Introduction to Nemoh &
Hydrodynamic Coefficients
Understanding Added Mass, Radiation Damping, and Boundary Element
Methods
Applications in Research and Industry
Analyzing the heave, pitch, and roll motions of Spars, Semi-submersibles, and TLPs to ensure massive turbine stability.
Demystifying Radiation Forces
• Imagine a buoy bobbing up and down in perfectly calm water. As it moves, it creates ripples (waves) that travel
outward.
• To create these waves, the buoy must transfer energy to the water. The water, in turn, resists the buoy's movement.
• This fluid resistance (Radiation Force) is mathematically divided into two distinct components:
• A force proportional to the body's acceleration (Added Mass).
A force proportional to the body's velocity (Radiation Damping).
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Motion
Key Concept 1: Added Mass
• What is it? Added mass is the inertia added to a system because an accelerating or decelerating body must move
some volume of the surrounding fluid.
• Crucial Distinction: It is not a physical mass of water sticking to the hull. It is a kinetic energy effect caused by fluid
resistance.
• The force from added mass directly opposes the body's acceleration and is highly dependent on frequency.
Fadded_mass = - Aij (w) ■ x‘*
Fluid Inertia
(Resistance)
(accel)
Key Concept 2: Radiation Damping
What is it? When a floating body oscillates at the free surface, it generates outgoing waves carrying energy away from the
structure.
This loss of energy acts as a strong damping mechanism on the body's motion, completely distinct from friction or viscous
drag.
The damping force is proportional to the body's velocity.
Fdamping = - Bij (w) ■ x*
Enter Nemoh: What is it?
Nemoh is an open-source Boundary Element Method (BEM) code developed by Ecole Centrale de Nantes.
It acts as an industry-standard solver for calculating first-order hydrodynamic coefficients purely in the frequency domain.
Why use it? It is computationally efficient and provides the exact matrices needed to solve the equation of motion for offshore
platforms, wave energy converters, and ships.
The Three Forces on Floating Bodies
Excitation Forces
Forces exerted by incident ocean waves hitting the stationary structure, causing initial disturbances.
Hydrostatic Forces
The "spring-like" restoring forces pushing the body back to equilibrium, balancing buoyancy and gravity.
The Equation of Motion (Frequency Domain)
The General Equation
To accurately predict how a platform will behave in the ocean, we use Newton's Second Law applied in the
frequency domain.
[ - w2 ( M + A (w) ) + iw B (w) + C ] X (w) = Fexc (w)
Mathematical Legend
• M = Structural Mass matrix
• A(w) = Added Mass matrix
How Nemoh Solves the Problem (BEM)
1. Wetted Surface Meshing
Instead of creating an enormously complex mesh of the entire infinite ocean (like you would in general CFD
software like OpenFOAM), the Boundary Element Method only requires meshing the wetted surface of the
floating body itself.
2. Mathematical Reduction
Nemoh utilizes Green's functions to mathematically satisfy the fluid boundary conditions (Laplace equation, free
surface condition, seabed condition, and radiation at infinity). This effectively reduces a massive 3D fluid volume
problem into a much faster 2D surface problem.
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Summary & Next Steps
£ Key Takeaway: Added mass and radiation damping are frequency-dependent forces arising from
a structure's movement in water.
£ The Tool: Nemoh is an open-source BEM framework that efficiently computes these coefficients
by relying entirely on meshing the wetted surface.
Next Up: A live demonstration! We will open the terminal, run a basic floating cylinder
through the full Nemoh workflow, and visualize the added mass curve.
Questions?
Ready for the live terminal demonstration?