A novel approach for modelling stress fields induced by shallow water flows on movable beds

Abstract

Sediment transport in shallow waters occurs when the water flows over the bed for which the amount of generated sediments can be determined from the transport mechanism caused by the consequent flow. Recently, investigating the bedload and sediment transport using numerical models has been rapidly increased and various techniques have been developed to quantify both the hydrodynamics and morphodynamics in these systems but not the stress distributions in the deformed beds. In the present study, we propose a novel class of coupled finite element/finite volume methods to resolve the effect of sedimentary shallow water flows on the internal stresses in bed topographies. The coupled model employs the linear elasticity for the bed and the nonlinear shallow water equations for the water flow. Suspended sediments are also taken into consideration in this study, and impacts of the erosion and deposition are modelled using well-established empirical equations. The linear equations of elasticity are solved numerically using a finite element approach on unstructured meshes, while the nonlinear shallow water equations are numerically solved using a well-balanced finite volume method. We also introduce an accurate algorithm to sample forces on the interface between the water flow and bed topography to be implemented as coupling conditions between finite volume cells and finite element nodes. Distributions of stress fields in the bed topography due to erosion and sediment transport by shallow water flows are presented for several test examples. The novel coupled model is stable, efficient, accurate, well-balanced and it can be used for solving complex geometries. In addition, the proposed approach offers significant advancements in understanding sedimentary processes in shallow water environments and the induced underground stresses as a result of these processes.