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International Journal of Fluid Machinery and Systems DOI: http://dx.doi.org/10.5293/IJFMS.2018.11.1.063

Vol. 11, No. 1, January-March 2018 ISSN (Online): 1882-9554

Original Paper

Review of Fluid Structure Interaction Methods Application to

Floating Wave Energy Converter

Mohammed Asid Zullah1, Young-Ho Lee2

1Geoscience, Energy and Maritime Division, Pacific Community,

Private Mail Bag, Suva, Fiji, zullah.m@gmail.com 2Division of Mechanical Engineering, College of Engineering, Korea Maritime and Ocean University, 727

Taejong-ro, Yeongdo-Gu, Busan 49112, South Korea, lyh@kmou.ac.kr

Abstract

Computational fluid dynamics (CFD) is a highly efficient paradigm that is used extensively in marine renewable

energy research studies and commercial applications. The CFD paradigm is ideal for simulating the complex dynamics

of Fluid-Structure Interactions (FSI) and can capture all kinds of nonlinear fluid motions. While nonlinear simulations

are considered more expensive and resource intensive compared to the frequency domain approaches, they are much

more accurate and ideal for commercial applications. This review study presents a comprehensive overview of the

computation fluid dynamics paradigm in context of wave energy converter (WEC) and highlights different CFD tools

that are available today for commercial and research applications. State-of-the-art CFD codes such as ANSYS CFX that

are highly ideal for WEC simulation problems are highlighted and aspects such as time and frequency domains are also

thoroughly discussed along with efficacy of the nonlinear simulations compared to the linear models. The paper presents

a comparative evaluation of different WEC modelling codes available today and illustrates the code framework of

different CFD simulation software suites.

Keywords: CFD, FSI, Navier-Stokes equation, WEC, nonlinear, simulations.

1. Introduction

The concept of modern computational fluid dynamics first took shape in the early seventies when it essentially represented a

conglomeration of domains such as physics, mathematics and computer science used for the purpose of simulating fluid flow dynamics

[1]. A study carried out by Kopal (1947) is probably the very first significant example of CFD where he deduced supersonic flow

values that flowed over geometrical cone structures [2]. With the development of fast mainframes in the late fifties and sixties the first

generation of computational fluid dynamics solutions started becoming available. Computational fluid dynamic solutions that came

next started implementing governing equations such as the Navier–Stokes equations to solve fluid hydrodynamic problems.

Today, the relevance of computational fluid dynamics with regards to hydrodynamic problem solving and simulations has become very

high and with the progress in computational technology the stature of CFD is defined as a third dimension in the area of fluid dynamics

[1]. In the recent years researchers have extensively used the CFD (Computational Fluid Dynamics) paradigm to understand the

underlying hydrodynamic properties of WECs. In a recent study, researchers used CFD to analyze the impact of chamber-duct on the

inner water surface amplitude and nozzle air flow [3]. Another CFD study conducted in 2012 focused on an experiment carried out by a

group of researchers in 2007 and reported that there has been an overestimation of efficiency by up to 30% because the several aspects

such as complicated variations in pressure were never taken into account [4][5]. The experiment carried out by Thomas et al. (2007)

was further repeated by Kamath et al. (2015) where they carried out complicated computational fluid dynamics simulations to

understand if there is any effect on the operational efficiency of wave energy converters such as the Oscillating Water Column device

mediated by power take-off damping [5][6]. In essence, researchers today fully appreciate the efficacy and applicability of the

computational fluid dynamics paradigm for oceanic wave energy research and for better understanding of the interaction of oceanic

waves with the wave energy converters in a simulated environment. A common apprehension regarding the usage of computation fluid dynamics in marine engineering is that it is not very cost-

effectiveness and for that reason many commercial organizations prefer to go for the tried and tested frequency-based methods. As a

matter of fact, setting up massive turbines to capture energy from tidal streams could be very difficult [7]. However, given the broad

applicability and efficacy of computational fluid dynamics it is definitely a more desirable option compared to the traditional methods.

Computational fluid dynamics offer a highly detailed overview of the interaction between oceanic waves and structure and is definitely

not restricted to the linear motions alone unlike the traditional frequency-based methods. Computational fluid dynamics can also be

Received December 12 2016; revised January 9 2017; accepted for publication Agust 10 2017: Review conducted by Abdus Samad.

(Paper number O16042K)

Corresponding author: Young-ho Lee, lyh@kmou.ac.kr

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used to simulate the physics and the dynamics of waves breaking and overtopping and given the exceptional pace of development in

computational technologies more robust algorithms are being conceptualized and developed, making them highly ideal for sectors such

as marine engineering and wave energy conversions [8]. Algorithms implementing computational fluid dynamics executes the Navier-

Stokes equations that can handle both non-linear and rotational dynamics. This make that highly intensive computationally and their

implementation becomes extremely resource intensive. However this can definitely be considered an acceptable trade-off because

computational fluid dynamics allow simulation of analysis of complex aspects such as wave drag, viscosity and other forces that are

entirely non-linear in nature. Furthermore, numerical simulations can be carried out at minimal costs and are almost entirely risk-free.

They can be excellent tools to ascertain the impact of the tidal stream turbines on the environment and can also be very instrumental in

the modelling of the turbine blades [9, 10]. Other options that can be very useful for offsetting the high computation costs of CFD

applications are the nonlinear model-reduction methods that are projection-based [11, 12]. These projection-based approaches are very

ideal for systems that are linear and essentially time-invariant and also for those systems that are linear and stationary [13, 14]. The

projection based model reduction paradigms are also ideal for nonlinear systems based on quadratic nonlinearities and to solve

problems of structural dynamics [15, 16, 17]. These paradigms function by approximating a functional model with minimal dimension

and are highly ideal for aerodynamic problem solving [18,19,20,21,22]. As a result, the project-based models become ideal for

applications that are highly time-sensitive such as flow control, optimization of structure designs and estimation of structure

uncertainties [23,24,25]. The projection-based methods have also been found to be effective for problem solving in the aero elasticity

domain. [26,27,28].

In the recent times a wide range of studies have used complex computational fluid dynamics for device simulation in experimental

tanks. A recent study by Bhinder et al. (2011) successfully used computational fluid dynamics to calculate the viscous drag coefficients

of wave energy conversion devices [29]. Similarly multiple research studies are currently underway to further streamline the

applicability of computational fluid dynamics in wave energy conversion array problems and establish the efficacy of the same [30].

2. The Core of CFD: Reynolds-Averaged Navier-Stokes Equations

In any given engineering problem scenario, substantial fluctuations can be seen in the fluid flow levels, both in the time and

space domain. These fluctuations are mediated largely by turbulence but it needs to be noted that the fluctuation values are stable

and stays within a fixed range. The Reynolds averaged Navier-Stokes equations utilize the average fluid flow quantities and

properly address the influence or the effect of turbulence. The average flow quantities are deduced in Reynold’s averaged

quantities and this allows expression of every dependent variable. Each dependent variable is made up of average time value and

the value of the fluctuating component [31]. Advanced computational fluid dynamics address the engineering problem of fluid

flow by executing the governing Reynolds averaged Navier-Stokes equations shown below.

(1)

(2)

In the above governing equations, u stands for the average velocity value over a specific time period t. The fluid density value is

represented by ρ and the pressure is represented by p. The fluid kinematic viscosity value is represented by ν and the eddy

viscosity is represented by νt. Finally, the fluid acceleration due to the gravitational pull is represented by g [6]. To analyze the

effects of diverse hydrodynamic forces during any kind of wave energy converter simulation, it is important that factors such as

turbulence, overtopping and oceanic wave breaking are properly taken into consideration. All of these are not possible to account

for using the standard potential flow paradigm and that is one of the main reasons why researchers prefer the Navier-Stoke

equation methods [32].

While implementing CFD approaches based on Navier-Stokes equations to simulate hydrodynamic models of floating

structures such as wave energy convertors, the free surface values are deduced for a numerical wave tank along with the

simulation of the flow turbulence. There are two main ways or methods to calculate the free surface values called the surface

tracking method and the interface-capturing method. The surface tracking method considers the free surface as a clear and distinct

boundary and carries out regular updating of the same in progressive time points [33]. However, this method is not capable of

taking into consideration other important factors such as overtopping and oceanic wave breaking. The second method called the

interface-capturing method involves a grid-based simulation where both air and water phases are taken into consideration. With

regards to the interface-capturing methods the most common choices that are available are Volume Of Fluid (VOF) method, the

level set approach and the Marker-and-Cell (MAC) method [34][35][36 ][37]. Majority of the computational fluid dynamics

paradigms that are commercially available utilize the Volume Of Fluid method for interface capturing and a highly detailed

analysis of all the above methods and their utilization in the simulation of the oceanic wave hydrodynamics can be found in two

separate studies carried out by Ferziger & Peric and Lin & Liu [38][39].Computational fluid dynamics paradigms that implement

the Navier-Stokes equations also routinely use the artificial damping layer method during wave-structure interaction studies as

seen in a study carried out by Lara et al. (2006). In this study, the researchers used two methods called the sponge-layer method

and the internal-wave maker method together to simulate the dynamics of the interaction between wave and structure [39].

There are four major numerical methods to simulate wave turbulence flow called the direct numerical simulations, large eddy

simulations, Reynolds-averaged Navier-Stokes methods and detached eddy simulations. While direct numerical simulations

method implement the Navier-Stokes equations to give a thorough description of wave turbulence, it is extremely intensive with

regards to computational resources. For this reason the direct numerical simulations method is not significant from a commercial

perspective but very ideal for research purposes [40]. The large eddy simulation method on the other hand is less resource

intensive compared to the direct numerical simulations method and can account for large as well as small wave turbulence [41].

None the less, the large eddy simulation method is still expensive from a commercial perspective when it comes to the simulation

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of the hydrodynamic properties of floating structures such as wave energy convertors and the best method from all aspects is the

Reynolds-averaged Navier-Stokes method, when it comes to simulation of wave flow turbulence. Moctar et al. used a the

Reynolds-averaged Navier-Stokes model to analyze load of waves on a structure platform where the Volume Of Fluid (VOF)

method was utilized for evaluating the stress on the structure and calculate the free-surface values [42]. This study clearly

indicated that efficacy of the Reynolds-averaged Navier-Stokes model that thoroughly took into account the stress values of wave

run-up and wave loads on the structure.

3. Computational Fluid Dynamics and WEC Design, Simulation And Implementation

During the design process of wave energy converters few critical aspects such as the hydrodynamic properties of the convertor,

mooring and power take-off needs to be thoroughly evaluated together to ensure that they do not influence the dynamics of one

another. It is also important that the time domain is properly taken into consideration for any type of modelling during wave

energy convertor studies and also for analyzing the wave-structure interaction processes that are nonlinear in nature. A study

carried out by Cummins involved the determination of impulse response functions for the purpose of frequency coefficient

conversions in the time domain [43]. The impulse response function allows evaluation and analysis of the system behavior and

response following the first impulse and it can also be used to formulate the equation of motions in the time domain. The use of

impulse response function allows the simulation of the irregular oceanic state but when multiple wave impulses are taken into

consideration together, aspects such as irrotational fluid flow and dynamics of the linear theory may get overlooked. In essence,

when large wave-structure interactions are considered it may be possible that the inherent frequency of the wave almost becomes

identical to the frequency of the wave energy convertor and this could lead to massive structural body movements due to non-

consideration of factors such as friction and viscosity induced drag or loss [8]. Furthermore, it has been observed that a proper

evaluation of the hydrodynamic properties of the interaction between wave and structure is not entirely possible, ideal or accurate

with linear theory and requires the use of non-linear numerical paradigms. In this context, implementation of the Navier-Stokes

equations can lead to thorough evaluation and understanding of the hydrodynamic properties of the interaction between wave and

structure.

As already mentioned earlier, computational fluid dynamics execute the Navier-Stokes equations and it commonly uses surface

capturing methods such as the VOF surface capture method. While doing so, the algorithm also takes into consideration the effect

of water volume in the given simulated cell. An approach such as this was successfully used by a group of researchers who tried to

simulate the movement of ships in massive oceanic waves [44]. The traditional approach that is adopted to evaluate and analyze

wave energy convertors involve the implementation of the linear potential flow theory where the time and frequency domain

parameters are deduced based on tiny amplitude oscillations. However, when seen from a real-world or practical perspective,

these small amplitude assumptions that sustain linearity are not adequate for wave energy convertors and the aspect of nonlinear

influences also become a problem. With the availability of sophisticated computational fluid dynamics paradigms, the time

domain parameters are properly addressed and the iterative implementation of the Navier–Stokes equations further allows

consideration of nonlinear power-take off process in a wave energy convertor [45]. During the analysis of wave energy convertors

linear hydrodynamic model approaches are necessary to take into account factors such as wave motions, wave loads and power

generation from the convertors. Navier-Stokes model that utilizes the Volume of Fluid (VOF) method have indicated that results

obtained from linear hydrodynamic models with regards to estimation of power production could be erroneous. In essence,

researchers have observed that linear models overestimate power production from WECs compared to the Navier-Stokes Volume

of Fluid (VOF) method [46] [47]. Another aspect that makes nonlinear approaches such as the Navier-Stokes Volume Of Fluid

(VOF) method more ideal compared to linear hydrodynamic models is during power estimation from WECs installed near the

shoreline. Close to the shoreline, nonlinear dynamic forces are more evident in the waves and standard linear hydrodynamic

model approaches are not capable to account for the same [48]. Table 1 below presents an overview of the different open-source

and commercially distributed CFD software tools that are available today. The different software tools are categorized as CFD

solvers, grid generators and those ideal for visualization. It however needs to be noted that this list is not exhaustive [49].

Simulation of the hydrodynamic properties of wave energy convertors is dependent on factors such as the cost-effectiveness of

the approach and its ability to describe every physical aspect of the fluid flow and its interaction with the structure. Table 2 below

highlights different approaches to carry out hydrodynamic modelling where the boundary integral equation method and the

Navier-Stokes equation method are ideal for more complex hydrodynamic modeling. The Morrison approach along with the

analytical approach on the other hand are more suitable for simple dynamics.

The hydrodynamic properties of wave energy convertors are also influenced by the mooring systems made up of mooring lines,

connectors and anchors that connect structures such as floating devices to the sea bed. A wide range of studies have been carried

out that that connect the wave energy convertors with the mooring systems in the time and frequency domains. Studies such as

that of Emmanuel B. A. et al. have simulated through commercial software the behavior of other devices that extract energy from

waves, such as buoys. In their research they used the COMET software to create the model that tries to describe the behavior of

the device, that device can be used in pattern form, such as wind turbines [50]. In essence, the governing equations of such

simulations take into account the behavior of the mooring devices as they withstand different forces such as viscous drag. A study

carried out by Johanning et al. demonstrates how the mooring systems behave under viscous effect and in order to provide an

accurate approximation of a wave energy convertor connected to a mooring device, a nonlinear time domain model becomes

necessary [51]. Fitzgerald & Bergdahl also studied the damping behavior of a mooring system connected to a structure (wave

energy convertor) by constructing a frequency map of the mooring system behavior [52]. This involved linearization of the

standard nonlinear equations and the resulting frequency map was then used to study the behavior of the wave energy device not

connected to a mooring system. This approach is highly resource intensive from a computing perspective but when carried out in

the frequency domain instead of the time domain, the computational cost can come down substantially.

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Table 1 Open-source and commercially distributed CFD software tools

Distribution CFD solvers Grid generation Visualization

Open source COOLFluiD Engrid COVISE

Open source Dolfyn GMSH DISLIN

Open source Dune SALOME GMV

Open source Edge NETGEN DISLIN

Open source ELMER TETGEN Mayavi

Open source HiFlow Triangle Tioga

Open source Gerris Flow Solver TwinMesh VAPOR

Open source MFIX Delaundo Vigie

Open source OpenLB Visit

Open source OpenFVM vtk

Open source TYCHO COVISE

Commercial AcuSolve BOXERMesh Fieldview

Commercial ADINA-FSI Cubit Tecplot

Commercial ANANAS GridPro HyperView

Commercial CFD2000 HyperMesh ViewZ

Commercial CharLES ANSA ADINA-AUI

Commercial COMSOL

Multiphysics

SolidMesh CFView

Commercial EasyCFD TwinMesh CFX-Post

Commercial FluSol Harpoon Fieldview

Commercial NOGRID HyperMesh EnSight

Commercial SHIPFLOW ICEM CFD VU

Commercial SPLASH

Commercial TURBOcfd

Table 2 Different hydrodynamic modelling approaches

Analytical

method

Morison

method

Boundary

integral

equation

method

(Frequency

domain

Boundary

integral

equation

method (Time

domain)

Navier-Stokes

equation method

Viscosity

dynamics

Not accounted

but can be

integrated as

an input

Accounted

Not accounted

but can be

integrated as

an input

Not accounted

but can be

integrated as

an input

Accounted

Fluid-structure

interactions

Linear in

nature

No effect of the

structure

movement

Weak

Nonlinear

Nonlinear in

the time

domain

Robustly nonlinear

Wave-breaking None None None None

Accounted using

the Volume of

Fluid method

Accuracy of

the method in

general

Very

inaccurate

Acceptable

with the

modification of

the

hydrodynamic

coefficients

Very

inaccurate

Acceptable

results

Very accurate

results

Accuracy

under

resonance

effect

Very

inaccurate

Acceptable

with the

modification of

the

hydrodynamic

coefficients

Very

inaccurate

Acceptable

results

Very accurate

results

67

Yassir et al. adopted another interesting approach to analyze the mooring system behavior but it is applicable when nonlinear

aspects such as damping of mooring systems are linear in nature [51][53][54]. The benefits of wave energy are clearly defined in

researches such as W. B Wan Nik et al. [55], which highlights the main energy, economic and geographical aspects of the wave.

These researchers also highlight the advantages of this type of energy in a comparative criticism against the other renewable

energy sources [55]. Studies such as those of Masami Suzuki et al. show models of wave energy converters with different

configurations, emphasizing the profiles of the blades and how these profiles influence the efficiency of the converter [56]. There

are several devices that can extract energy from the waves, in a study conducted by Sangyoon K. et al., we can verify the

operation of a cross-flow turbine [57]. An advantage of this type of energy against hydroelectric power is the possibility of using

turbines that extract energy from the waves through the compression and expansion of the air in a chamber that expands and

contracts with the movement of waves, thus generating power in two phases [55]. Vicente et al. presented another study where

they analyzed the hydrodynamic properties of wave energy convertors along with factors such as power take-off damping for

different linear mooring configurations [58]. Though this approach can be directly applied to evaluate the hydrodynamics of wave

energy convertors, it is linear in nature and will not nonlinear effects such as viscous drag effect.

The CFD analysis of aerodynamic and hydrodynamic flows and their interaction with structure (WEC, rotor blades) is either a

nonlinear approach in the time domain or the frequency domain. Within the time domain paradigm the fluid flow equations are

represented in terms of a computational grid. The solution to the flow equations are then forwarded from one time point strata to

another using standard computational dynamics paradigms. This field of study is very open, there are even studies that explain

how to carry out an analysis using ANSYS CFX as a tool [59]. The hydrodynamic properties of wave energy advantages of this

approach in the sense that it is relatively straightforward to implement and can model nonlinear as well as linear disturbances.

However, a trade-off with this approach is that the computational processing periods could be quite large in order to ensure

accuracy [60]. The practical research carried out by C. Windt et al. is another very important point of these systems i.e. fatigue

loading. Using a FSI-based methodology and practical experiments, it shows that it is possible to bring this complex system to an

FEA. The accuracy of the results is relatively low, however the researchers note that there are other methods that could achieve

greater accuracy, however these methods have a higher computational cost, which is prohibitive. For that reason resorting to

obtain the data for its analysis of experimental tests [61].

The frequency domain on the other hand are linearized for time and involves deduction of the time-mean flow value. The

deduction of the time-mean flow value involves deduction of the steady-flow equations through standard computational fluid

dynamic paradigms. The governing frequency domain equations can be solved using minimal computational resources but they

are not able to model any nonlinear hydrodynamic properties [60]. In a recent study, Lin (2016) proposed a frequency domain

hydro elastic Boundary Element Method model that is ideal for studying wave-structure interaction dynamics [60]. The model

works well for offshore structures such as wave energy convertors but the waves becomes rough or large a nonlinear model

approach becomes necessary. For this reason the time domain hydro elastic Boundary Element Method model becomes more ideal

and easier to implement, especially when accounting for wave-structure dynamics under large waves.

A wide range of modelling tools are available today for the purpose of simulating wave energy conversion systems. These state-

of-the-art codes utilize the multimode dynamic paradigms in the time domain to simulate and model WEC movements and to

simulate the different hydrodynamic forces experienced by the structure, the codes make use of the hydrodynamic coefficients.

The past few years have witnessed a massive surge in the development and availability of software utilities that are specifically

designed for the simulation of the hydrodynamics of the wave energy convertors. These codes are well-equipped to model the

complex interactions that take place between fluid and structure and also the dynamics of power take off systems within a

simulated environment. Some of the codes that are specifically designed for the modelling of the WEC dynamics are discussed

below.

ProteusDS: This is a sophisticated software tool that specifically targets the offshore and marine applications and come with a

highly intuitive GUI. The software utility allows excellent 3D rendering of WEC simulations and it utilizes the multi-body

dynamic paradigms in the time domain to simulate and model WEC movements, making it ideal for the marine renewable energy

sector [63]. ProteusDS can be effectively used to simulate the effect of extreme forces such as wind and oceanic waves on virtual

WEC structures and ascertain their structural integrity. The software can be used to scale the risks and optimize the WEC structure

before its implementation in the real world and a major benefit with ProteusDS is its high computational efficiency. [64]. The

software is fully compatible with boundary element method paradigms, making it highly ideal for simulation and modelling of

structures exposed to forces such as oceanic waves and currents. The inherent physics model of ProteusDS has been the subject of

numerous studies and is well-validated for commercial and research implementations [65, 66, 67, 68].The software utility can

account for a wide range of aspects such as power-takeoff dynamics, fluid viscosity strains on the structure, moorings and hull

connections. Furthermore, Table 3 below presents a comparison of the features present in different WEC simulation/modelling

codes [78].

InWave: This is another software tool that utilizes the multibody dynamic paradigms in the time domain for modelling WEC

interactions. InWave is entirely nonlinear in nature and strongly connected to a linear flow solver, allowing it to account for all the

hydrodynamic interactions of fluid and structure [69]. The software package integrates with itself a range of solver codes such as

boundary element method, power take off and moorings in dedicated modules and they can all be programmed to run in a

sequential manner. Figure 1 below presents the organization of the InWave software suite [70].

WEC-Sim: WEC-Sim or Wave Energy Converter SIMulator is a MATLAB/SIMULINK based utility that utilizes the

multibody dynamic paradigms for modeling. The tool is highly ideal for modelling of rigid structures in the time domain and

simulation involves the use of the Cummins's paradigm for solving the governing wave energy converter equations [71]. Figure 2

below illustrates the schema of the WEC-Sim code [72].

WaveDyn is a fully coupled simulation tool designed for wave energy. It allows you to simulate the performance and loading on

a wave energy device. It enables you to model hydrodynamics calculations, and control and power take-off systems. Developed by

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DNV-GL specifically for evaluating WEC performance. The software allows a user to construct a numerical representation of a

WEC by connecting structural, hydrodynamic, power take-off (PTO) and mooring components using a flexible user interface.

Single machines may be modeled in isolation, or a user may choose to build a multiple WEC simulation model for a known array

layout. The hydrodynamics module in its most basic form is a quasi-linear formulation based on a boundary element method

(BEM), potential flow solver such as WAMIT. Diffraction, radiation, hydrostatic and viscous effects are included in the model.

WaveDyn has already been subject to a number of validation campaigns against experimental measurements on various device

types, scales, in isolation or in array [73, 74, 75].

ANSYS: One of the most sophisticated and robust computational fluid dynamics software suite available today is ANSYS and

it is highly ideal for the simulation and modelling of phenomena such as fluid structure interactions and fluid flow. The software

suite offers extensive analytical capabilities with regards to fluid flow and interaction simulations and is highly ideal for

optimization of virtual structures before installation as well as fault rectification with the existing installations. The software suite

packs in utilities such as ANSYS CFX and ANSYS Fluent that allows simulation and modelling of a very wide range of physical

phenomenon [76]. ANSYS CFX is highly ideal for simulation of WEC interactions and can handle almost all kinds of fluid flow

movements and fluid structure interactions. ANSYS CFX implements a robust solver paradigm that offers a wide range of models

to simulate almost every kind of fluid flow interactions and phenomena. The ANSYS CFX comes with a user-friendly graphical

interface and it allows extensive customization and adaptation. When ANSYS CFX is coupled with the ANSYS platform the user

gets access to powerful CAD utilities that allows simulation and modelling of all kinds of fluid structure interaction problems [77,

114]. An example is shown in Figure 3.

Fig. 1 Organization of the Inwave software suite

Fig. 2 WEC-SIM code framework

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Fig. 3 FSI simulation by ANSYS Fluent – AQWA

70

4. Fluid Structure Interaction Simulation

Evaluation, analysis and mathematical deduction of fluid structure interaction dynamics with state-of-the-art computational

fluid dynamic paradigms are becoming increasingly common in the recent years [79][80]. A major reason behind this is due to the

fact that approaches such as finite volume methods and tools such as equation solvers (linear/nonlinear) have become more

powerful and cost-effective from a commercial perspective. To arrive upon a conclusion and accurate deduction of fluid-structure

interaction problems two main approaches could be adopted. The first approach is more common with regards to its usage and

involves the fluid aspect handled using a Lagrangian–Eulerian formulation and the structure aspect, handled using a Lagrangian

formulation [79] [80][81] [82]. The second approach involves a standard Eulerian formulation along with a fixed fluid mesh for

the fluid aspect and the Lagrangian formulation for the structure aspect [79] [80]. A wide range of engineering simulations and

applications require that the fluid flow that is estimated is high accurate and holds ground in a practical scenario. With regards to

the simulation of the fluid flows that is three dimensional in nature, the computational load could be very high but the fluid

meshes can be highly efficient. This would in turn necessitate the grading of the fluid mesh which is directly dependent on the

dynamics of the fluid flow. For this reason the fluid structure interaction procedures that facilitates effective grading of the fluid

mesh in an adaptive manner are extremely ideal for application. For the benefit of scientific studies that focuses on fluid structure

interactions, it is important that such tools or solutions are implemented that can concurrently handle complex computation fluid

dynamics and fluid structure interaction problems at the same time [83]. Any complex fluid structure interaction problems could

involve fluid flows such as incompressible fluid flows or the compressible fluid flows and considering the structural deformations

that can take place in the structure, they can get strongly affected by the fluid flows (incompressible or compressible) [79]

[80][81][83].

When fluid structure interactions undergo computer simulation the structure and the fluid state are rendered mathematically

discrete and the algebraic equations need to be deduced together or one after the other. As mentioned earlier, deduction of fluid-

structure interaction problems can be through two main approaches involving the fluid and structure (solid) domains. However,

for the sake of clarity, a typical fluid structure interaction solver adds a third domain called the interface to the already existing

fluid and structure (solid) domains [84]. This extended approach is capable of accounting for other deductions such as traction

force transfer values and other kinematic information. The fluid structure interaction solver with the three domains (fluid,

structure and interface) is illustrated in figure 4 below [84].

Table 3 Different hydrodynamic modelling approaches

Code Name InWave WaveDyn ProteusDS WEC-Sim v1.0

Code Developer INNOSEA/ECN DNV GL DSA NREL/SNL

Multibody

Mechanics

Relative coordinate

algorithm

Proprietary

multibody

method

Articulated Body

Algorithm SimMechanics

Hydrodynamics

Linear potential,

Nonlinear Froude-

Krylov

Linear potential,

Nonlinear

Froude-Krylov

Linear potential,

Nonlinear

Froude-Krylov

Linear potential,

Nonlinear Froude-

Krylov

BEM Solver Integrated

(NEMOH)

Multiple options

(inc. WAMIT and

AQWA)

Multiple options

(inc. WAMIT and

SHIPMO3D)

Multiple options (inc.

WAMIT, AQWA, and

NEMOH)

Hydro-Mechanics

Coupling

Relative

coordinates

Generalized

coordinates

Generalized

coordinates

Generalized

coordinates

Hydrostatics Linear,

Nonlinear

Linear,

Nonlinear

Linear,

Nonlinear

Linear,

Nonlinear

Body-to-Body

Hydrodynamic

Interactions

Yes Yes Yes Yes

Viscous Drag

Formulation

Morison elements

with relative

velocity

Morison elements

with relative

velocity

Morison elements

with relative

velocity

Quadratic damping

using body velocity,

Morison elements

with relative velocity

Mooring (Linear

Stiffness/Quasi-

Static/Dynamic)

Yes/Yes/No Yes/Yes/No Yes/No/Yes Yes/No/No

PTO and Control

Linear,

Look-up table, and

API

Linear and API

Linear,

PID control, and

API

User-defined in

MATLAB/Simulink

License Commercial Commercial Commercial Apache 2.0

External Software None None None MATLAB, Simulink,

SimMechanics

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Fig. 4 Fluid Structure Interaction Solver Structure

In the fluid structure interaction solver, ui stands for the kinematic degrees of freedom of the interface and uf stands for the

degrees of freedom of the fluid domain that involves fluid velocity and fluid pressure. Furthermore, xf stands for the degrees of

freedom of the fluid mesh and ds stands for the degrees of freedom of the structure (solid) [84]. The governing equations for the

fluid structure interaction paradigm (with fluid, structure and interface domains) described above are given as follows:

rf (uf , ui) = 0; Representing the Fluid domain.

gf (uf , ui) + gs(ds, ui) = 0; Representing the interface domain.

rs(ds, ui) = 0 ; Representing the structure (solid) domain.

For every time point corresponding to ui, uf and ds, the three governing equations are solved. Also seen in the above

equations are two vectors, rf and rs that defines the residual forces on the solid and fluid domains and the vectors gf and gs defines

the traction experience by the interface between the fluid and the structure (solid) phase. These governing equations implement

the Newton-Raphson paradigms and are deduced together or in concurrent steps. The interface domain between the fluid and

structure (solid) phases are formulated using two main approaches called interface capturing and interface tracking. Interface

capturing involves sliding of the fluid and the structure mesh over each other and this approach is primarily used with Eulerian

fluid mesh. The approach does not have any limitations with regards to the degree of rotations but is not very accurate. Interface

tracking involves the fluid and the structure domains moving together instead of sliding and is more accurate than interface

capturing. A trade-off with Interface tracking is that it is not suitable when the degree of rotations or deformations are large [84].

The fluid structure interaction solvers can be categorized into four main types as illustrated in figure 5 below.

Fig. 5 Categorization of Fluid Structure Interaction Solvers (Dettmer, 2012)

The Newton-Raphson solvers in the above figure are highly robust and accurate but are highly resource intensive because the

equations for the fluid, structure, interface and mesh are combined to form a single matrix equation. The Gauß-Seidel iteration and

the staggered schemes on the other hand handle the domains separately and does not involve formation of any single matrix

equation. There are separate equations for each domain and they are deduced separately as independent equations making the

solvers fact and less resource intensive [84].

The FSI analysis have a very significant practical use, allowing to optimize the efficiency in turbo machines and thermal

machines. An example of this is the optimization study carried out by Hyun-Su and Youn-Jea Kim on a high-power centrifugal

compressor, where, thanks to the application of a FSI one-way coupling analysis, it was possible to increase its efficiency by 1%

[85]. Fluid Structure Interaction (FSI) is a part of a coupled-field analysis where various independent fields combine and interact

together to solve a global engineering problem with the result of one field dependent on the other. The coupling can either be

oneway or two-way. In one-way coupling, the effect of one field is imposed on the other but not the vice versa. A two-way

coupling is needed when the coupling between any two fields acquires significant response from each other. The coupling can be

addressed by one of the two methods-direct or iterative. In the direct method, a single set of monolithic equation is assembled,

72

leading to an increase in degrees of freedom of equations to be solved [86].

Other researchers have demonstrated through Francis turbine modal analysis, tested with air and water that the FEM methods

agree the experimental data, particularly the frequency reduction rates derived from the simulation. Based on these results, the

critical frequencies were identified, and these data were then used to perform a country based on the harmonic response. Finally,

they showed that the data obtained serve as a basis for the structural design based on the time of life [87]. Another research

indicates that current studies of CFD are not taking into account the deformation of turbine blades, caused by the force exerted by

the fluid on them, based on this fact, the researchers tested a model called "Two-way coupled FSI Simulations" in the

development of the study are left to see the shortcomings of the current tools in the FEA and the level of difficulty that this type of

analysis faces with the use of this methodology. This study suggests that to accurately predict the performance of hydraulic

machines in low head applications, an accurate representation of the physical phenomenon is essential [88]. The existing research

for unsteady flow field and the corresponding flow induced vibration analysis of centrifugal pump are mainly carried out

respectively without considering the interaction between fluid and structure. The ignorance of fluid structure interaction (FSI)

means that the energy transfer between fluid and structure is neglected. The average of total head with FSI was larger than the

total head without FSI. Therefore, the effect of FSI should be taken into account when the external characteristic of pump was

predicated by numerical simulation [89]

Other domains where Fluid structure interactions have also been applied for the purpose of simulation and problem solving

include aerodynamics, air/fluid turbulence, and sedimentation and particle assembly [90- 97]. Researchers have also found fluid

structure interactions to be effective to simulate the dynamics of complex flows in irregular domains, hydro-dynamics and

simulation of magneto-hydrodynamic flows [98, 99, 100, 101, 102]. Researchers have demonstrated the modelling of fluid

structure interaction problems based on fluid dynamic theory and the fluid structure interaction problem solving and simulation in

context of marine engineering have also been very well explored and presented [103,104]. Implementation of fluid structure

interaction approaches that are based on immersed boundary formulation paradigms have also be successfully demonstrated along

with boundary problem solving through fluid structure approaches [105, 106]. Another group of researchers also demonstrated the

efficacy of fluid structure interaction approaches by modelling the piston chamber in an enclosed gas chamber [107]. Fluid

structure interaction problems pertaining to the aspects such as fluid motion, traction movement and structure distortion have not

yet been adequately explored. Having said that, researchers have been very successful in modelling and simulating the

hydrodynamics of ships by concurrently using two approaches such as volume-of-fluid technique and immersed boundary

formulation [109, 110, and 111]. The same combination of approaches have also been used to model wave movement over

submerged oceanic structures and generation of waves [111]. Similarly, the level set approach conceived by Osher et al. has been

successfully integrated with a computation tool based on the Reynolds-averaged Navier-Stokes (RANS) model and also to model

and represent the free surface [112, 113].

5. Conclusion

It has become evident that the investigation of the hydrodynamic properties of devices such as wave energy convertors mainly

involve the linear potential flow theory. However, studies have clearly indicated that they have limitations associated with

ancillary assumptions of factors such as inviscid fluid, irrotational fluid flows, wave amplitudes and other structure movements.

These are critical limitations considering the fact that in a practical scenario the wave energy convertors would withstand massive

motions, wave drag forces and large wave amplitudes. All these aspects can be accommodated through the implementation of

the Navier-Stokes governing equations deduced by state-of-the-art computational fluid dynamic paradigms available today. A

sophisticated computational fluid dynamics model will encompass all forms of fluid structure interactions and forces such as

overtopping, massive structure/fluid motions and wave drag forces and can provide highly accurate simulations. Accurate

simulation results can go a long way in correct evaluation of hydrodynamic properties and estimation of other factors such as

power generation and structure survivability. Computational fluid dynamic approaches are nonlinear in nature and are considered

computationally intensive and not very cost-effective from a commercial perspective. However, it needs to be noted that unlike

linear frequency domain paradigms, the computational fluid dynamic paradigms can accommodate or account for every aspect of

wave structure interactions and given the rapid progress in computational technologies they are increasingly becoming cost

effective with fast. The use of computational fluid dynamics to study the wave-structure interactions is more common when

assumptions such as irrational fluid flow and small structure motions are not taken into consideration. During such computational

fluid dynamics modelling, a wide range of information with regards to the wave-structure interaction hydrodynamics become

available and the efficacy of the modelling process should ideally be weighed in light of the computational costs and the

executability of the CFD model. From an overall perspective, modern CFD solutions are the most ideal for the simulation of wave

energy convertors and evaluation of the wave structure interaction dynamics. Given the rate at which computational processing

speeds are increasing, the apprehensions surrounding CFD as being very resource intensive are also fast disappearing.

References

[1] J. Blazek, 2007, “Computational fluid dynamics,” Elsevier, Oxford.

[2] Kopal, Z., 1947, “Tables of Supersonic Flow Around Cones, Depart of Electrical Engineering,” Center of Analysis,

Massachusetts Institute of Technology, Cambridge.

[3] Liu Z., Hyun B. and Hong K, 2008, “Application of numerical wave tank to owc air chamber for wave energy conversion,”

Proceedings of the, 18th International Offshore and Polar Engineering Conference, Vancouver.

[4] Zhang Y., Zou QP. and Greaves D, 2012, “Air-Water two phase flow modelling of hydrodynamic performance of an oscillating

73

water column device,” Renewable Energy, 41, 159-170.

[5] Morris-Thomas MT., Irvin RJ. and Thiagarajan KP, 2006, “An investigation into the hydrodynamic efficiency of an oscillating

water column,” Journal of Offshore Mechanics and Arctic Engineering, 129, 273-278.

[6] Kamath, A,Bihs, H, and Arntsen, 2015, “THREE DIMENSIONAL CFD MODELING OF FLOW AROUND AN OWC WAVE

ENERGY CONVERTER,” E-proceedings of the 36th IAHR World Congress 28 June – 3 July, The Hague,

the Netherlands

[7] Willis, M., Masters, I., Thomas, S., Gallie, R., Loman, J., Cook, A., Ahmadian, R., Falconer, R., Lin, B., Gao, G.,Cross, M.,

Croft, N., Williams, A., Muhasilovic, M., Horsfall, I., Fidler, R., Wooldridge, C., Fryett, I., Evans, P., O'Doherty, T., O'Doherty D

and Mason-Jones, A, 2010, “Tidal Turbine Deployment in the Bristol Channel - A Case Study,” in: Proceedings of the Institution

of Civil Engineers.

[8] J. Westphalen, D. M. Greaves, A. Raby, Z. Hu, D. Causon, C. Mingham, P. Omidvar, P. Stansby and B. D. Rogers,2014,

“Investigation of Wave-Structure Interaction Using State of the Art CFD Techniques,” OJFD, vol. 04, no. 01, pp.18-43.

[9] S. Neill, J. Jordan and S. Couch, 2012, “Impact of tidal energy converter (TEC) arrays on the dynamics of headland sand

banks,” Renewable Energy, vol. 37, no. 1, pp. 387-397.

[10] T. O’Doherty, D. Egarr, A. Mason-Jones and D. O’Doherty, 2009, “An assessment of axial loading on a five-turbine array,”

Proceedings of the Institution of Civil Engineers - Energy, vol. 162, no. 2, pp. 57-65.

[11] A. C. Antoulas, 2005 “Approximation of Large-Scale Dynamical Systems,” Society for Industrial and Applied Mathematics,

Philadelphia, PA.

[12] D. Amsallem, J. Cortial, K. Carlberg and C. Farhat, 2009, “A method for interpolating on manifolds structural dynamics

reduced-order models,” International Journal for Numerical Methods in Engineering, vol. 80, no. 9, pp. 1241-1258.

[13] C. Prud’homme, D. Rovas, K. Veroy, L. Machiels, Y. Maday, A. Patera and G. Turinici, 2002, “Reliable Real-Time Solution

of Parametrized Partial Differential Equations: Reduced-Basis Output Bound Methods,” Journal of Fluids Engineering, vol.

124, no. 1, p. 70.

[14] G. Rozza, D. Huynh and A. Patera, 2008 “Reduced Basis Approximation and a Posteriori Error Estimation for Affinely

Parametrized Elliptic Coercive Partial Differential Equations,” Arch Computat Methods Eng, vol. 15, no. 3, pp. 229-275.

[15] K. Veroy, C. Prud’homme, D. V. Rovas, A. T. Patera, 2003 “A posteriori error bounds for reduced-basis approximation of

parametrized noncoercive and nonlinear elliptic partial differential equations,” AIAA Paper 2003-3847, 16th AIAA Computational

Fluid Dynamics Conference, Orlando, FL.

[16] N. C. Nguyen, K. Veroy, A. T. Patera, 2005, “Certified real-time solution of parametrized partial differential equations,”

Kluwer Academic Publishing, Dordrecht, pp. 1529–1564.

[17] K. Veroy and A. Patera, 2005, “Certified real-time solution of the parametrized steady incompressible Navier-Stokes

equations: rigorous reduced-basisa posteriori error bounds,” International Journal for Numerical Methods, Fluids, vol. 47, no. 8-9,

pp. 773-788.

[18] K. C. Hall, J. P. Thomas, E. H. Dowell, 1999, “Reduced-order modelling of unsteady small-disturbance flows using a

frequency domain proper orthogonal decomposition technique,” in: AIAA Paper 99-16520.

[19] P. A. LeGresley, J. J. Alonso, 2000, “Airfoil design optimization using reduced order models based on proper orthogonal

decomposition,” in: AIAA Paper 2000-25450, Fluids 2000 Conference and Exhibit, Denver, CO.

[20] K. C. Hall, J. P. Thomas, E. H. Dowell, 2002 “Proper orthogonal decomposition technique for transonic unsteady

aerodynamic flows,” AIAA Journal, vol. 38 pp. 1853–1862.

[21] W. K., J. Peraire, 2002, “Balanced model reduction via the proper orthogonal decomposition,” AIAA Journal, vol. 40,

pp.2323–2330.

[22] B. I. Epureanu, 2003, “A parametric analysis of reduced order models of viscous flows in turbomachinery,” Journal of Fluids

and Structures, vol 17, pp. 971–982.

[23] J. P. Thomas, E. H. Dowell, K. C. Hall, 2003 “Three-dimensional transonic aeroelasticity using proper orthogonal

decomposition-based reduced order models,” Journal of Aircraft, vol. 40, pp. 544–551.

[24] T. Kim, M. Hong, K. B. Bhatia, G. SenGupta, 2005 “Aeroelastic model reduction for affordable computational fluid

dynamics-based flutter analysis,” AIAA Journal, vol. 43, pp. 2487–2495.

[25] T. Lieu, C. Farhat, M. Lesoinne, 2006 “Reduced-order fluid/structure modeling of a complete aircraft

configuration,” Computer Methods in Applied Mechanics and Engineering, vol. 195, pp. 5730–5742.

[26] T. Lieu, C. Farhat, 2007 “Adaptation of aeroelastic reduced-order models and application to an F-16 configuration", AIAA

Journal, vol. 45, pp. 1244–1269.

[27] D. Amsallem, C. Farhat, 2008 “An interpolation method for adapting reduced-order models and application to aeroelasticity,”

AIAA Journal, vol. 46, pp. 1803–1813.

[28] D. Amsallem, J. Cortial, C. Farhat, 2010 “Toward real-time CFD-based aeroelastic computations using a database of

reduced-order information,” AIAA Journal, vol. 48, pp. 2029–2037.

[29] M. A. Bhinder, A. Babarit, L. Gentaz, and P. Ferrant, , 2011, “Assessment of viscous damping via 3D-CFD modelling of a

floating wave energy device,” in Proceedings of the 9th European Wave 1 Tidal Energy Conference, Southampton, UK.

[30] M. Folley and T. Whittaker, 2011, “The adequacy of phase-averaged models for modelling wave farms,” in ASME2011 30th

International Conference on Ocean, Oshore 1 Arctic Engineering (OMAE2011) June 19-24, 2011 , Rotterdam,The Netherlands.

[31] 2001, “Comet v.2 user manual,” CCM GmbH Germany

[32] Y. Li and Y. Yu, 2012 “A synthesis of numerical methods for modeling wave energy converter-point absorbers,” Renewable

and Sustainable Energy Reviews, vol. 16, no. 6, pp. 4352-4364.

[33] Gentaz, L., Alessandrini, B., and Delhommeau, G., 1999, “2D nonlinear diffraction around free surface piercing body in a

viscous numerical wave tank,” in Proceedings of 9th Int. Offshore and Polar Eng. Conf., vol. 3, pp. 420-426.[34] Harlow, F. and

74

Welch, J. , 1965, “Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface,” Physics of

fluids, vol. 8, no. 12, p. 2182.

[35] Hirt, C. and Nichols, B., 1981, “Volume of fluid (VOF) method for the dynamics of free boundaries,” Journal of

Computational Physics, vol. 39, no. 1, pp. 201-225.

[36] Sussman, M., Smereka, P., and Osher, S., 1994, “A level set approach for computing solutions to incompressible two-phase

flow,” Journal of Computational Physics, vol. 114, no. 1, pp. 146-159.

[37] Sethian, J. and Smereka, P., 2003, “Level set methods for fluid interfaces,” University of California, Berkeley, California and

University of Michigan, Ann Arbor, Michigan.

[38] Ferziger, J. H. and Peric, M., 2002, “Computational methods for fluid dynamics,”

[39] Lin, P. and Liu, P. L.-F., 1999, “Free surface tracking methods and their applications to wave hydrodynamics,” Advances

in Coastal and Ocean Engineering, vol. 5, pp. 213-240.

[40] Moin, P. and Mahesh, K., 1998, “Direct numerical simulation: a tool in turbulence research,” Annual Review of Fluid

Mechanics, vol. 30, no. 1, pp. 539-578.

[41] Lesieur, M. and Métais, O., 1996, “New Trends in Large-Eddy Simulations of Turbulence,” Annu. Rev. Fluid Mech, vol. 28,

pp. 45-82.

[42] El Moctar, O., Schellin, T., Jahnke, T., and Peric, M. , 2009, “Wave Load and Structural Analysis for a Jack-Up Platform in

Freak Waves,” Journal of Offshore Mechanics and Arctic Engineering, vol. 131, p. 021602.

[43] Cummins, W.E. , 1962, “Impulse response function and ship motion,” Symposium on ship theory, University of Hamburg,

25-27, January.

[44] I. Hadžić, J. Hennig, M. Perić and Y. Xing-Kaeding, 2005, “Computation of flow-induced motion of floating bodies,”

Applied Mathematical Modelling, vol. 29, no. 12, pp. 1196-1210.

[45] E. Agamloh, A. Wallace and A. von Jouanne, 2008, “Application of fluid–structure interaction simulation of an ocean wave

energy extraction device,” Renewable Energy, vol. 33, no. 4, pp. 748-757.

[46] M. von Scheven and E. Ramm, 2010, “Strong coupling schemes for interaction of thin-walled structures and

incompressible ows. International Journal of Numerical Methods in Engineering, 87(1-5):214 231.

[47] W.A.Wall and E. Ramm, 1998, “Fluid-structure interaction based upon a stabilized element method,” In S.R Idelsohn,

E.O~nate, and E.N Dvorkin,editors, Computational Mechanics - New Trends and Applications.

[48] Claes Eskilsson, Johannes Palm, Allan Peter Engsig-Karup, Umberto Bosi, Mario Ricchiuto, 2015, “Wave Induced Motions

of Point-Absorbers: a Hierarchical Investigation of Hydrodynamic Models,” 11th European Wave and Tidal Energy Conference

(EWTEC), Sep 2015, Nantes, France.

[49] “Codes - CFD-Wiki, the free CFD reference,” Cfd-online.com, [Online]. Available: http://www.cfd-online.com/Wiki/Codes.

[Accessed: 22- Jul- 2016].

[50] Emmanuel B. Agamloh, Alan K. Wallace and Annette von Jouanne, 2008, “Application of fluid–structure interaction

simulation of an ocean wave energy extraction device,” School of Electrical Engineering and Computer Science, Oregon State

University, Corvallis, OR 97331, USA.

[51] Johanning, L., Smith, G. H., & Wolfram, J., 2007 “Measurements of static and dynamic mooring line damping and their

importance for floating WEC devices,” Ocean Engineering, 34, 1918-1934.

[52] Fitzgerald, J., & Bergdahl, L., 2008 “Including moorings in the assessment of a generic offshore wave energy converter: A

frequency domain approach,” Marine Structures, 21, 23-46.

[53] Yassir, M., Kurian, V., Indra, S., & Nabilah, A., 2010, “Parametric Study on Multi-component Catenary Mooring lines for

Offshore Floating Structures,” Kuala Lumpur: Asian-Pacific-Offshore Conference.

[54] Kreuzer, E., & Wilke, U., 2003, “Dynamics of mooring systems in ocean engineering,” Applied Mechanics, 73, 270-281

[55] W. B. Wan Ni k, A. M. Muzathik, K. B. Samo and M. Z. Ibrahim, 2009, “A Review of Ocean Wave Power Extraction; the

primary interface,” International Journal of Fluid Machinery and Systems, Vol. 2, No. 2.

[56] Masami Suzuki and Chuichi Arakawa, 2008, “Influence of Blade Profiles on Flow around Wells Turbine,” International

Journal of Fluid Machinery and Systems, Vol. 1, No. 1.

[57] Sangyoon Kim, Byungha Kim, Joji Wata and Young-Ho Lee, 2016, “Hydraulic Model Test of a Floating Wave Energy

Converter with a Cross-flow Turbine,” International Journal of Fluid Machinery and Systems, Vol. 9, No. 3.

[58] Vicente, P. C., Falcao, A. F., & Justino, P. A, 2011, “Slack-chain mooring configuration analysis of a floating wave energy

converter”, IDMEC, Instituto Superior Técnico, Technical University of Lisbon, Lisboa, Portugal.

[59] Finnegan W., Goggins J., 2012, “Numerical simulation of linear water waves and wave-structure interaction,” Ocean

Engineering 43 (2012) 23–31.

[60] K. Hall, J. Thomas and W. Clark, 2002, “Computation of unsteady nonlinear flows in cascades using a harmonic

balance technique,” AIAA Journal, vol. 40, pp. 879-886.

[61] Windt, C., Schmitt, P., Nicholson, J., & Elsaesser, B., 2014, “Development and validation of Fluid Structure Interaction

Methods for an Oscillating Wave Surge Converter,” Paper presented at International Conference on Renewable Energies Offshore,

Lisbon, Portugal.

[62] Lin, F., 2016, “Hydroelasticity Analysis in Frequency Domain and Time Domain,” Journal of Shipping and Ocean

Engineering 6, pp. 65-81.

[63] R. S. Nicoll, C. F. Wood, and A. R. Roy, 2012, "Comparison of physical model tests with a time domain simulation model of

a wave energy converter,” in ASME 2012 31st International Conference on Ocean, Offshore and Arctic Engineering, pp. 507–516.

[64] R. Featherstone, 2014, “Rigid body dynamics algorithms,” Springer Science+Business Media .

[65] M.-A. Kerbiriou, M. Prevosto, C. Maisondieu, A. Clement, A. Babarit, 2007, “Influence of sea-states description on wave

energy production assessment,” in: Proceedings of the 7th European Wave and Tidal Energy Conference, Porto, Portugal, Sept.

75

[66] R.S. Nicoll, D.M. Steinke, J. Attia, A. Roy, B.J. Buckham, 2011, “Simulation of a highenergy finfish aquaculture site using a

finite element net model,” in: ASME 2011 30th International Conference on Ocean, Offshore and Arctic Engineering.

[67] D. Steinke, R. Nicoll, T. Thompson, B. Paterson, 2013 “Design Methodology and Numerical Analysis of a Cable Ferry,”

Society of Naval Architects and Marine Engineers Transactions.

[68] B. Robertson, H. Bailey, D. Clancy, J. Ortiz and B. Buckham, 2016, “Influence of wave resource assessment methodology on

wave energy production estimates,” Renewable Energy, vol. 86, pp. 1145-1160.

[69] A. Babarit and G. Delhommeau, 2015, “Theoretical and numerical aspects of the open source BEM solver NEMOH,” in Proc.

Of the 11th European Wave and Tidal Energy Conference, Nantes, France.

[70] A. Combourieu, M. Philippe, F. Rongère and A. Babarit, 2014, “INWAVE: A NEW FLEXIBLE DESIGN TOOL

DEDICATED TO WAVE ENERGY CONVERTERS,” in: Proceedings of the ASME 2014 33rd International Conference on

Ocean, Offshore and Arctic Engineering OMAE2014, June 8-13, San Francisco, California, USA.

[71] Cummins, WE, 1962, “The Impulse Response Function and Ship Motions,” David Taylor Model Basin-DTNSRDC.

[72] "WEC-Sim Aims to Bring New Wave Energy Devices to the Surface of an Emerging Industry", 2016, nrel.gov,. [Online].

Available: http://www.nrel.gov/tech_deployment/news/2014/14380.html [Accessed: 30- Jul- 2016].

[73] E. B. L. Mackay, J. Cruz, M. Livingstone, and P. Arnold, 2013, “Validation of a Time-Domain Modelling Tool for Wave

Energy Converter Arrays,” in European Wave and Tidal Energy Conference, Aalborg, Denmark.

[74] E. Mackay, J. Cruz, C. Retzler, P. Arnold, E. Bannon, and R. Pascal, 2012, “Validation of a new wave energy converter

design tool with large scale single machine experiments,” in 1st Asian Wave and Tidal Conference Series.

[75] J. Lucas, M. Livingstone, M. Vuorinen, and J. Cruz, 2012, “Development of a wave energy converter (WEC) design tool–

application to the WaveRoller WEC including validation of numerical estimates,” in 4th International Conference on Ocean

Energy, vol. 17.

[76] "Computational Fluid Dynamics: ANSYS CFX and FLUENT CFD Software", 2016, caeai.com, [Online]. Available:

https://caeai.com/ansys-software-support/ansys-software/computational-fluid-dynamics-ansys-cfx-and-fluent-cfd-software

[Accessed: 29- Jul- 2016]

[77] "Fluid Dynamics Solution,s," 2016, mallett.com, [Online]. Available: HYPERLINK "http://www.mallett.com/ansys-

products/fluid-dynamics-solutions/"http://www.mallett.com/ansys-products/fluid-dynamics-solutions/ [Accessed: 29- Jul- 2016]

[78] A. Combourieu et al., 2015, “WEC3: Wave Energy Converter Code Comparison Project,” in Proceedings of the 11th

European Wave and Tidal Energy Conference, Nantes, France.

[79] Bathe KJ, editor, 2007, “Proceedings of the fourth M.I.T. conference on computational fluid and solid mechanics,” Elsevier

Science.

[80] Wang X, 2008, “Fluid–solid interaction,” Elsevier Science.

[81] Rugonyi S, Bathe KJ, 2001 “On finite element analysis of fluid flows fully coupled with structural interactions,” Comput

Model Eng Sci 2, pp:195–212.

[82] P. Ryzhakov, R. Rossi, S. Idelsohn and E. Oñate, 2010, “A monolithic Lagrangian approach for fluid–structure interaction

problems,” Computational Mechanics, vol. 46, no. 6, pp. 883-899.

[83] Bathe KJ, Zhang H, 2004, “Finite element developments for general fluid flows with structural interactions,” Int J Numer

Meth Eng,60, pp:213–32.

[84] W.G. Dettmer, 2012, “Fluid-structure interaction. Lecture notes,” MSc in Computational Mechanics, Swansea University.

[85] Hyun-Su Kang and Youn-Jea Kim, 2016, “A Study on the Multi-Objective Optimization of Impeller for High-Power

Centrifugal Compressor,” International Journal of Fluid Machinery and Systems, Vol. 9, No. 2.

[86] Sailesh Chitrakar, Michel Cervantes and Biraj Singh Thapa, 2014, “Fully coupled FSI analysis of Francis turbines exposed to

sediment erosion,” International Journal of Fluid Machinery and Systems, Vol. 7, No. 3.

[87] Stefan Lais, Quanwei Liang, Urs Henggeler, Thomas Weiss, Xavier Escaler and Eduard Egusquiza., 2009, “Dynamic

Analysis of Francis Runners – Experiment and Numerical Simulation,” International Journal of Fluid Machinery and Systems, Vol.

2, No. 4.

[88] Hannes Schmucker, Felix Flemming and Stuart Coulson., 2010, “Two-Way Coupled Fluid Structure Interaction Simulation of

a Propeller Turbine,” International Journal of Fluid Machinery and System, Vol. 3 No. 4.

[89] Xu Huan, Liu Houlin, Tan Minggao and Cui Jianbao., 2013, “Fluid-Structure Interaction Study on Diffuser Pump With a

Two-Way Coupling Method,” International Journal of Fluid Machinery and Systems, Vol . 6,

[90] P. MUCHA, S. TEE, D. WEITZ, B. SHRAIMAN and M. BRENNER, 2004, “A model for velocity fluctuations in

sedimentation,” J. Fluid Mech., vol. 501, pp. 71-104.

[91] A. Tornberg and B. Engquist, 2004, “Numerical approximations of singular source terms in differential equations,” Journal of

Computational Physics, vol. 200, no. 2, pp. 462-488.

[92] J. Wang and A. Layton, 2009, “Numerical simulations of fiber sedimentation in Navier-Stokes flows,” Communications in

Computational Physics, Vol. 5, No. 1, pp. 61-83.

[93] W. Liu, D. Kim and S. Tang, 2005, “Mathematical foundations of the immersed finite element method,” Computational

Mechanics, vol. 39, no. 3, pp. 211-222.

[94] W. Haase, 2001, “Unsteady aerodynamics including fluid/structure interaction,” Air & Space Europe, vol. 3, no. 3-4, pp. 83-

86.

[95] L. Zhang and M. Gay, 2007, “Immersed finite element method for fluid-structure interactions,” Journal of Fluids and

Structures, vol. 23, no. 6, pp. 839-857.

[96] G. Kaligzin and G. Iaccarino, 2003, “Toward immersed boundary simulation of high Reynolds number flows,” Annual

Research Briefs, Center for Turbulence Research, Stanford University, pp. 369-378.

[97] J. Yang and E. Balaras, 2006, “An embedded-boundary formulation for large-eddy simulation of turbulent flows interacting

76

with moving boundaries,” Journal of Computational Physics, vol. 215, no. 1, pp. 12-40.

[98]E. Fadlun, R. Verzicco, P. Orlandi and J. Mohd-Yusof, 2000, “Combined Immersed-Boundary Finite-Difference Methods for

Three-Dimensional Complex Flow Simulations,” Journal of Computational Physics, vol. 161, no. 1, pp. 35-60.

[99] H. Udaykumar, R. Mittal, P. Rampunggoon and A. Khanna, 2001, “A Sharp Interface Cartesian Grid Method for Simulating

Flows with Complex Moving Boundaries,” Journal of Computational Physics, vol. 174, no. 1, pp. 345-380.

[100] H. Udaykumar, W. Shyy and M. Rao, 1996, “Elafint: A Mixed Eulerian-Lagrangian Method for Fluid Flows With Complex

and Moving Boundaries,” International Journal for Numerical Methods in Fluids, vol. 22, no. 8, pp. 691-712.

[101] J. Hoburg and J. Melcher, 1976, “Internal electrohydrodynamic instability and mixing of fluids with orthogonal field and

conductivity gradients", J. Fluid Mech., vol. 73, no. 02, p. 333.

[102] D. Grigoriadis, S. Kassinos and E. Votyakov, 2009, “Immersed boundary method for the MHD flows of liquid metals,”

Journal of Computational Physics, vol. 228, no. 3, pp. 903-920.

[103] E.H. Dowell and K.C. Hall, 2001, “Modeling of fluid-structure interaction,” Annual Review of Fluid Mechanics, Vol. 33, pp.

445-490.

[104] S.K. Chakrabarti (Ed.), 2005, “Numerical Models in Fluid Structure Interaction,” Advances in Fluid Mechanics, Vol. 42,

WIT Press.

[105] R. Mittal and G. Iaccarino, 2005, “Immersed boundary methods,” Annual Review of Fluid Mechanics, Vol. 37, pp. 239-261.

[106] W. Shyy, H.S. Udaykumar, M. M. Rao and R.W. Smith, 2007, “Computational Fluid Dynamics with Moving Boundaries,”

Dover Publications.

[107] E. Lefrancois and J.P. Boufflet, 2010, “An Introduction to Fluid-Structure Interaction: Application to the Piston Problem,”

SIAM Review, Vol. 52, pp. 747-767.

[108]. G. Weymouth, 2008, “Physics and Learning Based Computational Models for Breaking Bow Waves Based on New

Boundary Immersion Approaches,” Ph.D. Dissertation, MIT.

[109]. G. Weymouth, D.G. Dommermuth, K. Hendrickson and D.K.P Yue, 2006, “Advances in Cartesian-grid Methods for

Computational Ship Hydrodynamics,” 26th Symposium on Naval Hydrodynamics, Rome, Italy.

[110] C.W. Hirt and B.D. Nichols, 1981, “Volume of fluid (VOF) method for dynamics of free boundaries,” Journal of

Computational Physics, Vol. 39, pp. 201-225.

[111] L. Shen and E.S. Chan, 2008, “Numerical simulation of fluid-structure interaction using a combined volume of fluid and

immersed boundary method,” Ocean Engineering, Vol. 35, pp. 939-952.

[112] S. Osher and J.A. Sethian, 1988, “Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-

Jacobi formulations,” Journal of Computational Physics, Vol. 79, pp. 12-49.

[113] J. Sanders, J. Dolbow, P. Mucha and T. Laursen, 2010, “A new method for simulating rigid body motion in incompressible

two-phase flow", International Journal for Numerical Methods in Fluids, vol. 67, no. 6, pp. 713-732.

[114] M. A. Zullah, Y. H. Lee, 2016, “Fluid-structure interaction simulation of a floating wave energy convertor with water-

turbine driven power generation”, Journal of the Korean Society of Marine Engineering, Vol. 40, pp. 710-720.