Original Research3D numerical simulation of seagrass movement under waves and currents with GPUSPH
Introduction
Traditionally, to study fluid-structure interactions, structures usually are described with a Lagrangian formulation while fluids often are represented through an Eulerian formulation. The formulations generally are coupled using an Arbitrary Lagrangian-Eulerian formulation for the fluid. Numerous fluid-structure interactions have been studied according to such formulations, including valve springs (Rugonyi & Bathe, 2001), the interaction of compressible and incompressible fluids with structures (Bathe & Zhang, 2004), and the absorption of hydro-elastic shocks (Le Tallec & Mouro, 2001). The Lagrangian Smoothed Particle Hydrodynamics (SPH) method is a different approach to modeling in which fluids and/or solids are represented by a set of particles. Each solid particle has defined individual material properties and moves under the effects of the fluid, and represented by another set of particles. The use of a Lagrangian formulation for fluids can be more convenient for certain types of applications, such as fluid-free surface studies or large movements along a fluid-solid interface. Indeed, the SPH method does not require specifically processing the fluid-free surface (no surface tension) and the two groups of particles (fluid and solid) can be tracked simultaneously. The SPH method has already been successfully used to study interactions between fluids (Monaghan et al., 1999) and solids (Gotoh & Khayyer, 2018; Gray et al., 2001; Liang et al., 2017; Van Liedekerke et al., 2013; Zhang et al., 2017).
The SPH method was developed in 1977 (Gingold & Monaghan, 1977; Lucy, 1977) for applications in astrophysics. J. Monaghan (an Australian researcher in applied mathematics) contributed greatly to the development of the method. Since 1985, the method has been used for other applications. In the early 1990s, the SPH method was used for fluid simulations including free surface flows, waves (Dalrymple & Rogers, 2006; Monaghan, 1994; Randles; Libersky, 1996), multiphase fluids (Monaghan & Kocharyan, 1995) and weakly compressible flows (Morris et al., 1997). In the field of solid mechanics, simulations have mainly focused on the study of hypo-elastic solids (Gray et al., 2001). Recent developments in science and engineering have increased the need for modeling Fluid-Structure Interactions (FSI) to analyze multi-physics processes like retroactive loops, in which the pressure and viscous stresses of the fluid create deformation in the solid, which in turn affects stress, pressure, and velocity in the fluid.
Modeling FSI can, for instance, be useful for aerodynamics studies, biomechanics simulations, or airbag design (Agamloh et al., 2008; Farhat et al., 2006). The earliest models of stimulant-elastic solid and fluid interactions using the SPH method appeared a little more than ten years ago and focused on the laws of interaction (Amini et al., 2011; Antoci et al., 2007) and the definition of the solid interface (Ha et al., 2011). To date, the SPH method has not often been applied to fluid-structure interactions in environmental studies (Zhang et al., 2017). Here, it is proposed to use this method to evaluate the influence of submerged aquatic vegetation on waves and currents in natural hydrosystems.
Seagrasses form underwater meadows in the coastal zone. These meadows are known to attenuate waves (Bradley & Houser, 2009; Fonseca & Cahalan, 1992; Koftis et al., 2013; Kobayashi et al., 1993; Paul & Amos, 2011) and currents (Fonseca et al., 1982; Fonseca & Fisher, 1986; Peterson et al., 2004; Widdows et al., 2008), and to significantly influence sediment dynamics (Boscutti et al., 2015; Madsen et al., 2001). Depending on the biometric characteristics of the species (shoot density, leaf area index, plant stiffness, submergence ratio) and the morphological characteristics of the meadows (extension, fragmentation), the effect on hydrodynamics will vary (Fonseca & Koehl, 2006; Koftis et al., 2013; Paul & Amos, 2011; Stratigaki et al., 2011). The non-linear interactions of these parameters with hydrodynamics variables (wave height, wave period, water level, presence of a current) can also influence the attenuation of waves, the modification of currents, and sediment dynamics (Bradley & Houser, 2009; Paquier et al., 2019; Paul & Amos, 2011).
Large-scale hydrosystem models can integrate the role of vegetation through a change in the roughness coefficient. This can be done empirically through the modification of Manning's n value (for example, in the ADCIRC model (Luettich et al., 1992)). In other models, such as Xbeach (Roelvink et al., 2009) or Telemac (Hervouet, 2007), a specific vegetation roughness, as expressed by Mendez and Losada (2004), can be used. The calculation of this parameter is based on the geometric and physical characteristics of the vegetation meadow. This approach was very innovative in 2004, and is now widely used in modeling. However, it does not account for vegetation flexibility, which can be very important in subaquatic vegetation, especially when canopies are sparse (Paquier et al., 2019). As seagrass meadows are declining around the world (Waycott et al., 2009), it seems essential to better take into account vegetation flexibility in hydrodynamics modeling and to better understand the role of declining meadows or, more generally, sparse canopies. This could help to investigate seagrass meadows' limitations as coastal buffers protecting against erosion and storm surges, and could potentially enhance the protection of these declining ecosystems.
Sub-Aquatic Vegetation (SAV) is known to play a role in wave and storm surge mitigation, and thus, in coastal protection. The impacts of different species under different conditions have already been studied (see introduction of Paquier et al. (2019) for a review of the different processes observed). SAV has the ability to attenuate waves and currents and to modify turbulence. However, no study to date has compared the impacts of the different existing species. Such studies are nearly impossible to do in the field considering the variety of environments in which the different species live. Furthermore, the experiments in flumes with real marine plants often are forbidden to protect the marine plant species. A numerical study could, therefore, help remedy the lack of in-situ studies. However, the modification in hydrodynamics generated by the plants themselves is still difficult to estimate since plant movements under waves and currents are still not well simulated and no exact numerical model exists (Mendez & Losada, 2004; Sánchez-González et al., 2011). Generally, existing numerical studies use rigid bodies to simulate plants with different roughness coefficients (Dalrymple et al., 1984; Wallace & Cox, 2000). However, among the numerical studies dealing with plants, Beudin et al. (2017) describe a three dimensional (3D) modeling framework that simulates the interactions between waves, flow, and flexible vegetation. Beudin et al. (2017) evaluated a plant drag model against field measurements in eelgrass canopies and investigated the hydrodynamics in an idealized shallow-water setting.
The research presented herein aims to reproduce plant movement under waves and/or current using the SPH method. The method was tested by building numerical two dimensional (2D) and 3D flumes with the GPUSPH model (GPUSPH official website. www.gpusph.org. Accessed: 2017-03-31.; Gómez-Gesteira et al., 2010; Hérault et al., 2010, 2014), then comparing the simulations with the available data.
After a brief description of the SPH method (definition of the two numerical approaches used for plants and water), several tests of the FSI simulations are presented using the proposed model and these are compared with other simulations and experimental data (the FSI was calibrated and evaluated in the open source GPUSPH code (Hérault et al., 2011).
The numerical simulation results are compared with experimental results based on real or plastic seagrass meadows. The Young modulus is evaluated for real or fake plants for both the experimental and numerical approaches. The wave attenuation due to the seagrass meadow in the simulation also compared with experimental data. Finally, a first simulation also is run with field data, collected in a bay occupied by a Zostera Noltei meadow (another species of marine plant) in a large lagoon in Southern France.
Section snippets
SPH method and FSI approach
The SPH method is based on the theory of interpolation (Benz, 1990; Liu, 2002; Monaghan, 1982, 1992, 2005). Its formulation often is divided into two parts: (i) the integral representation, and (ii) the particle approximation. The equation for the integral representation generally used in SPH is given in Appendix A.
Calibration and comparison with experimental data
Antoci et al. (2007) did a laboratory experiment and compared the results with SPH simulations. The experiment consisted in deforming an elastic bundle acting as a dam in a water column. The configuration of the experiment is described in Antoci et al. (2007). Table 1 lists the size experiment parameters. The elastic properties of the beam can be determined from Antoci et al. (2007). For the current simulations, a Young's modulus that provided the results closest to the experimental results was
Results and discussion
The plant movements predicted with the proposed SPH simulations were compared with both experimental results (Le Bouteiller & Venditti, 2015; Luhar & Nepf, 2011) and field observations (Paquier et al., 2019).
Different species of seagrass colonize the shallow coastal waters around the world, often forming large underwater meadows. Seagrass meadows are known to reduce wave height and current velocity near the seabed, but the simulation meadow (see Fig. 4), could be also a problem for the
Conclusions
The results obtained for the various FSI simulations with the SPH method were reasonable, even though improvements can be made in the future. First, in a deformation test case of an elastic plate under a column of water, it was shown that it is possible to model the movement of a solid submitted to water effects with the SPH method and FSI. Plant movements also were successfully simulaed in a wave flume. The different curves taken by the plant under the passing waves show the role of the plant
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
The authors gratefully acknowledge the support of the NVIDIA Corporation who donated the GTX 780 GPU used for this research. This research was partially supported by the LabEx Tec 21 program (Investissement d’Avenirgrant agreement ANR-11-LABX-0030) and by financial support from the “Agence de l'Eau RM&C″ through the CANOPé research program. AEP was partially supported by the French National Research Agency (ANR) through ANR @RAction chair medLOC (ANR-14-ACHN-0007-01–project leader Thomas
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2021, Applied Ocean ResearchCitation Excerpt :Hermange et al. (2019a) have presented a 3D SPH-FEM model and simulated the case of sloshing with a bottom clamped elastic baffle. Based on the 3D GPUSPH, Paquier et al. (2021) have studied the seagrass movements under wave-current conditions and showed that the model can be used to estimate the Manning's coefficient (roughness friction) for coastal vegetation. A considerable percentage of the world's coastal structures (e.g., breakwaters and sea walls) consists of mounds or layers of quarried rock fill (Van der Meer et al., 2018).