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Smoothed Particle Hydrodynamics (SPH) is becoming a useful tool for examining hydrodynamic flows that are difficult to model with other existing numerical methods, such as time-dependent flows with convoluted free surfaces. This paper will describe the development of the method using interpolation, and then present some applications to free surface flows, primarily water waves. The ability of the method to easily 465 Advances in Numerical Simulation of Nonlinear Water Waves Downloaded from www.worldscientific.com by KAINAN UNIVERSITY on 02/08/15. For personal use only. 466 R.A. Dalrymple et al.handle large free surface deformations, including wave breaking, will be illustrated. Finally the ability of the SPH method to solve for other non-hydrodynamic variables is shown-here we solve for the suspended sediment concentration under waves.

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This paper demonstrates that numerical modeling tools such as a RANS-VOF model can be applied confidently to reduce the level of uncertainty from empirical guidance and provide for a deterministic quantification of the hydraulic response associated with any arbitrary Caisson breakwater superstructure geometry. The RANS-VOF model used for this paper is first satisfactorily validated against laboratory measurements (surface elevation, overtopping and pressure) of a caisson breakwater on a rubble-mound foundation and then applied to several prototype caisson breakwater superstructure geometries. Numerical simulations presented in this paper for prototype geometries demonstrate that curved/inclined parapets, when compared with vertical face caisson breakwaters with the same crest elevation, can lead to large increases in overtopping as well as downward forces. Expectedly, the landward forces are reduced by the implementation of a curved or recessed and inclined parapet when compared to a caisson with a completely vertical face. During large overtopping events, the model results show that much larger short-duration seaward loads can be generated for curved and inclined superstructures when compared to vertical face geometries. This is in general agreement with previous laboratory experiments as well as field observations of seaward caisson sliding and failure resulting from large overtopping events. Further, numerical experiments indicate that the overtopping response of a superstructure can vary noticeably due to small changes in the recessed length of an inclined or curved parapet. The numerical model also easily provides for the quantification of the variation of instantaneous and peak overtopping discharges along the crest of the caisson superstructure, and which can provide for useful guidance in the design of various crest infrastructure components, such as drainage systems, flow deflectors, wave power devices etc.