Numerical modelling of the diffraction of short time-harmonic linear waves

Abstract

It is well known that the Green's identity formula relative to the two-dimensional Helmholtz equation can be taken as a basis for the numerical modelling of problems concerning the diffraction of time-harmonic surface waves, within the limits of the linear and inviscid theory for shallow- or constant-depth water. The early applications of this kind of mathematical approach have been given by DAUBRT and LEBR~TO~ (1), for the diffraction of objects placed in the open sea, and by HWA~G and TUCK (2), for the calculation of the wave-induced oscillations in a har- hour. In these applications, however, as well as in other applications, the whole problem was described by a single integral equation, written for a contour of either finite or infinite length. L~s~ (3) has given to the problem of the harbour oscillations another planning, charac- terized by two main features. First, the solution was obtained not from a single equa- tion, but from a set of two equations, the former related to the internal harbour basin, and the latter to the external sea. Secondly, the elevation field was obtained only after the evaluation of the normal-velocity field along the junction line between the two subdomains. This line of research has been further developed by L~ and RAICHL~N (4) for a similar problem, in which the internal domain was considered as the junction of more domains of simpler form, so that the whole problem was solved in terms of a set of more than two integral equations. MATTIOLI and TINTI (5) presented an analogous approach for the propagation of waves from the sea to a lagoon through a channel, partitioning the whole domain in a finite subdomain and two semi-infinite regions. Finally, HARTV.~ and EFRONY (e) extended the previous results to the case of a problem of wave diffrac- tion or radiation defined in the vertical plane. However, in all the applications cited until now, the subdivision of the original domain was not arbitrary. In fact in no case two junction lines intersect each other