Simulating breaking waves using smoothed particle hydrodynamics

Detailed computational modelling of fluid motion in the surf zone (such as under breaking waves) is difficult, because model domains must be long and narrow, and very high resolutions are required to obtain sufficiently detailed simulations. Existing modelling methods have deficiencies: one class of methods are restricted to simulating waves only to the point where the lip of the wave hits the water, while a second class experience significant numerical errors. A third class of methods are the Lagrangian particle-based methods, and while some of these have been applied to simulating breaking waves, their general usefulness for such work is not yet established. Here a model is created (named MARIAN) using smoothed particle hydrodynamics (SPH), an example of a Lagrangian particle-based method. This model is tested, and then used to simulate a number of processes relevant to coastal modelling, namely the propagation of waves in a numerical wave tank, the breaking of solitary waves on plane slopes, and the breaking of cnoidal waves over a real bathymetry. From comparisons of the results, merits and demerits in the model and method can be identified, and general conclusions as to how useful the model is for the task can be established. It is found that while some simulations are very good (a bursting dam, for example), and others are average (a seiching basin), some simulations important for work in the coastal zone are not good ( the propagation of waves in a numerical wave tank) and others are very poor (breaking waves). Clearly, there are limits as to what MARIAN can be used to simulate, and what these limits are is not apparent. From the model developed in this study it should be concluded that Lagrangian particle-based models designed for simulating breaking waves have shortcomings, and based on this work, other methods would currently be preferred. However other researchers have recently had more success by using variations on the methods employed here. In particular by using better viscosity formulations they resolved breaking waves reasonably well. In the work performed here it was ascertained that some methods used in the literature cause SPH models to fail in enforcing the fundamental principles of physics. While the current state of the model created here is unsatisfactory, there are promising improvements that could be made, and further research is likely to resolve some of the problems discussed here. Topics that would benefit from further research include finding ways to reduce runtimes and increase resolutions (by parallelizing source code, improving algorithms and identifying the free surface), and ways to increase accuracy (improving the quality of kernels employed, including the "missing boundary integrals", and ensuring consistency) while still enforcing the fundamental principles