The accurate simulation of the fluid free surface, even in the presence of breaking waves and splashes, together with the automatic modeling of fluid convection and the good energy conservation properties, make the PFEM an ideal tool for the analysis of different hydraulic engineering problems [8].

The first PFEM simulation of hydraulic laboratory tests was presented in [1]. In this work, a thorough comparison of the PFEM results against experimental observations is carried out on four different free-surface flow configurations. The suitability of PFEM in modeling wave propagation was clearly demonstrated in [2,5] by reproducing accurately different types of propagating waves in laboratory channels.

Recently, [10] used a PFEM-FEM-DEM technique to simulate the propagation of a tsunami wave in a hydraulic laboratory channel, its impact against a concrete wall and the breakage of the solid structure.

Coupled Eulerian-PFEM simulation of the partial collapse of a rockfill dam due to an internal water flow [1]
Tsunami wave propagation and impact against a concrete wall [9]

Dam engineering is another main field of application of the PFEM. The first works in this area [3, 4] used a hybrid FEM-Eulerian approach to simulate overtopping and failure of rockfill dam and the related seepage phenomena. Salazar et al. [6] studied a real dam geometry and modeled the 3D air-water interaction to estimate the air demand at the bottom outlets.

Coupled air-water simulation of bottom outlets of dams done with the PFEM [6]. In the video the air phase is plotted

On the other hand, [8] focused on the water shock waves that form at the exit of dam spillways. A wider overview of applications of PFEM to hydraulic engineering problems can be found in [9].

Dam spillway 3D CFD simulation with PFEM [8]

In [7] a catastrophic collapse of a tank containing a water-oil mixture was replicated using PFEM-2. The amount of liquid inventory that overtops the container walls and maximum forces exerted by the fluid on breakwater and gates justified the consequences experienced after the accident according to the committee report.

Collapse of a tank containing a water-oil mixture simulated with PFEM-2 [7]


[1] Larese A, Rossi R, Oñate E, Idelsohn S (2008) Validation of the particle finite element method (PFEM) for simulation of free surface flows. Int J Comput Aided Eng Softw 25(4):385–425 
[2] Oliveira T, Sánchez-Arcilla A, Gironella X (2012) Simulation of wave overtopping of maritime structures in a numerical wave flume. J Appl Math. 
[3] Larese A, Rossi R, Oñate E, Idelsohn S (2012) A coupled PFEM-Eulerian approach for the solution of porous FSI problems. Comput Mech 50(6):805–819 
[4] Larese A, Rossi R, Oñate E, Toledo M, Morán R, Campos H (2013) Numerical and experimental study of overtopping and failure of rockfill dams. Int J Geomech 15(4):04014060 
[5] Oliveira T, Sánchez-Arcilla A, Gironella X, Madsen S (2017) On the generation of regular long waves in numerical wave flumes based on the finite element method. J Hydraul Res 55(4):538–556
[6] Salazar F, San-Mauro J, Celigueta M, Oñate E (2017) Air demand estimation in bottom outlets with the particle finite element method. Susqueda dam case study. Computat Part Mech 4(3):345–356 
[7] Gimenez JM, Ramajo DE, Márquez Damián S, Nigro N, Idelsohn S (2017). An assessment of the potential of PFEM-2 for solving long real-time industrial applications. Comp. Part. Mech. 4, 251-267
[8] Salazar F, San-Mauro J, Celigueta M, Oñate E (2020) Shockwaves in spillways with the particle finite element method. Comput Part Mech 7:87–99
[9] Cremonesi M, Franci A, Idelsohn SR, Oñate E (2020) A state of the art review of the Particle Finite Element Method (PFEM). Archives of Computational Methods in Engineering, 17, 1709-1735
[10] Oñate E, Cornejo A, Zárate F, Kashiyama K, Franci A (2022) Combination of the finite element method and particle-based methods for predicting the failure of reinforced concrete structures under extreme water forces. Engineering Structures, 251B, 113510