Advances in Modelling and Numerical Simulation of Sediment Transport in Shallow Water Flows

A class of novel models for sediment transport, for which multilayer fluid models are combined with a multi-sediment method, is developed and analysed. Turbulent effects in both water flow and sediment transport are also accounted for in the presented models. The aim of this thesis is to advance fast and accurate techniques that overcome some of the assumptions limiting current sediment transport models of this type. To the best knowledge of the author, this is the first time a two-dimensional multilayer model has been used for modelling and simulation of sediment transport. Sediment transport methods using the Shallow Water Equations (SWEs) are reviewed and some of the limiting assumptions are highlighted. Fast methods for modelling sediment transport with multiple sediments are developed in both one space dimension (1D) and two space dimensions (2D). A new formulation for multilayer SWEs is expanded in 1D and 2D to also include sediment transport. Turbulence modelling with the well-established k-epsilon$ model is also evolved to deal with a multilayer formulation. Each development is tested by itself to quantify its effects and then combined with all the other developments to create the final model. Two second-order accurate solvers are in this thesis: namely a Roe-type solver and a novel Eulerian-Lagrangian formulation. The latter is favoured and is used to solve the complete model, including turbulence and multiple sediment types. This creates a fast and easy-to-implement method that can handle complex flows and irregular bed topographies. The methods are compared to other shallow water systems along with Navier-Stokes results and data obtained from experiments performed in the Department of Engineering at Durham University. Overall, this thesis provides interesting and highly applicable results that add a new avenue of applications to sediment transport in shallow water flows.