A new 2D ESPH bedload sediment transport model for rapidly varied flows over mobile beds

A 2D Eulerian meshless bedload sediment transport model is developed using smoothed particle hydrodynamics (SPH) to simulate rapidly varied flows over mobile beds. In the developed model, we adopt a weakly coupled numerical approach to explicitly solve the governing equations, including 2D shallow water equations for fluid flow motion and the Exner equation for bed sediment movement at the same time step. A defined virtual bedload velocity in a weakly coupled approach is involved in the calculation of time step sizes. However, nonphysical virtual bedload velocities, which often occur in cases with nearly flat beds, require extremely small time step sizes. A formulation of the lower and upper bounds of information propagation speeds for an HLLC approximate Riemann solver is thus proposed to remedy the problem. Four case studies involving dam break flows in prismatic and erodible channels, knickpoint migration, dam erosion due to overtopping flow and dam-break flow in an erodible channel with an abrupt expansion are adopted to validate the developed model. In addition, to compare the performances of different particle interaction configurations under Cartesian uniform particle arrangements, four and eight interacting particles are obtained by changing the smoothing length. Against the measured results, the case of eight interacting particles shows more accurate predictions of erosion peaks along the measured cross-sections because the lateral flows are significant. The good agreement between the simulated and measured results shows that the developed 2D Eulerian SPH bedload sediment transport model with eight interacting particles is well suited for simulating complicated flow-induced bed erosion.