We present a sea-keeping boundary element method of computation. The diffraction-radiation with forward speed Green's function in the frequency domain with an analysis of the accuracy and computational time needed for the boundary integration is used. The results of an analytical surface integration of Green's function and of its first and second derivatives are compared with a numerical procedure based on a Gauss method and further optimisations dependent on the relative location of the source and field points and to their distances to the free-surface. The results are compared for a single panel and a field point in the whole domain. This domain is divided in various zones in which different techniques of integration are used. These surface integration techniques are introduced in a panel method for sea-keeping computations adapted to the case of surface-piercing bodies or ships in forced oscillations. The results are also compared with results available from other calculation methods or from test measurements for the DNV barge or a simple surface-piercing flat plate.
The study of sea-keeping for a ship is a very complex problem and no entirely satisfactory solution has yet been obtained. Most of the studies use the boundary element method (B.E.M.) assuming the fluid is inviscid, the main physical phenomena being the wave production and the RANSE methods requiring very high CPU time for unbound fluid. The advantage of using the diffraction-radiation with forward speed Green's function with respect to the corresponding function in an unbound domain (Rankine source) to solve the Laplace equation is that the free surface boundary and radiation conditions are automatically satisfied. This leads to a lower order system of equations to solve and avoids any problems with the reflection of gravity waves on the free surface grid boundaries as seen in the Rankine methods.
