Unstructured MEL modelling of nonlinear unsteady ship waves

An unstructured mixed-Eulerian-Lagrangian model (MEL) is described for the simulation of the nonlinear wave-body interaction, as opposed to the structured model used widely in this field. In present model, the free surface is interpolated accurately using a polynomial scheme coupled with the moving least-squares method, and is triangulated with a local interrogation method coupled with the advancing front method to provide a high quality mesh. A new method is devised to update the free surface intersection with the body, based on the desingularized boundary-integral method. Double desingularized point sources are used for a control point at the intersection, with one inside the body and the other above the free surface, to satisfy both the body and free surface boundary conditions over there. The desingularized point sources are positioned in terms of the element sizes as well as solid angles of the boundary surface, so as to avoid possible overcrowding of the sources at the corners of the surface. Solid angles on the surface are computed analytically using the spherical triangle theory. As an illustration, the algorithm is used to simulate the wave generation for a Wigley hull, which impulsively starts to move at a constant speed on a calm water surface. The anticipated Kelvin ship-wave pattern is well simulated. The wave profiles along the hull agree well with the measured results of Nobeless and McCarthy [Proceedings of the 2nd DTNSRDC Workshop, Maryland, 1983, pp. 5-35]. As compared to a structured approach, the unstructured model reduces the CPU time and memory requirements and, being robust in handling complex geometries, is more versatile in practical applications.