Zang, Jun (Department of Architecture & Civil Engineering, University of Bath, Bath, UK) | Ning, Dezhi (The State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology Dalian, China) | Liu, Shuxue (The State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology Dalian, China) | Liang, Qiuhua (School of Civil Engineering & Geoscience, Newcastle University, Newcastle upon Tyne, UK) | Taylor, Paul H. (Department of Engineering Science, University of Oxford, Oxford, UK) | Taylor, Rodney Eatock (Department of Engineering Science, University of Oxford, Oxford, UK) | Borthwick, Alistair G.L. (Department of Engineering Science, University of Oxford, Oxford, UK)
This paper presents a Cartesian cut-cell Boussinesq model for simulating nonlinear wave interaction with a curved structure. The Cartesian cut-cell technique permits accurate boundary-fitting of complicated, curved geometries in the numerical domain. A Godunov-type shock capturing scheme is used to solve the Boussinesq-type equations in hyperbolic form in order to provide accurate predictions of strongly nonlinear wave interactions with curved structures in shallow water. The numerical model is used to simulate the interaction of a focused wave with a circular cylinder, and excellent agreement is obtained with data from laboratory experiments conducted in a wave basin.
Numerical models based on the Boussinesq-type equations are becoming widely used to simulate wave transformation in shallow coastal regions and run-up at beaches. Such models can play a key role in design and re-assessment in coastal engineering. Boussinesq (1872) was the first to derive depth-integrated mathematical descriptions of shallow flows that included the influence of vertical accelerations and hydrodynamic pressure. During the past 20 years, considerable efforts have been made to improve the representation of nonlinearity and dispersion by Boussinesq-type formulations (see e.g. Madsen and Sørenson, 1992; Nwogu, 1993; Schäffer and Madsen, 1995; Agnon et al., 1999; Madsen et al., 2002). Many coastal structures, such as offshore wind-turbine foundations and piers, are composed of vertical surface-piercing circular cylinders. In order to estimate the local wave hydrodynamics and loading on such structures, there is a need to develop Boussinesq-type solvers that can model wave interaction with curved structures. The aim of the present work is to develop a simple, accurate and flexible method for modelling the hydrodynamics of coastal flows in the vicinity of surface-piercing structures of arbitrary plan-form geometry. The Cartesian cut-cell technique was implemented for body fitting for compressible flow by Yang et al. (1997) and for shallow water flow by Causon et al. (2000) using piece-wise linear segments.