Philippe St-Germain, Ioan Nistor, John Readshaw, Grant Lamont


This paper evaluates the results of two fundamentally different numerical models: DualSPHysics and SWASH, which can be used to assess the ability of coastal defense structures to offset or mitigate the water overtopping and subsequent implications for expected future sea level rise. The models are open source implementations of the smoothed particle hydrodynamics (SPH) method and of a non-hydrostatic adaptation of the non-linear shallow water (NLSW) equations, respectively. The small-scale physical experiment of Stansby and Feng (2004) is used to validate and asses the performance of the two numerical models for the case of breaking monochromatic waves overtopping a coastal dike. Numerical and experimental time-histories of water surface elevation are quantitatively compared and numerical velocity fields during the processes of wave breaking and overtopping are analysed in detail. In addition, to further validate the DualSPHysics model, numerical experiments are performed considering the more realistic case of irregular waves using the SWASH model as benchmark. Overall, results provided by both numerical models are generally comparable, although some strengths and shortcomings of each are highlighted. These results can provide guidance in selecting the most appropriate model for a particular situation given specific accuracy requirements and availability of resources.


SPH method; non-linear shallow water equations; wave overtopping; coastal protection structure; sea level rise

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Battjes, J.A. 1974. Surf similarity, Proceedings of 14th Int. Conf. on Coastal Engineering, ASCE, 466-480.

Casulli, V. and G.S. Stelling. 1998. Numerical simulation of 3D quasi-hydrostatic free-surface flows, J. of Hydraulic Engineering, 124, 678-686.

Carvalho, M.M. 1989. Sea wave simulations, in Martins, R., Recent advances in Hydraulic physical modeling, Kluwer Academic Publishers, Dordrecht, The Netherlands, pp. 447-502.

Crespo, A.J.C., J.M. Dominguez, M. Gómez-Gesteira, M. Barreiro, P., B.D. Rogers, S. Longshaw, R. Canelas and R. Vacondio. 2013. User guide for DualSPHysics Code v3.0.

Dalrymple, R.A. and O. Knio. 2001. SPH modelling of water waves, Proceedings of 4th Conference on Coastal Dynamics, ASCE, 749-778.

Dalrymple, R.A. and B.D. Rogers 2006. Numerical modeling of water waves with the SPH method, Coastal Engineering, 53, 141-147.

Didier, E. and M.G. Neves. 2009. Coastal flow simulation using SPH: Wave overtopping on an impermeable coastal structure, Proceedings of 4th International SPHERIC Workshop.

Didier, E. and M.G. Neves. 2010. A Lagrangian Smoothed Particles Hydrodynamics - SPH - method for modelling wave-coastal structure interaction, Proceedings of 5th European Conference on Computational Fluid Dynamics.

Hibberd, S. and D.H. Peregrine. 1979. Surf and run-up on a beach: a uniform bore, J. of Fluid Mechanics, 95, 323-345.

Lamont, G., J. Readshaw, C. Robinson, and P. St-Germain. 2014. Greening shorelines to enhance resilience – An evaluation of approaches for adaptation to sea level rise, guide prepared by SNC-Lavalin Inc. for the Stewardship Centre for British Columbia, Canada, and submitted to the Climate Change Impacts and Adaptation Division, Natural Resources Canada (AP040), 46p.

Monaghan, J.J. 1994. Simulating free surface flows with SPH, J. of Computational Physics, 110, 399-406.

Monaghan, J.J. and A. Kos. 1999. Solitary waves on a Cretan Beach, J. of Waterway, Port, Coastal and Ocean Engineering, 125, 145-154.

Oliveira, T.C.A., A. Sánchez-Arcilla, and X. Gironella. 2012. Simulations of wave overtopping of maritime structures in a numerical wave flume, Journal of Applied Mathematics, Volume 2012, Article ID 246146, 19 pages.

Stansby, P.K. and J.G. Zou. 1998. Shallow-water flow solver with non-hydrostatic pressure: 2D vertical plane problems, Int. J. Numerical Methods in Fluids, 28, 514-563.

Stansby, P.K. 2003. Solitary wave runup and overtopping by a semi-implicit finite-volume shallow-water Boussinesq model, J. Hydraulic Research, 41, 639-648.

Stansby, P.K. and T. Feng. 2004. Surf zone wave overtopping a trapezoidal structure: 1-D modeling and PIV comparison, Coastal Engineering, 51, 483-500.

Stelling, G.S. and Zijlema, M. 2010. Numerical modeling of wave propagation, breaking and run-up on a beach, in Koren, B. and Vuik, C., Advanced Computational Methods in Science and Engineering, Springer-Verlag, Berlin, Germany, pp. 373-401.

Verlet, L. 1967. Computer experiments on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules, Physical Review, 159, 98-103.

Wendland, H. 1995. Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree, Advances in Computational Mathematics, 4, 389-396.

Zijlema, M. and G.S. Stelling. 2008. Efficient computation of surf zone waves using the nonlinear shallow water equations with non-hydrostatic pressure, Coastal Engineering, 55, 780-790.

Zijlema, M., G.S. Stelling and P. Smit 2011. SWASH: An operational public domain code for simulating wave fields and rapidly varied flows in coastal waters, Coastal Engineering, 58, 992-1012.