David Matthew Kelly


In this paper a hybrid Eulerian Lagrangian solver based on the full–particle Particle–In–Cell (PIC) method is outlined. The solver is capable of simulating incompressible free–surface flows in domains with arbitrary, free–slip, solid boundaries. The flexibility of the approach allows for simulation of wetting and drying and pooling as well as wave breaking, splash–up over complex obstacles and the overtopping of coastal structures. The method has been validated for a wide variety of test cases and results are in good agreement with the numerical and experimental results of other researchers.


Surf; Swash; Wave breaking; Run–up; Topography; Structures

Full Text:



Aslam, T. (2004). "A partial dierential equation approach to multi–dimensional extrapolation." J. Comp. Physics, 193, 349–355.

Brackbill, J. and Ruppel, H. (1986). "FLIP: A method for adaptively zoned, particle-in-cell calculations of fluid flow in two dimensions." J. Comput Phys., 65, 314–343.

Camfield, F. and Street, R. (1969). "Shoaling of solitary waves on small slopes." J. Waterways and Harbours Div., 95, 1–22.

Chan, R. K. C. and Street, R. L. (1970). "A computer study of finite–amplitude water waves." J. Comp. Phys., 6, 68–94.

Chorin, A. J. (1968). "Numerical solution of the Navier–Stokes equations." Math. Comput., 22, 745–762.

Chorin, A. J. and Marsden, J. E. (1993). A mathematical introduction to fluid mechanics. Springer, New York.

Cooker, M. J., Peregrine, D. H., Vidal, C., and Dold, J. W. (1990). "The interaction between a solitary wave and a submerged semi–circular cylinder." J. Fluid Mech., 125, 51–55.

Dalrymple, R. and Rogers, B. D. (2006). "Numerical modeling of water waves with the SPH method." Coastal Eng., 53, 141–147.

Gibou, F., Fedkiw, R. P., Cheng, L. T., and Kang, M. (2002). "A second–order accurate discretisation of the Poisson equation on irregular domains." J. Comp. Physics, 176, 205–227.

Gray, J. P. P. and Monaghan, J. J. (1998). "A study of waves developed by caldera collapse." Proceedings of 13th Australian Fluid Mechanics Conference. 279–282.

Harlow, F. (1964). Methods in Computational Physics. Academic Press, London.

Harlow, F. H. and Welch, J. E. (1965). "Numerical computation of time–dependent viscous incompressible flow of fluid with free surface." Phy. Fluids, 8, 3–325.

Jiang, C., Chen, J., Tang, H., and Z., C. Y. (2011). "Hydrodynamic processes on a beach: Wave breaking, up–rush and backwash." Comm. Nonlin. Sci and Num. Sim., 16, 3126–3139.

Karambas, T. and Tozer, N. (2003). "Breaking waves in the surf and swash zone." J. Coast Res., 19, 514–528.

Kelly, D. M. (2012). "PICIN: A particle–in–cell solver for incompressible free surface flows in arbitrary domains." In Preparation.

Monaghan, J. J. and Kos, A. (1999). "Solitary waves on a cretan beach." J. Waterways and Harbours Div., 125, 145–154.

Ng, Y. T., Min, C., and Gibou, F. (2009). "An ecient fluid–solid coupling algorithm for single–phase flows." J. Comp. Physics, 228, 8807–8829.

Noh, W. F. (1964). Methods in Computational Physics. Academic Press, London.

Osher, J. and Fedkiw, R. P. (2002). Level set methods and dynamic implcit surfaces. Springer, New York.

Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P. (2007). Numerical Recipes: The Art of Scientific Computing. Cambridge University Press, 3rd edition.

Rogers, B., Dalrymple, R., and Stansby, P. (2008). "SPH modelling of floating bodies in the surf zone." Proc. 30th ASCE Int. Conf. Coast. Eng. ASCE, 965–972.

Seiichi, K., Nobe, A., and Oka, Y. (1998). "Numerical analysis of breaking waves using the moving particle semi–implicit method." Int. J. Numer. Meth. Fluids, 26, 751–769.

Tonelli, M. and Petti, M. (2009). "Hybrid finite volume – finite dierence scheme for 2DH improved Boussinesq equations." Coast. Engng., 56, 609–620.

Viecelli, J. A. (1969). "A method for including arbitrary external boundaries in the MAC incompressible fluid computing technique." J. Comput. Physics, 4, 543–551.

Zhu, Y. and Bridson, R. (2005). "Animating sand as a fluid." Proceedings ACM SIGGRAPH. SIGGRAPH, 965–972.

DOI: http://dx.doi.org/10.9753/icce.v33.currents.30