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Wave Generation and Absorption Techniques

Aggelos Dimakopoulos'[1] [2] and Pablo Higuera2 [2]

Introduction

Numerical modelling of wave propagation in the nearshore area has been around for several decades. Research work in this area has resulted in the development of a variety of theoretical and numerical methods and techniques to solve this problem. Initial efforts of modelling coastal wave propagation were performed using depth-integrated approaches, such as the Boussinesq equations (Peregrine (1967); Madsen et al. (1991); Karambas and Kouti- tas (1992); Nwogu (1993); Wei et al. (1995)) and the shallow water equations (Hibberd and Peregrine (1979), Kobayashi et al. (1987), Titov and Synolakis (1995)), although the latter concerned strictly shallow water wave propagation (wavelength > 20 times the water depth). Additional techniques were also developed to include flow evolution in the vertical (aligned with gravity) direction, initially by using simplified forms of mass and momentum conservation equations, e.g., potential (irrotational) flow coupled with the Boundary Element Method (Grilli et al. (1989, 2001); Belibassakis and Athanassoulis (2004)).

Models that used the Navier-Stokes equations for simulating wave propagation were also developed at about the same time, but were initially limited to 2D-vertical setups due to significant computational requirements (Johns and Jefferson (1980); Lemos (1992); Lin and Liu (1998); and Bradford (2000), among others). With the rapid improvement in computer performance during the 2000s and specially in the early 2010s, the simulation of 3D wave propagation processes using Navier-Stokes approaches became practical. Initial efforts that used three-dimensional flow domains aimed to investigate detailed turbulence structures under wave breaking with normal wave incidence (Christensen (2006); Watanabe et al. (2005)) or to simulate 3D wave transformation and breaking processes under oblique incidence (Huang et al. (2009); Dimakopoulos and Dimas (2011)).

All these early studies provided a template for establishing the concept of the numerical wave tank (NWT), i.e., a particular setup of the computational domain which allows numerical testing and performance evaluation of coastal engineering applications. These studies, nevertheless, did not yet offer a robust methodology for simulating fully developed sea states, which would allow testing realistic natural or man-made features encountered near the coast. Therefore, it was necessary to develop techniques for generating and absorbing regular and random waves at the offshore and landward boundaries in a consistent manner, in particular:

  • • at the offshore boundary, simultaneous wave generation and absorption techniques allow the representation of incident wave condition which often come from a wave fore- cast/transformation model (e.g., SWAN, Booij et al. (1996)) and prevent re-reflections from bathymetric or man-made features; and
  • • at the landwards boundary, wave absorption techniques allow the complete absorption of the waves to prevent unwanted wave reflection from the outlet boundary.

To some extent , the concept of the NWT is influenced by the layout of physical modelling flumes and basins, which is based on a technology that has been mature for few decades. But, fortunately for the numerical modellers, the absence of real world limitations such as space allocation, material type and strength, and laboratory safety considerations gave rise to a diversity of wave generation and absorption techniques for NWTs that were mostly based on abstract concepts. These techniques essentially enable performing long simulations by maintaining stable and fully developed wave statistics over time and by keeping a constant water level in the NWT.

Wave generation and absorption techniques in depth-integrated models, such as the Bouss2D model (Nwogu and Demirbilek, 2001) or the FUNWAVE model (Shi et al., 2016) were implemented relatively early, as these models were generally least computationally demanding. Similar and in some ways more advanced techniques have also been developed for Navier-Stokes equations, within the context of Computational Fluid Dynamics (CFD) models. NWTs in CFD models are in a maturing process over the last 5-10 years, having as key milestones the works of Jacobsen et al. (2012) and Higuera et al. (2013). These two key publications left a significant legacy within the research community, which is summarised in the following points.

  • • They both demonstrated that NWTs in CFD models are capable of efficient wave absorption which was at least equal, if not better than in the laboratory.
  • • They both implemented the techniques in OpenFOAM®, the leading open-source toolkit for CFD applications, thus allowing the research and scientific community to replicate these results and gain confidence that these methods work.
  • • They presented a set of benchmarks (particularly in Higuera et al. (2013)) that can be used to compare and evaluate similar or substantially different techniques for wave generation and absorption.

The aim of this work is to present an account of the most important concepts and techniques for wave generation and absorption, such as the Dirichlet-type and radiation boundary conditions, the relaxation zone methods, internal mass/momentum source wavemakers and moving paddles. These are presented in more detail in the next section, followed with relevant advantages and disadvantages. In the last sections, an overall assessment of the existing methods is given along with ideas for future development .

  • [1] 1 HR Wallingford, Wallingford, Oxon, 0X10 SBA, UK, - Department of Civil and Environmental Engineering, Faculty of Engineering, University of Auckland, Auckland, 1010,New Zealand.
  • [2] Corresponding authors: This email address is being protected from spam bots, you need Javascript enabled to view it ; This email address is being protected from spam bots, you need Javascript enabled to view it
  • [3] Corresponding authors: This email address is being protected from spam bots, you need Javascript enabled to view it ; This email address is being protected from spam bots, you need Javascript enabled to view it
 
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