This paper presents a novel numerical method for non-linear water wave interaction with a vertical structure of arbitrary horizontal shape. The wave motion is described by a set of non-linear Boussinesq-type equations. These are solved numerically using a Godunov-type finite volume method on Cartesian grids with cut cells. The higher-order dispersive Boussinesq terms are approximated by finite differences. The main advantage of this approach is that not only is the proposed scheme conservative, but also no special algorithm is required to simulate discontinuous flows such as hydraulic jumps and broken waves. Regular waves incident on a bottom-mounted cylinder are simulated and the predicted surface elevation on the body compares well to laboratory measurements.
In recent years, the demand for renewable energy has increased rapidly and wind turbines are one of the most popular means to satisfy this demand. Currently, the design methodology for offshore wind turbine is based on a simplified version of that for offshore oil and gas platforms. Most offshore oil and gas structures are installed in relatively deep water, and the effects of waves on the structures are normally analysed by potential-based and/or Morison methods. However, most offshore wind turbines are located in rather shallow water. The highly non-linear and possibly breaking waves experienced on shallow water may imply that design methods based on experience in deeper water could be significantly unconservative. In this paper, we present a new numerical method for non-linear water wave interaction with a vertical structure of arbitrary horizontal shape. The wave flow-field is described by a set of non-linear Boussinesq-type equations, which are solved numerically using a Godunov-type finite volume method on Cartesian cut-cell grids. The HLLC approximate Riemann solver is used to evaluate the interface fluxes. Higher-order dispersive Boussinesq terms are approximated by finite differences.
