Two-dimensional numerical modelling of shallow water flows over multilayer movable beds

Rowan, Thomas; Seaid, Mohammed

Abstract

The two-dimensional modelling of shallow water flows over multi-sediment erodible beds is presented. A novel approach is developed for the treatment of multiple sediment types in morphodynamics. The governing equations include the two-dimensional shallow water equations for hydrodynamics, an Exner-type equation for morphodynamics, a two-dimensional transport equation for the suspended sediments, and a set of empirical equations for entrainment and deposition. Multilayer sedimentary beds are formed of different erodible soils with sediment properties and new exchange conditions between the bed layers are developed for the model. The coupled equations yield a hyperbolic system of balance laws with source terms. As a numerical solver for the system, we implement a fast finite volume characteristics method. The numerical fluxes are reconstructed using the method of characteristics which employs projection techniques. The proposed finite volume solver is simple to implement, satisfies the conservation property and can be used for two-dimensional sediment transport problems in non-homogeneous isotropic beds without need of complicated three-dimensional equations. To assess the performance of the proposed models, we present numerical results for a wide variety of shallow water flows over sedimentary layers. Comparisons to experimental data for dam-break problems over movable beds are also included in this study.

Citation

Rowan, T., & Seaid, M. (2020). Two-dimensional numerical modelling of shallow water flows over multilayer movable beds. Applied Mathematical Modelling, 88, Article 474-497. https://doi.org/10.1016/j.apm.2020.06.052

• Journal Article Type: Article
• Acceptance Date: Jun 10, 2020
• Online Publication Date: Jul 8, 2020
• Publication Date: 2020-12
• Deposit Date: Oct 26, 2021
• Publicly Available Date: Nov 13, 2024
• Journal: Applied Mathematical Modelling
• Print ISSN: 0307-904X
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 88
• Article Number: 474-497
• DOI: https://doi.org/10.1016/j.apm.2020.06.052
• Public URL: https://durham-repository.worktribe.com/output/1230124