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

Frances M. Judge, Jana Orszaghova, Paul Taylor, Alistair G.L. Borthwick

Research output: Contribution to journalArticle

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.
Original languageEnglish
Pages (from-to)9-26
JournalCoastal Engineering
Volume142
DOIs
Publication statusPublished - Dec 2018

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Hydrodynamics
Induced currents
Beaches
Solitons
Wave propagation
Wave packets
Liquid sloshing
Conjugate gradient method
Pistons
Stretching
Coastal zones
Wetting
Water
Numerical models
Drying
Hydraulics
Calibration
Friction

Cite this

Judge, Frances M. ; Orszaghova, Jana ; Taylor, Paul ; Borthwick, Alistair G.L. / A 2DH hybrid Boussinesq-NSWE solver for near-shore hydrodynamics. In: Coastal Engineering. 2018 ; Vol. 142. pp. 9-26.
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A 2DH hybrid Boussinesq-NSWE solver for near-shore hydrodynamics. / Judge, Frances M.; Orszaghova, Jana; Taylor, Paul; Borthwick, Alistair G.L.

In: Coastal Engineering, Vol. 142, 12.2018, p. 9-26.

Research output: Contribution to journalArticle

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N2 - 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.

AB - 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.

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SN - 0378-3839

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