Multi scale smoothed particle hydrodynamics using particle agglomeration for simulating rainfall-runoff processes

We present a novel particle based numerical method, which supports regions of particle agglomeration, for simulating water flow in hydrological applications. This is done to tackle the difficulties that arise while modeling due to diverse operation scales, both in space and time. In this study we aim to concentrate only on multiple spatial scales. Smoothed particle hydrodynamics (SPH) is a mesh free method and it enables the interactions of particles in different media, for example media with different porosities. We use a technique of agglomerating particles based on parameters like velocity and treat the agglomerated mass as a single particle. With the presented method, the SPH method can be extended to rainfall-runoff models with multi-phase soil properties. First, the numerical method associated with SPH to solve the shallow water equation (SWE) is introduced. Then the way in which the mass term is replaced during agglomeration is derived. Calculating the modified parameters of a newly agglomerated particle to satisfy the continuity criteria is also introduced and derived. In order to validate the method, benchmark cases that align with our target application with experimental data were chosen from literature study. These include, uniform rainfall falling on an one-dimension flat slope channel, non-uniform rainfall with different duration over an one-dimension flat slope. In order to explore the extent of method a three-dimension test case, where water particles are allowed to pass through a different medium stacked on top of one another with different porosity, is chosen. The three-dimension benchmark case is not inspired from a real time application like the one-dimension test cases, but the results can be scaled and deployed into a flood-forecasting simulation. Also, the proposed method was proven robust and the one-dimension test cases show good agreement with experimental results. The three-dimension test case shows decent improvement in computational time and can provide new possibilities for simulating practical hydrological applications.