot with complex topography. The simulated results indicate that the proposed treatment can avoid the necessity of a source term function of mass variation, and no additional particles are needed for the increase of mass. Rainfall-runoff processes can be well captured in the presence of hydraulic jumps, dry/wet bed flows, and supercritical/subcritical/transcritical flows. The proposed treatment using mass-varied particles was proven robust and reliable for modeling rainfall-runoff processes. It can provide a new alternative for investigating practical hydrological problems.