2nd year – 1st alternative ECN - France

"Hydrodynamics for Ocean Engineering”


ECN (Nantes, France)



Contacts : P. Ferrant, L. Gentaz


The courses proposed here are dedicated to Hydrodynamics for ships and offshore structures, this means the mathematical models, numerical or experimental methods used to study and evaluate performance, hydrodynamic loads, motions of all floating structures used for maritime transport, production of energy on seas...

The 60 credits at ECN are composed of:

SEMESTER 3: Lectures (30 credits) 



M2-ECN-0 PREREQUISITES   (not mandatory lectures)

















SEMESTER 4: Lectures (30 credits) 

Course Code Course title


M2-ECN-8 Master Thesis and Internship



The Master thesis is formally under the responsibility of ECN, as ECN delivers his Master specialised in Hydrodynamics for Ocean Engineering (2nd year Master) at the end of the program.

Students can perform their Master thesis in ECN, in a university laboratory, in a private company, in a research centre in France or abroad.
Students can also perform their Master thesis in one of the partners of the EMSHIP consortium (including an internship with one EMSHIP industrial partner).
In all cases, the topic of the Master thesis must be in relation to Ship (free surface) Hydrodynamics and Ocean Engineering and has to be validated by ECN.
The duration of the Master Thesis is six months. Students must write a Master Thesis report and defend their work at the end of their Master Thesis. This defence is organized by ECN.


ECN Teaching team

The ECN teaching team involved in the EMSHIP+ program will be composed initially by :

  • Christian BERHAULT, Research Engineer
  • Félicien BONNEFOY, Associate Professor
  • Isabelle CALMET, Associate Professor, HDR(*)
  • Antoine DUCOIN, Associate Professor
  • Guillaume DUCROZET, Associate Professor
  • Silvia ERTL, Associate Professor
  • Pierre FERRANT, Professor
  • Lionel GENTAZ, Associate Professor
  • Boris HOREL, Research Engineer
  • David LE TOUZE, Professor
  • Zhe LI, Associate Professor
  • Jean-Marc ROUSSET, Research Engineer

(*) authorization to lead PhD Thesis in France

Others members of the Laboratory of Research in Hydrodynamics, Energetics and Atmospheric Environment (LHEEA) in ECN or people from other institutions (universities, laboratories, companies) will possibly contribute to the lectures given by ECN.


Full description of lectures – Semester 3 at ECN (30 credits):


Title:    PREREQUISITES        0 Credit

Ref :   EMSHIP+_M2-ECN-0

Prof : G. DUCROZET, D. LE TOUZE                                           Teaching Period: Sem 3

Link :

Course contents

1) Objectives

To remind basics of Fluid mechanics and mathematics, which are essential for a good understanding of all courses of the semester

2) Content

Fluid mechanics:

-          Continuous media

-          Navier-Stokes equations

-          Dimensional analysis

-          Kinematics

-          Calculation of stresses

Mathematics for engineers:

Short introduction to Matlab computer language with practical classroom

Learning outcomes of the course

To be comfortable with basics of Fluid Mechanics and Mathematics for Engineers




Ref :   EMSHIP+_M2 - ECN-1

Prof :  P. FERRANT, L. GENTAZ, D. LE TOUZE                      Teaching Period: Sem 3

Link :

Course contents


1) Objectives

The purpose of this course is to give the students a general introduction to hydrodynamics preparing them to take the best out of more focused courses proposed in the sequel of the program.

2) Content

Industrial, R&D and research activities connected to free surface hydrodynamics and ocean engineering

A state of the art of problems of engineering or applied research where use of Hydrodynamics is required

Different classes of approximation used in Hydrodynamics

Presentation of different mathematical models which can be used in Hydrodynamics to describe free surface incompressible free surface flows (Navier-Stokes equations, Euler equations, Laminar and turbulent boundary layer equations, Potential flow model) and main problems of free surface Hydrodynamics for which each model is adapted

Introduction to Numerical Simulation

Following parts will be described :

-          Methodology for numerical simulation of a physical problem

-          Implementation of a numerical method

-          Pre- and post-treatment

-          High-performance computing

Hydrostatic and Stability of ships and marine structures

Intact and damaged stability of floating structures are investigated through theoretical and practical aspects. Computer lab work is done with state of art industry software

3) Recommended Reading

  • Biran, Ship Hydrostatics and Stability, Butterworth-Heinemann, 2003

Learning outcomes of the course

To know how Hydrodynamics is used today in naval and offshore engineering

To be able to define what mathematical model is adapted to a given problem in Hydrodynamics

To know fundamental aspects of numerical simulation in Hydrodynamics.

To know main parameters used to evaluate hydrostatic stability of a floating body


Basics of fluid mechanics

Title:    WATER WAVES AND SEA STATES MODELLING               4 credits

Ref : EMSHIP+_M2-ECN-2

Prof :  G. DUCROZET, F. BONNEFOY                                              Teaching Period: Sem 3

Link :

Course contents


1) Objectives

This course intends to describe the main source of loading for structures at sea (e.g. marine renewable energy systems), namely ocean waves. This is essential for the design of such structures and is the starting point of all hydrodynamics’ studies (see courses: wave-structure interactions, experimental hydrodynamics, marine renewable energy, etc.).

First we give an overview of some of the numerous mathematical models used to represent free surface gravity waves, and the associated underlying flow. The scope is voluntarily restricted to the most useful models generally used by naval engineers and researchers. In a few cases, a deeper theoretical insight is presented in order to allow the students to understand the subtleties of water wave theory.

In the second part, the use of the statistical approach is presented, both for the representation of sea states and for the sea structure’s response.


2) Contents

Introduction to marine environment

Description of the ocean and the different kind of waves existing. Focus on the gravity waves and the processes responsible for their generation.

2h theory

Gravity waves modelling

Derivation of the governing non-linear equations and introduction of the multiple scale method to generate particular subset of equations.

2h theory

Dispersive waves

  1. Airy Potential; derivation of the solution by separation of variables. Expression of all the related physical quantities: group velocity, energy density, energy flux, limits of the linear model.
  2. Higher order Stokes solutions (3rd order, 5th order). Sequential construction of the Stokes higher order solutions. Specific nonlinear features of Stokes waves.
  3. Stream function model. Explanation of the method – numerical application

4h theory + 2h practical classroom + 4h computer

From deep water to shallow water

  1. Refraction and shoaling of dispersive waves
  2. Shallow-water (non-dispersive) waves
    1. Derivation of Boussinesq equation.
    2. The solitary wave as a particular solution of Boussinesq equation.
    3. KdV equations: cnoidal waves.

2h theory

Statistical models for wave field description

  1. Random sea state modeling.
  2. Usual wave spectra models.
  3. Wave generation

4h theory + 2h practical classroom + 6h computer

Random responses of structures at sea

  1. Random responses of a linear system.
  2. Review of the results for ship responses by a deterministic theory.
  3. Motions on a real sea state.
  4. Extreme responses, design factors.

4h theory + 4h computer

3) Recommended Reading

  • Robert G. Dean & Robert A. Dalrymple, Water wave mechanics for engineers and scientists, Advanced Series on Ocean Engineering (vol.2).

Learning outcomes of the course

What are hypothesis used to defined different wave models which can be found in literature or in marine engineering community ?

To be able to calculate and use main parameters of a irregular wave state


Basics of fluid mechanics (Navier-Stokes equations, potential flow model, free surface conditions), General concepts of hydrodynamics


Title:    WAVE-STRUCTURE INTERACTIONS                                            5 credits

Ref (ECN):   EMSHIP+_M2-ECN-3

Prof : P. FERRANT                                            Teaching Period:  Sem 3

Link :

Course contents

1) Objectives

The objective of the first part is to give a complete presentation of the available models for the determination of marine structures response in a seaway, emphasizing the advantages and drawbacks of each approach.

A complete presentation of the linearized theory of wave-body interactions, treated in a deterministic sense, is first given. Both frequency domain and time domain approaches are described. Fundamental relations between both solutions are systematically emphasized. High and low frequency second order effects are explained and illustrated.

Then, an overview of the available nonlinear theories and numerical models for wave-structure interactions is given. Different levels of approximation are described, from the simple addition of nonlinear hydrostatics to fully nonlinear time domain models.

The second part addresses the modelling of mooring systems. Different options in terms of mooring systems and arrangements are presented in order to give students the main information necessary for undertaking a mooring design process.

For both parts lectures and seminars are completed by practical exercises based on state of the art software for wave-structure interaction and mooring modelling.

2) Contents

Objectives, theoretical framework

1h theory

Short review of linear systems theory

1h theory

Formulation of the boundary value problem. Linearization

2h theory

Frequency domain approach

  1. Definition of diffraction and radiation sub-problems
  2. Hydrodynamic loads: added mass and damping
  3. Calculation of motions
  4. Relations between elementary solutions

4h theory + 2h tutorial + 8h practical classroom

Time domain approach

  1. Forced motion of a floating body
  2. Formulation of the diffraction problem in the time domain
  3. Equations of motion
  4. Relation to frequency domain response

2h theory

Second order effects

  1. Drift forces
  2. Low and high frequency loading in irregular waves

2h theory

Introduction to nonlinear models

  1. Nonlinear hydrostatics and Froude-Krylov loading
  2. Weak scattered hypothesis
  3. Fully nonlinear models

2h seminar

Moorings for marine structure

  1. Some examples in Oil and Gas energy
  2. Different types of mooring systems
  3. Offloading operations
  4. Some examples in Marine Renewable energy
  5. Mooring main functions
  6. Mooring arrangement
  7. Mooring components
  8. Environmental conditions
  9. Mooring Design basis

4h theory + 8h computer lab

3) Recommended Reading

  • Adrian Biran (2003) Ship Hydrostatics and Stability, Butterworth-Heinemann.
  • API recommended Practice 2SK (2005) Design and analysis of Stationkeeping Systems for Floating Structures.
  • Vryhof anchors (2010) Anchor Manual, The Guide to Anchoring.

Learning outcomes of the course

To know hypothesis and limitations of seakeeping study done with a linearized potential flow model; To be able to calculate and use basic results (added mass, radiation damping, excitation forces, drift, RAOs) obtained with a software simulating seakeeping in potential flow theory and frequency domain approach

Prerequisites :

Elements on water waves modeling given in the “Water Waves and Sea States Modelling” lecture described before will be useful here.

Title:    NUMERICAL HYDRODYNAMICS                         5 credits

Ref :    EMSHIP+_M2-ECN-4                         

Prof : D. LE TOUZE, L. GENTAZ, Z. LI                  Teaching Period: sem 3



Link :



Course contents

1) Objectives

The goal of this class is to provide students with an overview of the Computational Fluid Dynamics (CFD) methods and simulation environment for the computation free-surface unsteady flows of ocean engineering. The different methods rely on different physical approximations of the wave-structure interaction problem. The latter approximations are based upon the space-time scales (from hours and km² to seconds and m²) at stake and the engineering objective at aim (energy convertion quantification, design for standard operation, extreme condition design, maintenance operations, etc.). According to the approximations made, different numerical methods can be developed.

The primary objective is that students gain a clear vision of the use of the different approximations and methods, and of their respective range of application, computational cost, human and resource cost of use, versatility, limitations, ease of use, space discretization (mesh), etc. The methods reviewed range from potential flow theory ones (BEM: Boundary Element Method, HOS: High-Order Spectral), to full description of the Navier-Stokes equations (FD: Finite Differences, FD: Finite Volumes, FE: Finite Elements) associated with interface models (VoF: Volume of Fluid, LS: Level Set).

For each method, the mathematical model, discretization and implementation principles are explained. Turbulence modeling principles (RANS: Reynolds Averaged Navier-Stokes, LES: Large-Eddy Simulation, hybrid RANS/LES) are provided. The link with the space discretization (structured surfacic meshes, unstructured volumic meshes, meshless...) is detailed. Numerical properties (convergence, stability, consistency) are reviewed.

Finally, the links between the numerical method and the current simulation environment are developed: existing commercial software, human and computational resources, choice of software depending on the targetted problem, link with hardware (High-Performance Computing, cloud resources)...

Practical projects using software based on different methods studied in courses (BEM, FV...) are proposed to students with use of commercial software or software developed in Ecole Centrale de Nantes. In other lab works students will have to implement their own simple numerical model.


2) Contents

Knowledge and understanding of potential flow solvers

Potential flow methods (BEM), Integral methods solving, Surfacic meshing, Hydrodynamic loading calculation

4h theory + 2h tutorials

Numerical methods for free surface flows

Volumic discretization methods (FD, FV), Time integration and stability, Interface methods (VoF, LS), Turbulence models (RANS, LES)

4h theory + 2h tutorials

Navier-Stokes equations solution techniques

Pressure-velocity coupling, Linear system solving, Volumic meshing

Hydrodynamic loading calculation

4h theory + 2h tutorials + 14h computer lab work

3) Recommended Reading

  • Proceedings of the ONR (Office on Naval Research) conferences
  • Proceedings of ITTC conferences on numerical methods and recent developments in numerics
  • Computational Fluid Dynamics for engineers, Cambridge Univ. Press,2011


Learning outcomes of the course

To know different numerical methods which are existing, their capacities and their limitations and drawbacks.



Prerequisites : 

Basics of Fluid mechanics and numerical analysis


Title:    EXPERIMENTAL HYDRODYNAMICS                                              5 credits

Ref :  EMSHIP+_M2 - ECN-5                        

Prof :F. BONNEFOY                                         Teaching Period: sem 3

Link :

Course contents

1) Objectives

To provide students with state of the art knowledge on experimental fluid dynamics in the field of Offshore renewable energy. Despite the development of numerical modelling, the experimental approach remains a major source of knowledge development in ship hydrodynamics and marine renewable energy. The contribution to the selection of adequate hypothesis and to the validation of analytical or numerical models is of primary importance. In numerous situations, the experimental approach remains the most reliable, economical and fast way to validate new designs. Specific instrumentations and facilities are presented in this course and used in lab work.


2) Contents

Introduction to experimental hydrodynamics

The students find the main topics in MRE experiments. Static vs perturbation approaches are presented.

2h theory + 1h visit of ECN experimental facilities

Experimental ocean engineering

Experimental tests in offshore basins.

3h theory + 8h practical classroom


Ship resistance and experiments in towing tanks. Reynolds and Froude similitude; extrapolation at full scale.

2h theory + 4h practical classroom

Ship manoeuvrability

Mathematical formulation, experimental determination of hydrodynamic coefficients. Modelling of towed structures.

2h theory + 4h practical classroom

Measurements and signal processing

Sensors and transducers, sampling theory. Signal processing, Fourier analysis.

2h theory + 4h practical classroom

Learning outcomes of the course

The purpose is to give elements to students about capacities in experimental hydrodynamics, what phenomena can be studied, what measurements can be obtained

Prerequisites :

Water Waves and Sea States Modelling

Wave-Structure interactions

Numerical Hydrodynamics

Title:    NAVAL ENGINEERING                                                                        5 credits

Ref :  EMSHIP+_M2-ECN-6                        

Prof : Z. LI, F. BONNEFOY, L. GENTAZ                               Teaching Period: sem 3

Link :

Course contents

1) Objectives

This course is divided into three main parts which are all oriented towards fundamental knowledge about ship design. The students learn about ship manoeuvrability, optimization and computational fluid dynamics.

  • Introduction of the concepts required for ship manoeuvrability studies.
  • Description and practice of the principal scientific methods and tools in optimization for naval architects and ship designers.
  • Application of CFD tools to ship simulation

Direct applications of the concepts introduced in Numerical hydrodynamics and Wave-structure interactions course.

  1. Contents

In manoeuvrability, the students learn how to use the mathematical formulation and the analytical resolution of the linearized problem in simple examples such as turning circles. Realistic configurations are then studied by means of numerical simulations of the nonlinear problem.

In optimization, the multi-objective approach is used through various examples in naval applications.Different algorithms are presented (gradient, genetic…) and the Mode-Frontier software is applied to optimize the bulb of a ship in order to minimize the wave resistance.

In CFD, the knowledge seen in the Numerical hydrodynamics course is applied to the simulation of a ship with forward speed.

More precisely lectures are organized following description given below :

Manoeuvrability - introduction

The students discover the basics of manoeuvrability : hydrodynamic loads on the hull, propeller loads, rudder action… The mathematical framework is presented to express the problem in the ship reference frame.

2h theory + 4 h  tutorials

Experimental manoeuvrability

Experimental tests at seas (full scale) and in basins (model scale).

2h theory

Computational manoeuvrability

Presentation of the state of the art in terms of numerical computations of manoeuvring performance of ships

Numerical modelling of turning circle problem

2h theory + 4h computer classroom

Optimization – basics.

Presentation of two typical optimization methods: the geometrical method and the gradient-based method. The students learn how to use the software ModeFrontier with some simple examples.

2h theory + 4h computer classroom

Optimization – advanced

Presentation of the genetic optimization method. The students will use ModeFrontier to optimize the shape of the bulbous bow in order to minimize the resistance exerted to the ship.

2h theory + 6h computer classroom on ship resistance and bulb optimization


The students use the software Star-CCM+ (solving Navier-Stokes equations for a viscous flow) to build a simulation of a practical case of a ship advancing in calm water

4h computer classroom on ship resistance

Learning outcomes of the course

To know theory and principles of numerical modelling for the problem of maneuverability

To be able to use an optimization software for a practical case of hull optimization

To be able to use a viscous flow CFD software for a practical case of calculation of the drag of a ship advancing in calm water

Prerequisites : All courses attended previously during the semester at ECN

Title:    FRENCH LANGUAGE                                                                3 credits

Ref :  EMSHIP+_M2 - ECN-7                        

Prof : S. ERTL                                                                                Teaching Period: sem 3

Link :

Course contents

1) Objectives

The objective is to familiarise the learner with the French language and French culture through an entertaining task-based communicative language teaching, focused on speaking combined with

  • Phonetics
  • Self-correcting exercises on our pedagogical platform
  • Learning Lab activities
  • Project work
  • Tutoring

Course objectives include the acquisition and reinforcement of vocabulary, syntax, and pronunciation by both traditional means and through the use of digital resources.

Allow students to learn general french, develop language skills of oral and written comprehension and expression.

2) Contents

Giving and obtaining factual information

  • personal information (e.g. about name , address, place of origin, date of birth, education, occupation)
  • non-personal information (e.g. about places and how to get there, about the time of day, about various facilities and services, about rules and regulations, about opening hours, about where and what to eat, etc.)

Establishing and maintaining social and professional contacts, particularly

  • meeting people and making acquaintances
  • extending invitations and reacting to being invited
  • proposing/arranging a course of action
  • exchanging information, views, feelings, wishes, concerning matters of common interest, particularly those relating to

-          personal life and circumstances

-          living conditions and environment

-          educational/occupational activities and interests

-          leisure activities and social life

Carrying out certain transactions

  • making arrangements (planning, tickets, reservations, etc.) for

-          travel

-          accommodation

-          appointments

-          leisure activities

  • making purchases

Learning outcomes of the course

After completing this course, the students will be able to communicate in spoken and written French, in a simple but clear manner on familiar topics in the context of study, hobbies etc.  Another important goal of this course is to introduce to French culture. At the end of the course, the complete beginners can achieve the level A1 and some aspects of A2 of The Common European Framework of Reference for Languages. More advanced students may aim the levels B1/B2.

Prerequisites :