#### General course objectives

After completing this course, the student should be able to use linear potential flow theory to predict the wave induced motions of floating maritime structures. An understanding of the strengths and weaknesses of different numerical solution techniques will allow the student to make the appropriate choice depending on the application. The primary focus, for example applications, is on ships, offshore wind turbines and wave power devices.

#### Content

Starting from the basic conservation laws for a fluid flow (the Navier-Stokes equations) we derive the potential flow approximation for the hydrodynamic interaction between a fixed or floating marine structure and ocean waves. This problem is linearized, assuming small amplitude waves and small body motions, to express the structure as a linear harmonic oscillator. The relationship between the time- and frequency-domain expressions is stressed. Green's theorem is used to derive a number of useful relations between coefficients, as well as high- and low-frequency limits. Green's theorem also leads to the Boundary Integral form of the problem and further to the Boundary Element Method (BEM) which is the most widely used numerical solution technique for obtaining the hydrodynamic coefficients. A number of variants of the BEM are discussed including both 2D strip-type methods and 3D methods based on either the free-surface or the Rankine Green function. As exercises, the student will develop their own 2D, BEM solver is both for infinite fluid problems and for wave radiation and diffraction. Finite difference and finite volume solutions are also discussed. Weekly exercises are solved to illustrate the theory. A solver for the equations of motion is built in Matlab and applied to analyse several typical structures. Several short concept tests will also be given during the course of the Semester.

## Prerequisites

##### Recommended prerequisites

41201 Fundamentals of ships and other floating structures. (41312 Basic fluid mechanics/41102 Hydrodynamics 1/10346 Continuum Physics).41226 Advanced Wave Hydrodynamics.02631 Introduction to programming and data processing, Basic naval architecture and ocean engineering, basic fluid mechanics, linear wave theory and programming in Matlab are expected. Ordinary and partial differential equations and nonlinear wave theory are desirable.

## Learning outcomes

A student who has met the objectives of the course will be able to:

- Express the equations of motion for a floating marine structure in terms of linear coefficients
- Go back and forth between the time- and frequency-domain representations of the problem
- Derive relationships between different scattering problems and their asymptotic limits
- Use Green's theorem to derive the boundary integral formulation of the problem
- Discretize the boundary integral equation to obtain a numerical method suitable for calculations
- Decide which numerical solution technique is best suited to a particular application
- Write a solver for the equations of motion in Matlab
- Compute the response of a floating structure in waves and compare with established benchmark solutions
- Understand how weakly-nonlinear effects can be incorporated into a time-domain analysis
- Describe how nonlinear effects can be included in the analysis

## Files/Documents

## ISCED Categories