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

/pdf/mathematical-modelling-of-wave-energy-converters-a-review-of-26x5med31l.pdf

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

This paper presents the recent development on the nonlinear directional wave generation process in a 3D Numerical Wave Tank (NWT). The NWT is based on a nonlinear model using the High-Order Spectral (HOS) method, which exhibits high level of accuracy as well as efficiency properties provided by a Fast Fourier Transform (FFT) solution. The wavemaker modeling appears to be a key point in the simulation and it is carefully detailed. Different levels of approximation of the wave generation (up to third-order in nonlinearity) are studied. The properties of the numerical scheme in terms of convergence, stability and accuracy are discussed. This NWT features all the characteristics of the real wave tank (directional wavemaker, absorbing zone, perfectly reflective side walls). Furthermore, several validation results and practical applications where numerical simulations are successfully compared to experiments on 2D and 3D wave fields are presented.

A modified High-Order Spectral method for wavemaker modeling in a numerical wave tank

. In the present paper we propose a method for studying extreme-wave appearance based on the Higher-Order Spectral (HOS) technique proposed by West et al. (1987) and Dommermuth and Yue (1987). The enhanced HOS model we use is presented and validated on test cases. Investigations of freak-wave events appearing within long-time evolutions of 2-D and 3-D wavefields in open seas are then realized, and the results are discussed. Such events are obtained in our periodic-domain HOS model by using different kinds of configurations: either i) we impose an initial 3-D directional spectrum with the phases adjusted so as to form a focused forced event after a while, or ii) we let 2-D and 3-D wavefields defined by a directional wave spectrum evolve up to the natural appearance of freak waves. Finally, we investigate the influence of directionality on extreme wave events with an original study of the 3-D shape of the detected freak waves.

https://nhess.copernicus.org/articles/7/109/2007/nhess-7-109-2007.pdf

3-D HOS simulations of extreme waves in open seas

https://hal.archives-ouvertes.fr/hal-01299487/document

HOS-ocean: Open-source solver for nonlinear waves in open ocean based on High-Order Spectral method

Time domain simulation of nonlinear water waves using spectral methods

In the present paper two numerical schemes for propagating waves over a variable bathymetry in an existing High-Order Spectral (HOS) model are introduced. The first scheme was first developed by Liu and Yue (1998), and the second one is an improved scheme which considers two independent
orders of non-linearity: one for the bottom and one for the free-surface elevation. We investigate the numerical properties (accuracy, convergence rate, efficiency) of both schemes with respect to the numerical parameters on a simple configuration. To validate the proposed schemes, we first consider
Bragg reflection from a sinusoidal bottom patch — as an example of a small bottom variation around a mean water depth. The second validation case focuses on a larger bottom variation with the study of the shoaling of linear waves. Finally, an application is performed to demonstrate the applicability of the proposed model to non-linear cases where the bottom variation is important. In this concern, the very well documented test case of a 2D underwater bar is studied in detail. Comparisons are provided with both experimental and numerical results.

/pdf/development-and-validation-of-a-non-linear-spectral-model-2cmnu76jly.pdf

Guillaume Ducrozet

Papers

A modified High-Order Spectral method for wavemaker modeling in a numerical wave tank

3-D HOS simulations of extreme waves in open seas

HOS-ocean: Open-source solver for nonlinear waves in open ocean based on High-Order Spectral method

Time domain simulation of nonlinear water waves using spectral methods

Development and validation of a non-linear spectral model for water waves over variable depth