The Proceedings Fifth International Conference on Numerical Ship Hydrodynamics (1990) / Chapter Skim
Currently Skimming:
Numerical Evaluation of the Complete Wave-Resistance Green's Function Using Bessho's Approach
Numerical Evaluation of the Complete Wave-Resistance Green's Function Using Bessho's Approach
Pages 133-144
The Chapter Skim interface presents what we've algorithmically identified as the most significant single chunk of text within every page in the chapter.
Select key terms on the right to highlight them within pages of the chapter.
From page 133... ...
In the far field case, the use of modern day remote sensing technology makes it of interest to assess the ship wake for wavelengths which are significantly shorter than those applicable to the wave resistance problem. Efforts at rendering the initial double integral representation of the Green's function amenable to numerical calculation usually involve expressing it as a series of single integrals.
|
From page 134... ...
2.2 Concise Statement of Bessho's Approach The usual way of simplifying the double integral expression for Go is to perform an initial integration over k or 8, thus reducing the double integral to a single integral. The integrand, however, is not entirely in terms of elementary functions but contains the higher order derived exponential integral function E~(u)
|
From page 135... ...
(4) and thus the double integral is converted to a single integral entirely in terms of elementary functions.
|
From page 136... ...
(15) , in the single integral resulting from the residue evaluation, the following expressions are obtained for A2 and B2, where each is given in terms of a single integral and a double integral A2 = —km| dm I°° dw 7r~-o 0 1 —im -= exp (—imp sinh w + imp sinh I)
|
From page 137... ...
As mentioned previously, our analysis starts from the four component complex single integrals given in Eqs.
|
From page 138... ...
Equation (32c) shows that Go is odd about x = 0 and has an infinite upper limit of integration while Eqs.
|
From page 139... ...
. Our principal effort has been to determine minimum integration domains for the two integrals which have theoretically infinite upper limits of integration: Go and (as x /p— m)
|
From page 140... ...
by adding Go, Go, and Gx. 3.5 Computer Time Requirements Computer time depends on various factors, of which the values of x, y, and z, the error criterion I, the type of integral, and the integration rule are the most important.
|
From page 141... ...
Figure 7c shows the familiar far field wave patterns confined to the Kelvin sector. Figure 7d shows that the near field integral N has contour lines which are nearly circular and asymptotically decay as 2/R.
|
From page 142... ...
/ ~# ~^ a = Figure ah. Conlour Plol of at, z = a.
|
From page 143... ...
By simple rearrangement, we can also express our results in terms of the more physical near field and wavelike components N and W Computer time depends on a number of factors, principally the submergence of the source z, the required accuracy a, and the horizontal distances x and y from the source.
|
From page 144... ...
Noblesse, F., "Alternative integral representations for the Green function of the theory of ship wave resistance," Journal of Engineering Mathematics, Vol.
|
Key Terms
This material may be derived from roughly machine-read images, and so is provided only to facilitate research.
More
information on Chapter Skim is available.