A 2DH hybrid Boussinesq-NSWE solver for near-shore hydrodynamics

Abstract

This paper presents a numerical model that simulates the nearshore circulation and the propagation of waves in two horizontal dimensions (2DH) across the coastal zone, from intermediate depth to zero depth. Pre-breaking, wave propagation is calculated using a Boussinesq equation set with enhanced dispersion characteristics, discretised using second-order central differences and solved using the conjugate gradient method with fourth order Runge-Kutta time integration. In the breaker zone, the Boussinesq dispersive terms are gradually switched off, and the resulting non-linear shallow water equations solved using a finite volume MUSCL-Hancock scheme with an HLLC approximate Riemann solver. Broken waves are treated as hydraulic bores. A wetting and drying algorithm models the moving wet/dry front at the shore. Waves are generated by a line of independently moving piston paddles which are represented through a linear mapping, stretching and compressing the grid in the region of the paddles. Model verification tests include wave sloshing in a frictionless basin, seiching in a parabolic basin with bed friction, solitary wave propagation over a horizontal bed, and the interaction of a solitary wave with a conical island. After calibration, the model simulates the generation of wave-induced currents by regular waves as they interact with sinusoidal and tricuspate beaches, and the propagation of a uni-directional focused wave group over a plane beach. Results are compared against previously published laboratory data. The validation tests confirm that the 2DH model reproduces several important coastal hydrodynamic phenomena including wave-induced currents and multi-component wave packets. The model can thus be used to replicate wave basin experiments, and could be extended to multi-directional waves, leading to a better understanding of hydrodynamic processes in shallow coastal waters.