The wave resistance problem in a boundary integral formulation (Q1338292)

The wave resistance problem in naval hydrodynamics for both two- and three-dimensional bodies is considered. The mathematical model is based on the Laplace equation in an unbounded domain with Neumann boundary condition on the body surface and two nonlinear boundary conditions on the (non-compact) free boundary. Under the physically appropriate asymptotic conditions at infinity, the flow perturbation velocity is written as the gradient of a simple layer potential distributed on the wetted hull and the free boundary (a formal proof of that representation is also discussed). As a consequence, the problem can be formulated in terms of BIEs and solved numerically by means of BEM. The exact (linearised) solutions found by Havelock for a two- and three-dimensional submerged dipole are recovered and compared with the numerical solutions.