Modeling 2D swash zone hydro/morphodynamics using discontinuous Galerkin finite element method

This PhD study aims to develop a new robust and efficient 2D numerical coupled hydro/morphodynamics model for general swash zone simulation. Non-linear shallow water equations (NSWEs) are used for describing the swash zone hydrodynamics, while a modified advection diffusion equation (ADE) is used for suspended sediment transport simulation, and an Exner type equation is used for bed change simulation. The Discontinuous Galerkin finite element method (DG-FEM) is used for solving this system of governing equations. However, to be able to simulate general swash zone processes, absorbing generating boundary condition is implemented, as well as a new efficient wet/dry treatment is developed. Even though, solving the fully coupled NSWEs and bed change equation using DG-FEM is very difficult, solving the weakly coupled system was not in a strait forward manner. Three different methods using two different approaches are tested, nonetheless, none of them offered satisfactory results for fast bed changing simulations. This motivated the development of a new approach (bed reconstruction method). The model hydrodynamics is verified against analytical solution of 1D dam-break over flat bed problem and compared against other FVM models for simulation 1D dam break over rectangular bump, cylindrical dam break, and partial dam break problems. The model showed very accurate predictions against the 1D analytical solution of the dam-break problem, and comparable results and robust performance against the other FVM models in the other cases, while the other FVM models were not very successful in simulating the dam-break over rectangular bump case, which is characterized by discontinuous bed. Then, the implementation of the absorbing generating boundary condition and the newly developed wet/dry treatment are verified against the well known periodic analytical solution of Carrier and Greenspan [1958] (CG58), 1D quasi analytical solution of shock trains on plane beach case of Antuono [2011], 1D analytical solution of single bore collapse on the shoreline of Peregrine and Williams [2001] (PW01), and the 2D periodic analytical solution of spinning water in elliptic bowl by Thacker [1981]. The model showed very accurate predictions in general for water depth, depth averaged velocities, and more important shoreline position, with less accurate predictions of the depth averaged velocities near the shoreline. Moreover, the model is tested for simulating very subtle swash zone process such as subharmonic edge wave excitation and development, showing very good performance. Which demonstrated the present model ability of simulating wide range of different swash zone flows. The ADE is verified against the analytical solutions of tracer transport in rectangular channel, and the analytical solution of suspended sediment transport under CG58 periodic event by Pritchard and Hogg [2003], showing very accurate results for simulating the transport of tracer, and good agreement with the analytical solution of Pritchard and Hogg [2003] for simulating suspended sediment entrainment, advection, and deposition. The bed change equation is verified against the analytical solution of mobile dune under steady flow, dam-break over dry mobile bed, and the quasi analytical solution of single bore collapse over mobile plane beach. The model results are compared against Huynh et al. [2017] results for simulating a storm scale swash event. The comparison showed general good agreement with Huynh et al. [2017] results in the inner surf zone, and less accurate agreement in the swash zone. The present model showed very good and robust performance under wide range of different hydro/morphodynamic tests, which motivated the investigation into swash zone morphodynmics. The model is used to investigate the beach cusp formation. The model hydrodynamics and morphodynamics results were first compared against Dodd et al. [2008] results. Then, the model is used to study the effect of suspended sediment transport and sediment motion threshold on the development of the beach cusps. In addition, a sensitivity analysis for the effect of the bed friction and beach sand grains size on the beach cusp formation is carried out. The model predictions showed that the bed friction is a very important factor for both beach cusps evolution and sustainability. It also showed that the suspended sediment transport offers a negative feedback mechanism for beach cusp formation, while the motion threshold offers a positive feedback mechanism. And confirmed that the beach cusps are more likely to be present in coarser sand beaches