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Abstract
The objective of this project was to develop a calculation tool for the added
resistance of ships in ocean waves. To this end a linear potential flow timedomain
numerical seakeeping solver has been developed. The solver is based on highorder
finitedifference schemes on overlapping grids and has been implemented
using the Overture framework for solving partial differential equations on overset,
boundaryfitted grids. This library includes support for parallel processing and
a variety of direct and iterative system solvers. The nonlinear water water wave
problem is linearised about two base flows namely: the uniform stream, and the
double body flow. The resulting linearised initial boundary value problem has
been solved in the time domain. In order to march the free surface in time, the
fourthorder RungeKutta integration scheme has been used to integrate the
kinematic and dynamic freesurface boundary conditions.
The field continuity equation has been discretised by a centered fourthorder
finite difference scheme which also includes ghost layers at the boundaries. For
the zerospeed hydrodynamic problem, the same centered scheme can be utilised
to calculate the freesurface derivatives. In the case of the forwardspeed problem
however, the convective terms in the freesurface conditions have been calculated
using an upwind biased scheme, where the stencil is weighted in the upwind
direction. As an alternative to using the biased scheme, a flexible filtering scheme
has been implemented which can be applied to the solution after each time step.
The filtering scheme can be used with the centered finite difference scheme. Both
of these strategies introduce numerical diffusion into the model to ensure the
stability in the case of the forwardspeed hydrodynamic problems.
The developed computational strategy has been applied to solve three hydrodynamic problems: the wave resistance problem, the radiation problem, and
the diffraction problem. The main objective was to find the firstorder velocity
potentials, freesurface elevation and the body motions that are required to
calculate the wave drift force or the added resistance. Instead of solving the
timedomain water wave problem by the impulse response function approach,
a pseudoimpulsive Gaussian motion is used in this project. In the case of the
diffraction problem the pseudoimpulse describes the elevation of the incident
waves. In the radiation problem this is the displacement which will be applied to
the body in the timedomain. The timedomain solutions of the hydrodynamic
problems are then Fourier transformed to get the frequencydomain solutions.
In the case of the radiation problem these are the added mass and damping
coefficients. For the diffraction problem we obtain the wave exciting forces in the
frequency domain. By solving the equation of motion the response amplitude
operators for six degrees of freedom are also calculated. For each hydrodynamic
problem, the freesurface elevation along the waterline, the velocity potential
and its gradients on the body surface, are obtained in the frequency domain
via Fourier transform of the transient solutions. All this frequencydomain data
is then used to calculate the added resistance in the frequency domain. This
has been implemented using the nearfield formulation. The solver has been
validated against analytical solutions for simple exact geometries like a cylinder
and a sphere. The solver is now ready to be exercised on real ship geometries.
Original language  English 

Publisher  DTU Mechanical Engineering 

Number of pages  156 
ISBN (Electronic)  9788774753933 
Publication status  Published  2014 
Series  DCAMM Special Report 

Number  S171 
ISSN  09031685 
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Dive into the research topics of 'Towards Predicting the Added Resistance of Slow Ships in Waves'. Together they form a unique fingerprint.Projects
 1 Finished

Predicting the added resistance of slow ships in waves
Amini Afshar, M., Bingham, H. B., Jensen, J. J., D. Henshaw, W., Faltinsen, O. M. & Andersen, P.
15/09/2011 → 19/03/2015
Project: PhD