The Neumann-Kelvin method for solving the flow past a body moving at a steady speed requires that the body boundary condition be satisfied exactly, while the free-surface condition is satisfied in a linearized sense. The solution is generally obtained by discretizing the body surface into panels, each of which has an unknown singularity strength. In the present work, two types of numerical experiments have been carried out. In the first approach, the body condition is satisfied at one point on each panel (the collocation method). In the second approach, the body condition is satisfied in an integrated sense on each panel (the Galerkin method). Improved convergence properties are demonstrated by the second approach.
Convergence Properties of the Neumann-Kelvin Problem for a Submerged Body
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Doctors, Lawrence J., and Robert F. Beck. "Convergence Properties of the Neumann-Kelvin Problem for a Submerged Body." J Ship Res 31 (1987): 227–234. doi: https://doi.org/10.5957/jsr.1918.104.22.168
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