Abstract
The evaluation of the Green function is considered for the three-dimensional Laplace equation, in the interior of a rectangular channel subject to homogeneous Neumann conditions on the boundaries. To complement the Fourier eigenfunction expansion which is effective in the far-field, a near-field algorithm is developed based on the simpler Green function for a channel of infinite width, using images to account for the channel sides. Examples are given of numerical applications including the added mass of a sphere in a square channel, and the interaction force between a ship and an adjacent canal wall.
Similar content being viewed by others
References
S.R.Breit, The potential of a Rankine source between parallel planes and in a rectangular cylinder. J. Engg. Math. 25 (1991) 151–163.
J.N. Newman, The approximation of free-surface Green functions, Meeting in honour of Professor Fritz Ursell, University of Manchester, in Wave Asymptotics, Cambridge University Press (1991).
I.S.Gradshteyn and I.M.Ryzhik, Tables of Integrals, Series and Products, Academic Press, New York (1965).
F.T. Korsmeyer, C.-H. Lee and J.N. Newman, The computation of ship-interaction forces in restricted waters, submitted to J. Ship Research.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Newman, J.N. The Green function for potential flow in a rectangular channel. J Eng Math 26, 51–59 (1992). https://doi.org/10.1007/BF00043225
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF00043225