Applicability of Smoothed Particle Hydrodynamics for estimation of sea wave impact on coastal structures
Introduction
The design of coastal defences requires proper assessment of actions exerted by sea waves on structures, such as run-up heights, overtopping flow rates and velocities, and wave forces and pressures. For hard structures (e.g., quay walls and breakwaters), these values represent boundary conditions that can be used to assess local damage and overall structural stability. Wave forces can be generally characterised and measured by physical and/or numerical modelling. Analytical or semi-empirical formulations can also help for the purpose. In recent years, new building technologies and the latest standards for environmental safety and public use of coastal zones have encouraged designers to seek new solutions and more complex layouts than those traditionally used as coastal defences. For example, limiting the height of storm return walls that are built on top of existing coastal structures often is necessary to protect coastal areas from flooding and to keep them attractive and accessible at the same time. Scenarios such as this one require engineers to explore different solutions parapet or curve-shaped walls and stilling water basins that are integrated within the urban architecture. Application of existing analytical or empirical formulas to such cases is not always possible, as they may have different hydraulic boundary conditions and structural layouts. Although physical model tests can provide the data needed by designers, physical modelling can be very time consuming and expensive. Numerical modelling offers a useful and complementary tool to assess the effects of sea wave impact on coastal structures.
Traditional empirical methods to predict wave forces on dikes and return walls (e.g., Goda, 1974, Kortenhaus et al., 1999, Takahashi et al., 1994) were developed from physical model experiments largely focused on deep-water wave conditions and simple geometries. However, in cases such as Belgian coastal defences, the additions of new crest elements on existing sea dikes or quay walls are used as countermeasures against wave forces. For example, construction of storm return walls on top of existing quay walls is planned for Zeebrugge Harbour to protect the boroughs that are located in low-lying areas next to the harbour. New storm return walls either with or without parapets may be built on the top of the existing sea dikes in the Blankenberge Marina. However, not much of the existing data is applicable to these cases due to the peculiar geometries and hydraulic conditions of these harbours. The storm return walls will be built at a certain distance from the seaward edge of the dike crest, which will create a sort of crest berm over which the waves will propagate and transform before reaching the wall. The influence of the length and elevation of this crest berm coupled with the storm return wall has not yet been comprehensively analysed. Previous studies (e.g., Trouw et al., 2012, Van Doorslaer et al., 2012a, Van Doorslaer et al., 2012b, Verwaest et al., 2010) did not provide a complete and general description of the problem, and they were often restricted to particular geometries or boundary conditions. Thus, the behaviour of these new storm return walls under wave attacks must be characterised for proper design of coastal defences. Recent events struck the entire coast of the North Sea such as the storm “Xaver” occurred in the night between 5th and 6th December 2013 and hit the coasts of the Northern Countries confirming how important a proper re-design of the existing sea dikes is.
While semi-empirical approaches or physical model results have been useful for the design of coastal structures, numerical modelling is a powerful tool that can be used to solve complex problems in the fields of engineering and science. Its main advantage is its ability to simulate any scenario without building expensive physical models. Numerical models do not suffer from scale effects, and numerical simulations can provide physical data that can be difficult or even impossible to measure in a real model. Hardware development has reduced the computational cost, which once was a bottleneck for numerical modelling. Finally, numerical modelling can reduce the number of physical tests required, which translates to significant savings in money and time.
Traditional computational fluid dynamics (CFD) techniques such as volume-of-fluid methods (VOF) have been used to study wave-structure interactions (Kleefsman et al., 2005) and to design breakwaters (Higuera et al., 2013, Vanneste and Troch, 2012). However, Eulerian numerical methods, such as those based on the finite volume technique, require expensive mesh generation and have severe technical challenges associated with implementing conservative multi-phase schemes that can capture the nonlinearities within rapidly changing geometries. Thus, the emergence of meshless schemes has provided a much needed alternative, and meshfree methods, such as Monte Carlo methods (Geeraerts et al., 2009) or the particle finite element method (PFEM) (Oñate et al., 2011), are becoming popular.
Developed originally for astrophysics in the 1970s (Lucy, 1977), the meshless Smoothed Particle Hydrodynamics (SPH) method has been developed rapidly during the last decade due to its applications in engineering. This method uses particles to represent a fluid, and these particles move according to the governing dynamics. When simulating free-surface flows, the Lagrangian nature of SPH allows the domain to be multiply-connected with no need for a special treatment of the surface; this property makes the technique ideal for studying violent free-surface motion (Violeau, 2012).
SPH has been used to describe a variety of free-surface flows, including wave propagation over a beach, plunging breakers, impact on structures, and dam breaks. Monaghan (1994) presented the first attempt to study free-surface flows. Monaghan also studied the behaviour of gravity currents (Monaghan, 1996), solitary waves (Monaghan et al., 1999) and wave arrival at a beach (Monaghan and Kos, 1999). Later, the model was applied to the study of wave-structure interactions (Colagrossi and Landrini, 2003). Gómez-Gesteira and Dalrymple (2004) used SPH to study the classical dam break problem in three dimensions. Within the field of coastal engineering, Gotoh et al. (2004) and Shao (2005) used SPH to study the wave-breakwater interaction, and Khayyer and Gotoh (2009) used it to predict wave impact pressure due to sloshing waves. More recently, Ren et al. (2014) validated SPH model results by comparing them to other available numerical results and to experimental data for wave damping over a porous seabed with different levels of permeability. St-Germain et al. (2014) used SPH to investigate the hydrodynamic forces induced by the impact of rapidly advancing tsunamis. SPH also was successfully used for other engineering applications, such as to simulate free-surface flows encountered in Pelton turbines (Marongiu et al., 2010) and to study a real spillway in France that connects the reservoir of a river dam to a valley with a complex bottom shape (Lee et al., 2010).
The DualSPHysics code (Crespo et al., 2011, Gómez-Gesteira et al., 2012a, Gómez-Gesteira et al., 2012b), which was developed to use SPH for real engineering problems, includes software that can be run on either CPUs or GPUs (graphics cards with powerful parallel computing). GPUs offer greater computing power than CPUs, and they are an affordable option to accelerate SPH modelling. Therefore, the simulations conducted in this study were executed using a GPU card installed on a personal computer. DualSPHysics is open source and can be freely downloaded from www.dual.sphysics.org. The first rigorous validation of the GPU implementation of DualSPHysics code was presented in Crespo et al. (2011), and more details about the implementation of DualSPHysics can be found in Domínguez et al., 2011, Domínguez et al., 2013a, Domínguez et al., 2013b. In addition, the computation of forces exerted by large waves on the urban furniture of a realistic promenade was presented in Barreiro et al. (2013). That study presented a very preliminary analysis of the accuracy of the model when simulating hydraulics loadings (e.g., hydrostatic force, dam break, etc.), and it illustrated the abilities of DualSPHysics to handle complex geometries in a straightforward way. However, only qualitative results for wave impacts on a real coastal structure were presented. In addition, Ren et al. (2014) and St-Germain et al. (2014) used previous versions of DualSPHysics in their studies, and Altomare et al. (2014) used DualSPHysics code to study the run-up on a real armour block coastal breakwater.
The goal of the present study was to demonstrate the accuracy of DualSPHysics to quantify the sea wave forces on coastal defences such as storm return walls. Several validation test cases are presented and compared with solutions proposed in the literature and with experimental data. Relatively short time series of regular waves and random waves were considered. An absorption model is not used in DualSPHysics, but the modelling can be considered to be accurate because the scope of the work was not to reproduce very long times series of sea waves in the numerical flume but rather to focus on identified short wave groups or wave trains.
Section snippets
SPH method
SPH is a Lagrangian and meshless method in which the fluid is discretised into a set of particles. Each of these particles is a nodal point for which physical quantities (such as position, velocity, density, and pressure) are computed as an interpolation of the values of the neighbouring particles. The contribution of the nearest particles is weighted according to distance between particles, and a kernel function (W) is used to measure this contribution depending on the inter-particle distance
Comparison with analytical and semi-empirical solutions
Prior to application of the model, proper validation of the DualSPHysics code was necessary to illustrate that the numerical tool could reliably simulate fluid-structure interaction phenomena and assess the forces exerted by waves on coastal structures. Thus, the model was applied to classical problems for which formulae are well known and described in literature.
Wave-generated forces on structures are complex functions of the wave conditions and the geometry of the structure. The following
Comparison with physical model data
DualSPHysics was also validated against experimental data from physical model tests carried out at Ghent University, Belgium. The experimental campaign studied the response of new coastal defences proposed for the Belgian coast, in particular for Zeebrugge Harbour and Blankenberge Marina. The capabilities and limitations of the numerical model are analysed in the following subsections.
Conclusions
The applicability of the SPH-based DualSPHysics model for assessing the impacts of wave forces on coastal structures was investigated in this study. The capabilities and drawbacks of the numerical modelling also were examined.
The model was first validated using well-known analytical and semi-empirical formulae that are generally used throughout the coastal engineering community worldwide. Three different kinds of impacts were modelled: standing waves on impermeable fully reflective vertical
Acknowledgements
The authors acknowledge Daphné Thoon, Michaël Pauwels, and Niels Vanmassenhove from the Flemish Agency of Coastal Division (Afdeling Kust) and Prof. Peter Troch, Dr. Dieter Vanneste, and David Gallach from the Department of Civil Engineering of Ghent University for providing all of the data regarding the designs and analysis carried out for Zeebrugge Harbour and Blankenberge Marina. This work was partially financed by Xunta de Galicia under project Programa de Consolidación e Estructuración de
References (53)
- et al.
Numerical modelling of armour block sea breakwater with Smoothed Particle Hydrodynamics
Comput. Struct.
(2014) - et al.
Smoothed particle hydrodynamics for coastal engineering problems
Comput. Struct.
(2013) Introduction to fluid dynamics
(1974)- et al.
Numerical simulation of interfacial flows by smoothed particle hydrodynamics
J. Comput. Phys.
(2003) - et al.
Boundary conditions generated by dynamic particles in SPH methods
Comput. Mater. Continua
(2007) - et al.
GPUs, a new tool of acceleration in CFD: efficiency and reliability on Smoothed Particle Hydrodynamics methods
PLoS ONE
(2011) - et al.
Numerical modeling of water waves with the SPH method
Coast. Eng.
(2006) - et al.
Neighbour lists in Smoothed Particle Hydrodynamics
Int. J. Numer. Methods Fluids
(2011) - et al.
Optimization strategies for CPU and GPU implementations of a smoothed particle hydrodynamics method
Comput. Phys. Commun.
(2013) - et al.
New multi-GPU implementation for Smoothed Particle Hydrodynamics on heterogeneous clusters
Comput. Phys. Commun.
(2013)
Effects of new variables on the overtopping discharge at steep rubble mound breakwaters — The Zeebrugge case
Coast. Eng.
New wave pressure formulas for composite breakwaters
Random seas and design of maritime structures
Adv. Ser. Ocean Eng.
Using a 3D SPH method for wave impact on a tall structure
J. Waterw. Port Coast. Ocean Eng.
State-of-the-art of classical SPH for free-surface flows
J. Hydraul. Res.
SPHysics — development of a free-surface fluid solver — Part 1: Theory and Formulations
Comput. Geosci.
SPHysics — development of a free-surface fluid solver — Part 2: Efficiency and test cases
Comput. Geosci.
SPH-LES model for numerical investigation of wave interaction with partially immersed breakwater
Coast. Eng. J.
Simulating coastal engineering processes with OpenFOAM®
Coast. Eng.
Wave impact pressure calculations by improved SPH methods
Int. J. Offshore Polar Eng.
Description of loading conditions due to violent wave impacts on a vertical structure with an overhanging horizontal cantilever slab
Coast. Eng.
A volume-of-fluid based simulation method for wave impact problems
J. Comput. Phys.
Wave impact loads – pressures and forces
Application of weakly compressible and truly incompressible SPH to 3-D water collapse in waterworks
J. Hydraul. Res.
Integration Methods for Molecular dynamic IMA Volume in Mathematics and its application
A numerical approach to the testing of fusion process
J. Astron.
Cited by (221)
Numerical modelling of a vertical cylinder with dynamic response in steep and breaking waves using smoothed particle hydrodynamics
2024, Journal of Fluids and StructuresNumerical investigation of hydrodynamic characteristics of a dual floating breakwater
2024, Ocean EngineeringMultiphase SPH analysis of a breaking wave impact on elevated structures with vertical and inclined walls
2024, Applied Ocean ResearchInvestigating the effects of box girder bridge geometry on solitary wave force using SPH modeling
2024, Coastal EngineeringAn efficient correction method in Riemann SPH for the simulation of general free surface flows
2023, Computer Methods in Applied Mechanics and Engineering