On the accuracy of DualSPHysics to assess violent collisions with coastal structures
Introduction
Understanding the laws that rule extreme hydrodynamic processes requires an in-deep analysis of their intrinsic characteristics. For this purpose, either physical or numerical modelling are employed. In general, physical model tests constitute the most used approach for analysis purposes despite being costly, time consuming and strongly dependent on the accuracy of the measurement equipment. As an alternative numerical models are shown as a useful complementary option to be used in a wide range of practical applications. One of the main advantages of numerical modelling is its capability to simulate any scenario with reduced costs. Moreover, numerical models do not suffer from scale effects and can provide information on physical quantities that could be difficult to measure in scaled models or in prototypes. In general, there are two main methodological approaches to numerical modelling: mesh-based and mesh-free approaches. Traditionally, computational techniques are based on the mesh-based approach. The mesh-based models, also called Eulerian models, discretise the domain using some type of mesh to analyse the variable of interest at fixed nodes by solving the governing equations by means of some numerical methodologies as, for example, finite differences, finite elements or finite volumes techniques. These methods have shown to be robust and reliable although they require, in some cases, expensive mesh generation and have severe technical challenges associated with implementing conservative multi-phase schemes. The mesh-free models, also called Lagrangian models, discretise the domain in particles and analyse the variables of study by following these particles. These methods allow overcoming part of the drawbacks that characterise the mesh-based schemes. However, these methods have their own limitations, mainly associated to the lack of completeness of the kernel functions. In addition, the computational cost is usually higher than associated to mesh-based methods. Approaches such as the Smoothed Particle Hydrodynamics (SPH) technique [1], Monte Carlo methods [2] or the particle finite element method (PFEM) [3] are examples of mesh-free schemes. In the particular case of SPH-based models large deformations can be efficiently treated since there is no mesh distortion due to the Lagrangian nature the method. This property makes SPH an ideal technique to study highly non-linear phenomena as, for example, violent free-surface motion. In addition, the structure of the SPH algorithms allows their easy adaptation to GPU cards, which alleviates the computational costs associated to the method.
SPH method was developed originally for astrophysics in the 1970s [4], [5]; since then, SPH has been successfully applied to several fields of engineering as solid mechanics [6], [7], [8] or Computational Fluid Dynamics (CFD) [9], [10]. Li and Liu [11] and Violeau [1] show a review of some mesh-free methodologies and their applications. In SPH the continuum is replaced by particles, which move according to the governing dynamics. Differently from Eulerian methods, for whom the free-surface elevation is obtained using volume of fluid methods (VOF), no special tracking is needed in SPH to detect the free surface and, as mentioned before, the domain is multiply-connected due to the Lagrangian nature the method. Thanks to these properties, SPH has been used to describe a wide variety of free-surface flows like flooding scenarios [12], wave propagation over a beach [13], fluid-structure interaction [14], [15], [16], [17], [18], [19], dam breaks [20] and problems involving sloshing dynamics [21]. During the last decade SPH has been widely applied to coastal engineering [22], [23], [24], [25], [26], [27], [28]. St-Germain et al. [29] used SPH to investigate the hydrodynamic forces induced by the impact of rapidly advancing tsunamis. These previous works showed that SPH-based models have achieved a high level of accuracy to be successfully compared with experiments. However, as far as we know, only a few works have dealt with the convergence of SPH results to experimental measurements in terms of the spatial resolution [30] or the comparison between mesh-free and mesh-based models have been analysed in detail [31]. Furthermore, Neves et al. [32] compared the time series of free-surface elevation and horizontal velocity for IHFOAM and DualSPHysics and Židonis and Aggidis [33], studied the benefits and drawbacks of different mesh-based and mesh-free codes to simulate Pelton turbines.
In the present work, the accuracy of DualSPHysics and IHFOAM to simulate wave impacts on a particular coastal structure will be compared. Both models will be used to reproduce the experimental data described in Kisacik et al. [34].
The paper is organized as follows. First a brief description of the numerical models DualSPHysics and IHFOAM is shown. Then the experimental and numerical setups are presented along with the statistical tools used to analyse the results. Finally, results on the wave shape development near the structure, the free-surface elevations along the flume and the horizontal force exerted onto the vertical part of the structure are compared.
Section snippets
DualSPHysics model
DualSPHysics is a numerical model based on the Smoothed Particle Hydrodynamics (SPH) method. A complete description of DualSPHysics can be found in [35]. SPH is a Lagrangian and mesh-less method where the fluid is discretised into a set of particles that are nodal points where physical quantities (such as position, velocity, density, pressure) are computed as an interpolation of the values of the neighbouring particles. The contribution of these neighbours is weighted using a kernel function (W
The physical model
The physical model tests were carried out in the wave flume (30 m × 1 m × 1.2 m) of Ghent University (Belgium). A vertical structure with horizontal cantilever slab was located 22.5 m away from the wavemaker on a uniform slope (1/20). The structure was 0.3 m high and 0.6 m long. A series of flush-mounted Kistler sensors were used to measure wave impact pressures. These sensors are based on the piezoelectric measurement principle: the force acting on the highly sensitive transversal measuring
Wave shape development
A visual comparison between the wave shape development obtained from simulations and from experimental tests is shown in Fig. 3. Red dots represent the experimental free-surface profile observed in the physical tests [34]. The three instants immediately before the collision on the horizontal part of the structure show a good agreement between the physical model test and both numerical models. The impact on the top of the structure takes place at Time = 34.58 s for DualSPHysics and
Conclusions
The accuracy of a mesh-less model (DualSPHysics) and a mesh-based model (IHFOAM) to reproduce the experimental data obtained from the physical tests described in [34] have been compared. The experimental setup corresponds to the propagation of a regular wave train and its collision with a vertical sea wall with a hanging horizontal cantilever slab. Free-surface elevation and the horizontal force exerted onto the wall were the variables chosen for comparison.
Different metrics were used to
Acknowledgments
This work was partially financed by Xunta de Galicia under Project ED431C-20177/64 “Programa de Consolidación e Estructuración de Unidades de Investigación Competitivas (Grupos de Referencia Competitiva)” and project “NUMANTIA ED431F 2016/004”. The work was also funded by the Ministry of Economy and Competitiveness of the Government of Spain under project “WELCOME ENE2016-75074-C2-1-R” and project IMDROFLOOD (Water JPI WaterWorks, 2014). The authors wish to thank Prof. Peter Troch and Tom
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