A novel Eulerian SPH shallow water model for 2D overland flow simulations

A 2D Eulerian meshless shallow water model based on smoothed particle hydrodynamics (SPH) is proposed to study overland flow. Rain on a dry bed to generate a runoff flow is one common hydraulic phenomenon. However, it is difficult for existing Lagrangian SPH shallow water models to present the flow because no computational particle exists on a dry bed. To overcome this difficulty, the Eulerian form of the 2D shallow water equations is used to describe flow behavior in the proposed model. An HLLC approximate Riemann solver is applied to calculate fluxes between two neighboring particles to smear out the instabilities caused by the discretization of the nonlinear convective term and the discontinuity of wet-dry beds. Additionally, we use a surface reconstruction method (SRM) to ensure that the proposed model has well-balanced and positivity-preserving properties. Bed friction and infiltration effects are also analytically considered. Eight case studies involving various overland flows with wet-dry transitions, rainfall, infiltration, bed friction and complex topography are adopted to test the proposed model capacity. The first-order convergence rate is obtained in the convergence analysis. Against the exact and measured results, in the analytical case studies, the relative root-mean-square errors of depth and velocity are approximately 0.02% to 0.3% and 1.3% to 1.7%, respectively. In the experimental case studies, the relative root-mean-square errors of depth and discharge (velocity) are approximately 3.8% and 1.2% to 6.1%, respectively. The good agreement demonstrates between the results shows the reliability of the proposed 2D Eulerian SPH shallow water model for real-world overland flows.