A finite-element series-expansion technique for linear surface water waves

Abstract

Abstract A numerical method is presented to deal with the propagation of surface water waves in the framework of the linear theory for an inviscid fluid. For particular geometrical configurations of the region in which wave propagation occurs, refraction, diffraction and reflection phenomena can arise simultaneously, so that the solution of the original Berkhoff equation with appropriate boundary conditions becomes essential to achieve an adequate picture of the resulting field. The method is based on a finite element scheme, in which the element matrices are computed by a series expansion technique. The elements are of arbitrary shape, although of constant depth, and two independent numerical approximations are given for the surface-elevation and velocity fields. An application of the method to the propagation of short water waves in a channel connecting two basins of larger dimensions shows that the method can deal with very large domains, at least when compared to the possibilities of the usual finite element approaches.