Smoothed particle hydrodynamics (SPH) is a meshfree particle method based on Lagrangian formulation, and has been widely applied to different areas in engineering and science. This paper presents an overview on the SPH method and its recent developments, including (1) the need for meshfree particle methods, and advantages of SPH, (2) approximation schemes of the conventional SPH method and numerical techniques for deriving SPH formulations for partial differential equations such as the Navier-Stokes (N-S) equations, (3) the role of the smoothing kernel functions and a general approach to construct smoothing kernel functions, (4) kernel and particle consistency for the SPH method, and approaches for restoring particle consistency, (5) several important numerical aspects, and (6) some recent applications of SPH. The paper ends with some concluding remarks.

Smoothed Particle Hydrodynamics (SPH): an Overview and Recent Developments

https://hal.archives-ouvertes.fr/hal-02266584/document

Declutching control of a wave energy converter

The wave energy sector has made and is still doing a great effort in order to open up a niche in the energy market, working on several and diverse concepts and making advances in all aspects towards more efficient technologies However, economic viability has not been achieved yet, for which maximisation of power production over the full range of sea conditions is crucial Precise mathematical models are essential to accurately reproduce the behaviour, including nonlinear dynamics, and understand the performance of wave energy converters Therefore, nonlinear models must be considered, which are required for power absorption assessment, simulation of devices motion and model-based control systems Main sources of nonlinear dynamics within the entire chain of a wave energy converter - incoming wave trains, wave-structure interaction, power take-off systems or mooring lines- are identified, with especial attention to the wave-device hydrodynamic interaction, and their influence is studied in the present paper for different types of converters In addition, different approaches to model nonlinear wave-device interaction are presented, highlighting their advantages and drawbacks Besides the traditional Navier-Stokes equations or potential flow methods, ‘new’ methods such as system-identification models, smoothed particle hydrodynamics or nonlinear potential flow methods are analysed

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Mathematical modelling of wave energy converters: A review of nonlinear approaches

Nonlinear modulational instability of wavepackets is one of the mechanisms responsible for the formation of large-amplitude water waves. Here, mechanically generated waves in a three-dimensional basin and numerical simulations of nonlinear waves have been compared in order to assess the ability of numerical models to describe the evolution of weakly nonlinear waves and predict the probability of occurrence of extreme waves within a variety of random directional wave fields. Numerical simulations have been performed following two different approaches: numerical integration of a modified nonlinear Schrodinger equation and numerical integration of the potential Euler equations based on a higher-order spectral method. Whereas the first makes a narrow-banded approximation (both in frequency and direction), the latter is free from bandwidth constraints. Both models assume weakly nonlinear waves. On the whole, it has been found that the statistical properties of numerically simulated wave fields are in good quantitative agreement with laboratory observations. Moreover, this study shows that the modified nonlinear Schrodinger equation can also provide consistent results outside its narrow-banded domain of validity.

https://researchbank.swinburne.edu.au/file/7b2611ba-9886-49fb-8279-afc8dda44401/1/PDF (Published version).pdf

Evolution of weakly nonlinear random directional waves: laboratory experiments and numerical simulations

http://empslocal.ex.ac.uk/people/staff/mm411/documents/LiWeissMuellerTownleyBelmont12pp.pdf

Wave energy converter control by wave prediction and dynamic programming

The propagation of water waves is characterized by a slow dynamics, with few energy dissipation This phenomenon thus largely differs from the classical application of free-surface SPH to fluid-structure impact flows or violent flows involving breaking waves and interface reconnections, to which the SPH method is well adapted The present work analyzes the capability of the SPH method to deal with propagation of such wave trains by comparing various SPH formulations Results on damping and phase shifting show that the use of Riemann solvers and renormalization techniques brings significant improvements to the standard SPH scheme

Water Wave Propagation using SPH Models

We present a comparison between two distinct numerical codes dedicated to the study of wave energy converters. Both are developed by the authors, using a boundary element method with linear triangular elements. One model applies fully nonlin-ear boundary conditions in a numerical wavetank environnment (and thus referred later as NWT), whereas the second relies on a weak-scatterer approach in open-domain and can be considered a weakly nonlinear potential code (referred later as WSC). For the purposes of comparison, we limit our study to the forces on a heaving submerged sphere. Additional results for more realistic problem geometries will be presented at the conference. INTRODUCTION Among the marine renewable energy sources, wave energy is a promising option. Despite the great number of technologies that have been proposed, currently no wave energy converter (WEC) has proven its superiority over others and become a technological solution. Usual numerical tools for modeling and designing WECs are based on boundary elements methods in linear potential theory [1-4]. However WECs efficiency relies on large amplitude motions [5], with a design of their resonance frequencies in the wave excitation. Linear potential theory is thus inadequate to study the behavior of WEC in such configuration.

/pdf/comparison-of-fully-nonlinear-and-weakly-nonlinear-potential-2w9w4i3gtu.pdf

Comparison of Fully Nonlinear and Weakly Nonlinear Potential Flow Solvers for the Study of Wave Energy Converters Undergoing Large Amplitude Motions

Comparison of wave modeling methods in CFD solvers for ocean engineering applications

This paper presents recent offshore applications of the SWENSE (Spectral Wave Explicit Navier-Stokes Equations) approach which is an original solution scheme for the time simulation of wave-body interactions using a combined potential / RANSE approach and a decomposition of the nonlinear flow in incident and diffracted parts. The viscous free surface flow around an TLP is computed in cases of regular and irregular waves. The incoming regular wave field is given by an algorithm based on stream function theory (Rienecker & Fenton, 1981) while the incoming irregular wave field is computed by a Higher Order Spectral (HOS) model (Bonnefoy et al, 2004). This latter model is validated against the previous one for a case of regular waves. Concerning results on the TLP structure, time histories of free surface elevations and pressure loads are compared to results from a time domain nonlinear potential flow solver (Ferrant, 1996; Ferrant et al, 2003b). Results obtained with the SWENSE method show an overall good agreement with second order potential flow results. Essential non linear effects associated with the interaction with the free surface are captured, while noticeable viscous effects are also observed, in the form of vortices shed by pontoons corners. More in-depth comparisons with experimental or numerical data have to be undertaken but these preliminary results are a good indication of the capacity of the SWENSE scheme for simulating wave-body interactions in the offshore context.

Simulation of a TLP In Waves Using the SWENSE Scheme

The scattering of nonlinear and non-breaking surface gravity waves propagating over a three-dimensional varying bathymetry is considered in this paper. In a recent study (Gouin et al., 2016) two numerical schemes for propagating waves over a variable bottom in an existing High-Order Spectral (HOS) model have been introduced. Both the computational effort and the accuracy of the model were shown to be conserved with the introduction of these new schemes. Moreover, they have been extensively validated in 2D, but the propagation of regular and irregular waves over 3D varying bottoms remains to be addressed with such spectral methods. In this paper, the three-dimensional formalism is introduced as well as the practical implementation of 3D configurations. Then the method is applied to a three-dimensional varying bathymetry consisting of an elliptical lens, as used in the Vincent and Briggs (1989) experiment. Incident waves passing across the lens are transformed and a strong convergence region is observed after the elliptical mound. The wave amplification depends on the incident wave. Numerical results for regular waves, unidirectional and directional irregular waves are analysed and compared with experimental data, demonstrating the efficiency and practical applicability of the present approach to treat the nonlinear propagation of various sea states over a varying bathymetry.

Guillaume Ducrozet

Papers

Water Wave Propagation using SPH Models

Comparison of Fully Nonlinear and Weakly Nonlinear Potential Flow Solvers for the Study of Wave Energy Converters Undergoing Large Amplitude Motions

Comparison of wave modeling methods in CFD solvers for ocean engineering applications

Simulation of a TLP In Waves Using the SWENSE Scheme

Propagation of 3D nonlinear waves over an elliptical mound with a High-Order Spectral method