The Proceedings Fifth International Conference on Numerical Ship Hydrodynamics (1990) / Chapter Skim
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The Numerical Solution of the Motions of a Ship Advancing in Waves
The Numerical Solution of the Motions of a Ship Advancing in Waves
Pages 529-538
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From page 529... ...
Wu and R Eatock Taylor University College London London, UK Abstract The hydrodynamic problem of a surface ship advancing in regular waves at constant forward speed is analysed using a three dimens tonal theory based on the linearized velocity potential.
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From page 530... ...
In this particular problem, as the body surface condition on the waterline is averaged over the body surface, we can avoid the difficulty of both the source and field points being on the free surface when solving the integral equation. The use of the Galerkin method also avoids another serious numerical difficulty: the second order derivatives of the steady potential due to forward speed (which appear in the body surface condition on the unsteady potential due to the ship oscillation)
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From page 531... ...
¢jxx~2ir~ix~~¢i~o on SF (8) where r=wU/g and ~c~2/g; and where G is the Green function for a pulsating translating source, which is taken in the form derived by Wu & Eatock Taylor (1987b)
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From page 532... ...
Initially, a coarse mesh can be refined by using more of the coordinates of the ship hull provided by the offsets; but this process is limited by the number of coordinates available. When a still finer mesh is needed, the commonly adopted procedure is to interpolate using the shape functions.
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From page 533... ...
It should be noted, however, that these results are not the same as those in Wu & Eatock Taylor (1988) , since the latter included the effect of the steady disturbance potential on the body surface boundary condition.
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From page 534... ...
he found that the former provides results within 3.1% and 5.3% of the finer mesh results for added mass in heave and pitch respectively, while these two meshes give virtually identical area and volume fqr the ship. Next we calculated the hydrodynamic coefficients by using the translating pulsating source Green's function in equation (22)
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From page 535... ...
The added masses of the series 60 (Cb=0.7)
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From page 536... ...
pitch Figure 3. The damping coefficients of the series 60 (Cb=0.7)
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From page 537... ...
The numerical techniques introduced have been found to be effective in overcoming some difficulties encountered previously. A major remaining difficulty is the evaluation of the Green function when both source and field points are near the free surface, which appears to be the direction towards which further work in this area should be directed.
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From page 538... ...
From our experience using quadratic boundary elements for the problem, we are certainly not surprised that using 850 or so constant elements to represent the series 60 hull did not always provide satisfactory results. Our own coarse mesh used 1085 nodes for the submerged hull (the numbers in Fig.1 referring to one half of the hull)
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