Modeling Swash Zone Hydrodynamics Using Discontinuous Galerkin Finite-Element Method

Abstract

A 2D numerical model for the solution of the Nonlinear Shallow Water Equations (NSWEs) using the Discontinuous Galerkin Finite Element Method (DGFEM) is presented. A new adaptation of the thin film approach is developed for the wetting/drying treatment. The model is applied to a number of test cases that can be characterized as swash flows, or as cases that are particularly useful for swash flow modelling. The DGFEM model shows robustness and provides accurate predictions of water depth, velocities, and shoreline movement. For the case of bore collapse on a plane beach the model performs well against a state-of-the-art finite volume swash code. The new wetting/drying algorithm is tested against a previous algorithm within the same framework for simulating a solitary wave propagating on a beach with bottom friction, showing a noticeable improvement in the shoreline prediction. The model is also tested against a more subtle test case, including generation of subharmonic edge waves, in order to test the effectiveness of DGFEM in reproducing second order effects. The model simulates the excitation and development of the 1 Aboulatta, September 3, 2020 sub-harmonic edge waves when compared to the analytical solutions in the literature. Overall, it is shown here for the first time that the DGFEM technique can be used to simulate accurately a wide range of swash zone flows and therefore swash zone processes.

A laboratory study of the effect of varying beach slopes on bore-driven swash hydrodynamics

“…Bergsma et al (2019) carried out experimental measurements to analyze the hydrodynamic parameters at the collapse point and investigated the link between broken wave properties at bore collapse and wave runup. Recent studies have alternatively established numerical models to describe the hydrodynamic process (e.g., Guard and Baldock, 2007;Puleo et al, 2007;Kelly and Dodd, 2010;Mory et al, 2011;Deng et al, 2012;Jiang et al, 2013;Briganti et al, 2016;Hammeken and Simons, 2017;Kim et al, 2017;Aboulatta et al, 2020;Wu et al, 2020). The abovementioned studies show that successful efforts have been made to measure and simulate the hydrodynamics of swash flow, and these studies have provided us with an improved understanding of the hydrodynamic characteristics of the swash zone.…”