Michel BENOIT

Chercheur Senior LHSV

Publications

Resolved DEM-CFD coupling for wave-armour blocks interactions
- Barcet Matthieu
- Benguigui William
- Laviéville Jérôme
- Benoit Michel
- Wachs Anthony
- Fede Pascal
- Bonometti Thomas
Ocean Engineering, Elsevier , 2025, 337, pp.121865 . The present work aims to tackle breakwater stability challenges through an innovative numerical deterministic method using a resolved DEM-CFD (Discrete Element Method—Computational Fluid Dynamics) strategy, which simulates the individual motions of armour units within a fluid solver. To achieve this, a coupling between a DEM code and a CFD code is implemented and validated. The fluids (air and water) are solved using a Eulerian–Eulerian CFD solver, and the contacts between blocks are solved using a DEM code. The solids are defined within the fluid solver using a discrete forcing approach and are therefore fully resolved. In this way, the fluid solver enables the prediction of object motions with complex shapes such as tetrapods. To couple the codes, forces exerted on the solids are calculated in the fluid solver and sent to the DEM solver. Then, contact and gravity forces are computed and added to the fluid forces. The DEM solver then computes the new positions and velocities of the bodies, which are retrieved by the fluid solver. An experimental study is performed on a fixed and instrumented idealized breakwater to evaluate the wave forces acting on a coastal structure. The experiments are then numerically reproduced to validate the numerical model. Simulations of the impact of solitary waves on a row of mobile isolated tetrapods laid on a horizontal berm are then performed using the DEM-CFD coupling. The importance of initial placement and friction parameters is investigated to show the sensitivity to these parameters. (10.1016/j.oceaneng.2025.121865)
DOI : 10.1016/j.oceaneng.2025.121865
Numerical modelling of nearshore wave transformation, breaking and overtopping of coastal protections with the enhanced Serre-Green–Naghdi equations
- Coulaud Guillaume
- Teles Maria
- Benoit Michel
Coastal Engineering, Elsevier , 2025 . Admissible average overtopping discharges in given storm conditions are typically used to design coastal protections, in particular dykes or breakwaters. These discharges are usually estimated using semi-empirical formulas relying on wave conditions at the toe of the structure. These formulas, unfortunately, only work for simple configurations, invariant alongshore, and can be insufficient for complex sea states. Therefore, numerical modelling could be a more flexible alternative for estimating these discharges. This work presents the development and validation of a Boussinesq-type numerical model solving the fully-nonlinear weakly-dispersive enhanced Serre-Green-Naghdi equations for the simulation of random wave overtopping over impermeable structures in one horizontal dimension. Wave breaking is modelled with an eddy viscosity approach based on the turbulent kinetic energy, which is robust and accurate at describing energy dissipation in the surf zone. Two distinct experimental datasets, with 184 trials in total and very dissimilar wave conditions and foreshore seabed profiles, are used to validate the model regarding wave propagation, shoaling, breaking and overtopping. Both unimodal and bimodal sea states are considered. Average overtopping discharges in configurations with deep and very shallow foreshores, as well as for breaking and non-breaking waves, are well reproduced by the model. For instance, typical mean relative errors on the simulated mean overtopping rates are found to lie within ±20% compared with the measurements, at least for the largest discharges of the considered campaigns. The scatter of simulated discharges is somewhat higher for lower discharges, but the results remain in an acceptable range. (10.1016/j.coastaleng.2025.104857)
DOI : 10.1016/j.coastaleng.2025.104857
On a high-order shallow-water wave model with canonical non-local Hamiltonian structure
- Papoutsellis Christos
- Benoit Michel
Physica D: Nonlinear Phenomena, Elsevier , 2025, 479, pp.134691 . We derive and study a new family of non-local partial differential equations (PDEs) that model free-surface long gravity waves over a flat bottom. To derive the model equations we approximate the velocity potential as a series of vertical polynomials derived from the shallow-water expansion of the Dirichlet-to-Neumann problem in the Hamiltonian formulation of free-surface potential flow and invoke Luke's variational principle. The resulting evolution equations exhibit a non-local Hamiltonian structure being coupled with a system of linear elliptic spatial PDEs on the horizontal plane. A key advantage of this approach is that it directly yields canonical Hamiltonian equations, which are well-suited for numerical solutions using standard methods. This class of model equations offers high-order shallow-water approximations of the water-wave problem. It contains terms whose spatial derivatives are at most of order two, distinguishing it from asymptotic methods involving higher-order mixed spatio-temporal derivatives. We explore the first non-trivial member of this family, highlighting its connections to other mathematical models and emphasizing its practical utility. We then analyze and discuss its linear dispersive properties and demonstrate that it does not exhibit a specific type of instability known as wave-trough instability. Additionally, we demonstrate its effectiveness in simulating the long-distance steady propagation of strongly non-linear solitary waves and the head-on collision of two counter-propagating solitary waves. In the latter case, comparisons with experimental data confirm the model's ability to capture complex wave dynamics, including wave transformation in the presence of strong non-linearity and dispersion. The extension of this approach to accommodate variable bottom topography is briefly discussed. (10.1016/j.physd.2025.134691)
DOI : 10.1016/j.physd.2025.134691
Wave–structure interaction by a two–way coupling between a fully nonlinear potential flow model and a Navier–Stokes solver
- Landesman Paul
- Harris Jeffrey
- Peyrard Christophe
- Benoit Michel
Ocean Engineering, Elsevier , 2024, 308, pp.118209 . A two-way domain decomposition coupling procedure between a fully nonlinear potential flow model and a Navier–Stokes solver capturing the free surface with a Volume of Fluid method is used to study wave–structure interaction applied to offshore wind turbines. Away from the structure, the large-scale inviscid wave field is modeled by the potential code. Wave generation and absorption in this 3D hybrid model take place in the outer potential domain. The codes exchange data in the region around their common boundaries. Through the two-way coupling, waves propagate in and out of the viscous subdomain, making the hybrid algorithm suitable to study wave diffraction on marine structures, while keeping the viscous subdomain small. Each code uses its own mesh and time step. Subdomains are overlapping, therefore continuity conditions on velocity and free surface have to be verified on two distinct coupling surfaces at any time. Parallel implementation with communications between the models relying on the Message Passing Interface library allows calculations on large spatial and temporal scales. The coupling algorithm is first tested for regular nonlinear waves and then applied to simulate wave loads exerted on a vertical monopile in 3D. Attention is paid to the high-order components of the horizontal force. (10.1016/j.oceaneng.2024.118209)
DOI : 10.1016/j.oceaneng.2024.118209
Equilibration process of out-of-equilibrium sea-states induced by strong depth variation: Evolution of coastal wave spectrum and representative parameters
- Zhang Jie
- Benoit Michel
- Ma Yuxiang
, 2022, pp.104099 . Recent studies showed both experimental and numerical evidence that the occurrence probability of freak waves could be significantly enhanced as results of non-equilibrium dynamics induced by strong depth variations. The sea-state is characterized by strong non-Gaussian behavior in a short spatial extent after the depth transition, covering a few wavelengths. In this work, we investigate the complete equilibration process of an out-of-equilibrium sea-state via high-fidelity numerical simulations. In the simulations, the region after the depth transition is set as long as around one hundred wavelengths, such that the spectral adaptation develops and terminates eventually. The results are analyzed with spectral, cross-spectral and statistical approaches. It is shown that there are two stages with different spatial scales in the equilibration process. In the short scale, the sea-state is characterized by significant changes in wave statistics, freak wave occurrence probability is intensified. In the long scale, the wave spectrum undergoes strong modulation, the spectral peak disintegrate into a relative broad band, and low-frequency waves are enhanced as well. We show evidence that the spectral changes in the long scale are due to interactions of free components. The wave nonlinearity is shown to be positively correlated to the magnitude of the dynamical responses, but irrelevant to the length of the spatial scales in the equilibration process. In the established shallow-water equilibrium, the freak wave occurrence probability becomes less than Gaussian expectation and the waves are asymmetric in the vertical direction and symmetric in the horizontal. (10.1016/j.coastaleng.2022.104099)
DOI : 10.1016/j.coastaleng.2022.104099
Enhanced extreme wave statistics of irregular waves due to accelerating following current over a submerged bar
- Zhang Jie
- Ma Yuxiang
- Tan Ting
- Dong Guohai
- Benoit Michel
Journal of Fluid Mechanics, Cambridge University Press (CUP) , 2023, 954, pp.A50 . We present experimental results of irregular long-crested waves propagating over a submerged trapezoidal bar with the presence of a background current in a wave flume. We investigate the non-equilibrium phenomenon (NEP) induced by significant changes of water depth and mean horizontal flow velocity as wave trains pass over the bar. Using skewness and kurtosis as proxies, we show evidence that an accelerating following current could increase the sea-state non-Gaussianity and enhance both the magnitude and spatial extent of the NEP. We also find that below a ‘saturation relative water depth’ $k_p h_2 \approx 0.5$ ( $k_p$ being the peak wavenumber in the shallow area of depth $h_2$ ), although the NEP manifests, the decrease of the relative water depth does not further enhance the maximum skewness and kurtosis over the bar crest. This work highlights the nonlinear physics according to which a following current could provoke higher freak wave risk in coastal areas where modulation instability plays an insignificant role. (10.1017/jfm.2022.1022)
DOI : 10.1017/jfm.2022.1022
Assessment of one-way coupling methods from a potential to a viscous flow solver based on domain- and functional-decomposition for fixed submerged bodies in nonlinear waves
- Robaux Fabien
- Benoit Michel
European Journal of Mechanics - B/Fluids, Elsevier , 2022, 95, pp.315-334 . To simulate the interaction of ocean waves with marine structures, coupling approaches between a potential flow model and a viscous model are investigated. The first model is a fully nonlinear potential flow (FNPF) model based on the Harmonic Polynomial Cell (HPC) method, which is highly accurate and best suited for representing long distance wave propagation. The second model is a CFD code, solving the Reynolds-Averaged Navier-Stokes (RANS) equations within the \openfoam toolkit, more suited to represent viscous and turbulent effects at local scale in the body vicinity. Two one-way coupling strategies are developed and compared in two dimensions, considering fully submerged and fixed structures. A domain decomposition (DD) strategy is first considered, introducing a refined mesh in the body vicinity on which the RANS equations are solved. Boundary conditions and interpolation operators from the FNPF results are developed in order to enforce values at its outer boundary. The second coupling strategy considers a decomposition of variables (functional decomposition, FD) on the local grid. As the FNPF simulation provides fields of variables satisfying the irrotational Euler equations, complementary velocity and pressure components are introduced as the difference between the total flow variables and the potential ones. Those complementary variables are solutions of modified RANS equations. Extensive comparisons are presented for nonlinear waves interacting with a horizontal cylinder of rectangular cross-section. The loads exerted on the body computed from the four simulation methods (standalone FNPF, standalone CFD, DD and FD coupling schemes) are compared with experimental data. It is shown that both coupling approaches produce an accurate representation of the loads and associated hydrodynamic coefficients (inertia and drag) over a large range of incident wave steepness and Keulegan-Carpenter number, for a small fraction of the computational time needed by the complete CFD simulation. (10.1016/j.euromechflu.2022.05.011)
DOI : 10.1016/j.euromechflu.2022.05.011
Nonlinear time-domain wave-structure interaction: a parallel fast integral equation approach
- Harris Jeffrey C
- Dombre Emmanuel
- Benoit Michel
- Grilli Stephan T.
- Kuznetsov Konstantin I
International Journal for Numerical Methods in Fluids, Wiley , 2022, 94, pp.188-222 . We report on the development and validation of a new Numerical Wave Tank (NWT) solving fully nonlinear potential flow (FNPF) equations, as a more efficient variation of Grilli et al.'s NWT [Grilli et al., A fully nonlinear model for three-dimensional overturning waves over arbitrary bottom, International Journal for Numerical Methods in Fluids 35 (2001) 829-867], which was successful at modeling many wave phenomena, including landslide-generated tsunamis, rogue waves, and the initiation (10.1002/fld.5051)
DOI : 10.1002/fld.5051
Experimental and numerical characterization of swell type waves effect on wind sea growth with fetch
- Villefer Antoine
- Benoit Michel
- Violeau Damien
- Teles Maria João
- Harris Jeffrey C.
- Branger Hubert
- Luneau Christopher
, 2021 .
Influence of swell on wind-wave growth with fetch: an experimental and numerical study
- Villefer Antoine
- Teles Maria João
- Benoit Michel
- Violeau Damien
- Harris Jeffrey C.
- Branger Hubert
, 2021 .
Comparing methods of modeling depth-induced breaking of irregular waves with a fully nonlinear potential flow approach
- Simon Bruno
- Papoutsellis Christos
- Benoit Michel
- Yates Marissa L.
Journal of Ocean Engineering and Marine Energy, Springer , 2019 . The modeling of wave breaking dissipation in coastal areas is investigated with a fully nonlinear and dispersive wave model. The wave propagation model is based on potential flow theory, which initially assumes non-overturning waves. Including the impacts of wave breaking dissipation is however possible by implementing a wave breaking initiation criterion and dissipation mechanism. Three criteria from the literature, including a geometric, kinematic, and dynamic-type criterion, are tested to determine the optimal criterion predicting the onset of wave breaking. Three wave breaking energy dissipation methods are also tested: the first two are based on the analogy of a breaking wave with a hydraulic jump, and the third one applies an eddy viscosity dissipative term. Numerical simulations are performed using combinations of the three breaking onset criteria and three dissipation methods. The simulation results are compared to observations from four laboratory experiments of regular and irregular waves breaking over a submerged bar, irregular waves breaking on a beach, and irregular waves breaking over a submerged slope. The different breaking approaches provide similar results after proper calibration. The wave transformation observed in the experiments is reproduced well, with better results for the case of regular waves than irregular waves. Moreover, the wave statistics and wave spectra are predicted well in general, and in particular for regular waves. Some differences are observed for irregular wave cases, in particular in the low-frequency range. This is attributed to incomplete absorption of the long waves in the numerical model. Otherwise, the wave spectra in the range [0.5fp, 5fp] are reproduced well, before, inside, and after the breaking zone for the three irregular wave experiments. (10.1007/s40722-019-00154-7)
DOI : 10.1007/s40722-019-00154-7
Modelling of depth-induced wave breaking in a fully nonlinear free-surface potential flow model
- Papoutsellis Christos
- Yates Marissa L.
- Simon Bruno
- Benoit Michel
Coastal Engineering, Elsevier , 2019, 154, pp.103579 . (10.1016/j.coastaleng.2019.103579)
DOI : 10.1016/j.coastaleng.2019.103579
Development and validation of a 3D RBF-spectral model for coastal wave simulation
- Raoult Cécile
- Benoit Michel
- Yates Marissa L.
Journal of Computational Physics, Elsevier , 2019, 378, pp.278-302 . With the objective of simulating wave propagation in the nearshore zone for engineering-scale applications, a two dimensional (2DV) model based on the Euler-Zakharov equations (Yates and Benoit, 2015; Raoult et al., 2016) is extended to three dimensions (3D). To maintain the flexibility of the approach with the goal of applying the model to irregularly shaped domains, the horizontal plane is discretized with scattered nodes. The horizontal derivatives are then estimated using the Radial Basis Function-Finite Difference (RBF-FD) method, while a spectral approach is used in the vertical dimension. A sensitivity analysis examined the robustness of the RBF-FD approach as a function of RBF parameters when estimating the derivatives of a representative function. For a targeted stencil size between 20 and 30 nodes, Piecewise-Smooth (PS) polyharmonic spline (PHS) functions are recommended, avoiding the use of Infinitely-Smooth (IS) RBFs, which are less appropriate for the desired applications because of their dependence on a shape parameter. Comparisons of simulation results to observations from two wave basin experiments show that nonlinear effects induced by complex bottom bathymetries (10.1016/j.jcp.2018.11.002)
DOI : 10.1016/j.jcp.2018.11.002
A 3D parallel boundary element method on unstructured triangular grids for fully nonlinear wave-body interactions
- Dombre E.
- Harris J.C.
- Benoit Michel
- Violeau D.
- Peyrard C.
Ocean Engineering, Elsevier , 2019, 171, pp.505-518 . This paper presents the development and validation of a three-dimensional numerical wave tank devoted to studying wave-structure interaction problems. It is based on the fully nonlinear potential flow theory, here solved by a boundary element approach and using unstructured triangular meshes of the domain's boundaries. Time updating is based on a second-order explicit Taylor series expansion. The method is parallelized using the Message Passing Interface (MPI) in order to take advantage of multi-processor systems. For radiation problems, with cylindrical bodies moving in prescribed motion, the free-surface is updated with a fully Lagrangian scheme, and is able to reproduce reference results for nonlinear forces exerted on the moving body. For diffraction problems, semi-Lagrangian time-updating is used, and reproduces nonlinear effects for diffraction on monopiles. Finally, we study the nonlinear wave loads on a fixed semi-submersible structure, thereby illustrating the possibility to apply the proposed numerical model for the design of offshore structures and floaters. (10.1016/j.oceaneng.2018.09.044)
DOI : 10.1016/j.oceaneng.2018.09.044
FULLY NONLINEAR MODELING OF NEARSHORE WAVE PROPAGATION INCLUDING THE EFFECTS OF WAVE BREAKING
- Papoutsellis Christos E
- Yates Marissa L.
- Simon Bruno
- Benoit Michel
, 2018, 1 (36), pp.78 . INTRODUCTION Nearshore wave modeling over spatial scales of several kilometers requires balancing the fine-scale modeling of physical processes with the model's accuracy and efficiency. In this work, a fully nonlinear potential flow model is proposed as a compromise between simplified linear, weakly nonlinear or weakly dispersive models and direct CFD approaches. (10.9753/icce.v36.waves.78)
DOI : 10.9753/icce.v36.waves.78
FULLY NONLINEAR MODELING OF NEARSHORE WAVE PROPAGATION INCLUDING THE EFFECTS OF WAVE BREAKING
- Papoutsellis Christos
- Yates Marissa L.
- Simon Bruno
- Benoit Michel
, 2018, 1 (36) . INTRODUCTION Nearshore wave modeling over spatial scales of several kilometers requires balancing the fine-scale modeling of physical processes with the model's accuracy and efficiency. In this work, a fully nonlinear potential flow model is proposed as a compromise between simplified linear, weakly nonlinear or weakly dispersive models and direct CFD approaches. (10.9753/icce.v36.waves.78)
DOI : 10.9753/icce.v36.waves.78
Développement d’un modèle numérique non-linéaire et dispersif pour la propagation des vagues en zone côtière
- Raoult Cécile
- Benoit Michel
- Yates Marissa L.
Revue Paralia, Editions Paralia CFL , 2018, 11, pp.n01.1 - n01.14 . (10.5150/revue-paralia.2018.n01)
DOI : 10.5150/revue-paralia.2018.n01
Analysis of the linear version of a highly dispersive potential water wave model using a spectral approach in the vertical
- Benoit Michel
- Raoult Cécile
- Yates Marissa L.
Wave Motion, Elsevier , 2017, 74, pp.159 - 181 . h i g h l i g h t s • Highly dispersive potential flow model for water wave propagation. • Linear dispersion relation accurate in very deep water conditions (kh up to 100). • Accurate prediction of wave kinematics (orbital velocities) in deep water. • Validation of linear shoaling properties of the model. • Good prediction of reflected and transmitted waves on a Roseau-type bottom profile. a b s t r a c t The properties and accuracy of the linearized version of the fully dispersive and nonlinear wave model developed in Yates and Benoit (2015) and Raoult et al. (2016) are analyzed for both flat and variable bottom bathymetries. This model considers only a single layer of fluid and uses a basis of orthogonal Chebyshev polynomials to project the vertical structure of the potential. This approach results in an exponential convergence rate with the maximum degree of the Chebyshev polynomial, denoted N T , while only first-and second-order derivatives in space need to be evaluated. For the constant water depth case, the linear dispersion relation of the model is derived analytically, and expressions are established for N T ranging from 2 to 15. The analysis shows a rapid increase in accuracy in the deep water range with increasing N T. For instance, the relative error in the calculated wave celerity (in comparison with Stokes' analytical solution) remains smaller than 2.5% for deep water cases with kh up to 100 using N T ≥ 9 (k and h are the representative wavenumber and water depth, respectively). The wave kinematics, vertical profiles of the horizontal and vertical orbital velocities, converge to the Stokes profiles for kh up to 60 when using a sufficiently high value of N T. The vertically-averaged relative errors of the horizontal and vertical velocities remain below 6% and 3%, respectively, for kh up to 60 when using N T ≥ 11. The presented model shows better dispersive properties in deep water than several high-order Boussinesq-type models. For variable bottom bathymetries, the shoaling properties of the model are studied numerically, exhibiting good agreement with results from Stokes linear theory in the case of mild bottom slopes, using a sufficiently high value of N T with respect to the offshore relative water depth. For an offshore water depth of kh = 10 (i.e. more than 3 times the deep water limit), accurate wave heights in shallow water (kh = 0.25) are obtained with N T = 6 (or higher). Finally, the linear version of the model is validated with comparisons to analytical solutions of the reflection and transmission coefficients of regular waves over Roseau-type bathymetric profiles. Two bottom profiles are considered, including one with a steep slope, whose maximum value reaches about 1:0.7 (i.e. an angle of about 54.9 deg.). Using N T = 7, small differences (<0.4%) with the analytical solution are observed for the four considered cases, confirming the ability of the linear model to represent accurately the effects of steep bottom gradients on wave propagation dynamics. (10.1016/j.wavemoti.2017.07.002)
DOI : 10.1016/j.wavemoti.2017.07.002
Influence of timescales on the generation of seismic tsunamis
- Le Gal Marine
- Violeau Damien
- Benoit Michel
European Journal of Mechanics - B/Fluids, Elsevier , 2017, 65, pp.257 - 273 . (10.1016/j.euromechflu.2017.03.008)
DOI : 10.1016/j.euromechflu.2017.03.008
Resonance wave pumping with surface waves
- Carmigniani Rémi Arthur
- Benoit Michel
- Violeau Damien
- Gharib Morteza
Journal of Fluid Mechanics, Cambridge University Press (CUP) , 2017, 811, pp.1 - 36 . (10.1017/jfm.2016.720)
DOI : 10.1017/jfm.2016.720
Validation of a fully nonlinear and dispersive wave model with laboratory non-breaking experiments
- Raoult Cécile
- Benoit Michel
- Yates Marissa L.
Coastal Engineering, Elsevier , 2016, 114, pp.194 - 207 . With the objective of modeling coastal wave dynamics taking into account nonlinear and dispersive effects, a highly accurate nonlinear potential flow model was developed. The model is based on the time evolution of two surface quantities: the free surface position and the free surface velocity potential. A spectral approach is used to resolve vertically the velocity potential in the domain, by decomposing the potential using an orthogonal basis of Cheby-shev polynomials. With this approach, a wide range of relative water depths can be simulated, as demonstrated here with the propagation of nonlinear regular waves over a flat bottom with kh = 2π and 4π (where k is the wave number and h the water depth). The model is then validated by comparing the simulation results to experimental data for four non-breaking wave test cases: (1) nonlinear dynamics of a wave train generated by a piston-type wavemaker in constant water depth, (2) shoaling of a regular wave train on beach with constant slope up to the breaking point, (3) propagation of regular waves over a submerged bar, and (4) propagation of nonlinear irregular waves over a barred beach. The test cases show the ability of the model to reproduce well nonlinear wave interactions and the dynamics of higher-order bound and free harmonics. The simulation results agree well with the experimental data, confirming the model's ability to simulate accurately nonlinear and dispersive effects for non-breaking waves. (10.1016/j.coastaleng.2016.04.003)
DOI : 10.1016/j.coastaleng.2016.04.003
Construction of the Numerical Wave Databases Anemoc-2 on the Mediterranean Sea and the Atlantic Ocean Through Hindcast Simulations Over the Period 1979-2010
- Tiberi-Wadier Anne-Laure
- Laugel Amélie
- Benoit Michel
, 2016, pp.127--143 . no abstract (10.1007/978-981-287-615-7_9)
DOI : 10.1007/978-981-287-615-7_9
A database of validation cases for tsunami numerical modelling
- Violeau Damien
- Ata Riadh
- Benoit Michel
- Joly Antoine
- Abadie Stéphane
- Clous Lucie
- Martin Medina Manuel
- Morichon Denis
- Chicheportiche Jérémie
- Le Gal Marine
- Gailler A.
- Hebert Hélène
- Imbert David
- Kazolea Maria
- Ricchiuto Mario
- Le Roy Sylvestre
- Pedreros Rodrigo
- Rousseau Marie
- Pons Kévin
- Marcer Richard
- Journeau Camille
- Silva Jacinto R.
, 2016 . This work has been performed by a French national consortium within the framework of the national project Tandem, with aim to improve knowledge about tsunami risk on the French coasts. Workpackage #1 of this project was the opportunity to build a database of benchmark cases to assess the capabilities of 18 codes, solving various set of equations with different numerical methods. 14 test cases were defined from the existing literature with validation data from reference simulations, theoretical solutions or lab experiments. They cover the main stages of tsunami life: 1) generation, 2) propagation, 3) run-up and submersion, and 4) impact. For each case several of the numerical codes were compared in order to identify the forces and weaknesses of the models, to quantify the errors that these models may induce, to compare the various modelling methods, and to provide users with recommendations for practical studies. In this paper, 3 representative cases are selected and presented with an analysis of the results.
Sea-state modification and heaving float interaction factors from physical modelling of arrays of wave energy converters
- Stratigaki Vicky
- Troch Peter
- Stallard Tim
- Forehand David
- Folley Matt
- Kofoed Jens-Peter
- Benoit Michel
- Babarit Aurélien
- Vantorre Marc
- Kirkegaard J.
Journal of Renewable and Sustainable Energy, AIP Publishing , 2015, 7 (6), pp.061705 . Wave energy converters (WECs) extract energy from ocean waves and have the potential to produce a significant amount of electricity from a renewable resource. However, large “WEC farms” or “WEC arrays” (composed of a large number of individual WECs) are expected to exhibit “WEC array effects”. These effects represent the impact of the WECs on the wave climate at an installation site, as well as on the overall power absorption of the WEC array. Tests have been performed in the Shallow Water Wave Basin of DHI (Denmark) to study such “WEC array effects”. Large arrays of up to 25 heaving point absorber type WECs have been tested for a range of geometric layout configurations and wave conditions. Each WEC consists of a buoy with a diameter of 0.315 m. Power take-off was modeled by realizing friction based energy dissipation through damping of the WECs' motion. The produced database is presented: WEC response, wave induced forces on the WECs, and wave field modifications have been measured. A first understanding of WEC array effects is obtained. This unique experimental set-up of up to 25 individual WEC units in an array layout, placed in a large wave tank, is at present the largest set-up of its kind studying the important WEC array effects. The data obtained from these experimental tests will be very useful for validation and extension of numerical models. This model validation will enable optimization of the geometrical layout of WEC arrays for realistic wave farm applications and reduction of the cost of energy from wave energy systems. (10.1063/1.4938030)
DOI : 10.1063/1.4938030
Accuracy and efficiency of two numerical methods of solving the potential flow problem for highly nonlinear and dispersive water waves
- Yates Marissa L.
- Benoit Michel
International Journal for Numerical Methods in Fluids, Wiley , 2015, 77, pp.616-640 . SUMMARY The accuracy and efficiency of two methods of resolving the exact potential flow problem for nonlinear waves are compared using three different 1DH test cases. The two model approaches use high-order finite difference schemes in the horizontal dimension and differ in the resolution of the vertical dimension. The first model uses high-order finite difference schemes also in the vertical, while the second model applies a spectral approach. The convergence, accuracy, and efficiency of the two models are demonstrated as a function of the temporal, horizontal, and vertical resolution for (1) the propagation of regular nonlinear waves in a periodic domain, (2) the motion of nonlinear standing waves in a domain with fully reflective boundaries, and (3) the propagation and shoaling of a train of waves on a slope. The spectral model approach converges more rapidly as a function of the vertical resolution. In addition, with equivalent vertical resolution, the spectral model approach shows enhanced accuracy and efficiency in the parameter range used for practical model applications. (10.1002/fld.3992)
DOI : 10.1002/fld.3992