The Proceedings Fifth International Conference on Numerical Ship Hydrodynamics (1990) / Chapter Skim
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Numerical Evaluation of a Ship's Steady Wave Spectrum
Numerical Evaluation of a Ship's Steady Wave Spectrum
Pages 145-156
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From page 145... ...
The modified expression for the wave-spectrum function is considerably better suited than the usual expression for accurate numerical evaluation because the significant numerical cancellations which occur between the waterline and hull integrals in the usual expression are automatically and exactly accounted for in the modified expression, as is demonstrated mathematically and confirmed numerically. INTRODUCTION Near-field potential-flow calculations about ships advancing at constant speeds in calm water are routinely required for evaluating their hydrodynamic characteristics, both in calm water and in waves, and for determining the required propulsion and control devices.
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From page 146... ...
This new expression for the wave-spectrum function is considerably better suited than the usual expression for accurate numerical evaluation because the significant numerical cancellations which occur between the waterline and hull integrals in the usual expression are automatically and exactly accounted for, via a mathematical transformation, in the modified expression obtained in this study. The fundamental advantage of the new expression over the usual one may readily be appreciated from Fig.
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From page 147... ...
contains essential information directly relevant to a ship's wave resistance and wave pattern. In particular, the wave resistance, R say, experienced by the ship is defined in terms of the wavespectrum function by means of the well-known Havelock formula R/(pU L )
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From page 148... ...
for a wallsided ship. The major contributions to these two integrals thus are combined into the modified waterline integral Kw*
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From page 149... ...
2. The top row of this figure, corresponding to F = 0.1, shows that the lower-waterline integral KW'(t)
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From page 150... ...
The errors which inevitably occur in the numerical evaluation of the integrals Kw + Kw' and KH' cause imperfect numerical cancellations between these components and correspending large errors in their sum. Numerical errors in the sum Kid can be especially difficult to control because the errors associated with the numerical evaluation of the hull integral KH' and the waterline integral Kw + Kw' are not necessarily comparable (due to differences in the errors associated with numerical integration over hull panels and waterline segments)
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From page 151... ...
3. It may be seen that the waterline integral KW and the modified hull integral R}I are appreciably larger than their sum K`t,, especially for large values of t.
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From page 152... ...
(20) is ill suited for accurate numerical calculations, notably for evaluating the short divergent waves in the wave spectrum corresponding to large values of t.
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From page 153... ...
for accurate numerical evaluation because the large cancellations which occur between the waterline integral Kw + Kw' and the hull integral KH' in the usual expression (20 ) are automatically and exactly accounted for, via a mathematical transformation, in the new expression (44 )
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From page 154... ...
Ratclil5fe and A.M. Reed, "Comparative Accuracy of Numerical Kelvin Wake Code Predictions - Wake off," David Taylor Research Center Report OTRC/SHD-1260-01 (1988)
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From page 155... ...
for a simple strut-like bull form and an assumed simple expression for the potent tat at the hull surface. The real and i Imaginary parts of the ten functions K¢, 'Kw ~ Kw', Kw', KH', Kw ~ KH ~ KW ~ KH , Kw*
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From page 156... ...
. Large cancellations occur between the waterline integral Kw + Kw' and the hull integral KH' in the usual expression for Rip which is then ill suited for accurate numerical calculations, notably for evaluating the short waves in the spectrum corresponding to large values of tans.
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