Boussinesq cut cell model for non-linear wave interaction with coastal structures

D Ning, Jun Zang, Q Liang, P H Taylor, A G Borthwick

Research output: Contribution to journalArticle

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Abstract

Boussinesq models describe the phase-resolved hydrodynamics of unbroken waves and wave-induced currents in shallow coastal waters. Many enhanced versions of the Boussinesq equations are available in the literature, aiming to improve the representation of linear dispersion and non-linearity. This paper describes the numerical solution of the extended Boussinesq equations derived by Madsen and Sørensen (Coastal Eng. 1992; 15:371-388) on Cartesian cut-cell grids, the aim being to model non-linear wave interaction with coastal structures. An explicit second-order MUSCL-Hancock Godunov-type finite volume scheme is used to solve the non-linear and weakly dispersive Boussinesq-type equations. Interface fluxes are evaluated using an HLLC approximate Riemann solver. A ghost-cell immersed boundary method is used to update flow information in the smallest cut cells and overcome the time step restriction that would otherwise apply. The model is validated for solitary wave reflection from a vertical wall, diffraction of a solitary wave by a truncated barrier, and solitary wave scattering and diffraction from a vertical circular cylinder. In all cases, the model gives satisfactory predictions in comparison with the published analytical solutions and experimental measurements.
LanguageEnglish
Pages1459-1483
Number of pages25
JournalInternational Journal for Numerical Methods in Fluids
Volume57
Issue number10
DOIs
StatusPublished - 2008

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Wave Interaction
Nonlinear Interaction
Nonlinear Waves
Solitary Waves
Solitons
Boussinesq Equations
Cell
Diffraction
Vertical
Wave Diffraction
Immersed Boundary Method
Riemann Solver
Wave Scattering
Finite Volume Scheme
Induced currents
Shallow Water
Circular Cylinder
Information Flow
Circular cylinders
Cartesian

Cite this

Boussinesq cut cell model for non-linear wave interaction with coastal structures. / Ning, D; Zang, Jun; Liang, Q; Taylor, P H; Borthwick, A G.

In: International Journal for Numerical Methods in Fluids, Vol. 57, No. 10, 2008, p. 1459-1483.

Research output: Contribution to journalArticle

Ning, D ; Zang, Jun ; Liang, Q ; Taylor, P H ; Borthwick, A G. / Boussinesq cut cell model for non-linear wave interaction with coastal structures. In: International Journal for Numerical Methods in Fluids. 2008 ; Vol. 57, No. 10. pp. 1459-1483
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