Influence of Erodible Beds on Shallow Water Hydrodynamics during Flood Events

Flooding has become the most common environmental hazard, causing casualties and severe economic losses. Mathematical models are a useful tool for flood control, and current computational resources let us simulate flood events with two-dimensional (2D) approaches. An open question is whether bed erosion must be accounted for when it comes to simulating flood events. In this paper we answer this question through numerical simulations using the 2D depth-averaged shallow-water equations. We analyze the effect of mobile beds on the flow patterns during flood events. We focus on channel confluences where water flow and sediment mobilization have a marked 2D behavior. We validate our numerical simulations with laboratory experiments of erodible beds with satisfactory results. Moreover, our sensitivity analysis indicates that the bed roughness model has a great influence on the simulated erosion and deposition patterns. We simulate the sediment transport and its influence on the water flow in a real river confluence during flood events. Our simulations show that the erosion and deposition processes play an important role on the water depth and flow velocity patterns. Accounting for the mobile bed leads to smoother water depth and velocity fields, as abrupt fields for the non-erodible model emerge from the irregular bed topography. Our study highlights the importance of accounting for erosion in the simulation of flood events, and the impact on the water depth and velocity fields.

Efficient computational models for shallow water flows over multilayer erodible beds

Purpose The purpose of this paper is to present a new numerical model for shallow water flows over heterogeneous sedimentary layers. It is already several years since the single-layered models have been used to model shallow water flows over erodible beds. Although such models present a real opportunity for shallow water flows over movable beds, this paper is the first to propose a multilayered solver for this class of flow problems. Design/methodology/approach Multilayered beds formed with different erodible soils are considered in this study. The governing equations consist of the well-established shallow water equations for the flow, a transport equation for the suspended sediments, an Exner-type equation for the bed load and a set of empirical equations for erosion and deposition terms. For the numerical solution of the coupled system, the authors consider a non-homogeneous Riemann solver equipped with interface-tracking tools to resolve discontinuous soil properties in the multilayered bed. The solver consists of a predictor stage for the discretization of gradient terms and a corrector stage for the treatment of source terms. Findings This paper reveals that modeling shallow water flows over multilayered sedimentary topography can be achieved by using a coupled system of partial differential equations governing sediment transport. The obtained results demonstrate that the proposed numerical model preserves the conservation property, and it provides accurate results, avoiding numerical oscillations and numerical dissipation in the approximated solutions. Originality/value A novel implementation of sediment handling is presented where both averaged and separate values for sediment species are used to ensure speed and precision in the simulations.