Long wave amplification problems: Frequency and time domain analysis

This paper adresses the problem of modelling long waves in shallow water, and compares two ways of approach, in the time and in the frequency domains. Finite Element techniques are applied in both cases, and special attentional is paid to the analysis of suitable boundary conditions for the open boundaries. The first part of the paper presents the mathematical models which have been used, i.e., the non-linear shallow water wave equations and its simplification for harmonic waves. This is followed by a description of the boundary conditions corresponding to incident wave, absorbing and reflecting boundaries. The Taylor-Galerkin explicit algorithm developed by Peraire, Morgan and Zienkiewicz [ 1 , 2 ] is used to discretize the non-linear shallow equations, and a classical weighted residual technique for the harmonic wave simplification. The last is solved by Precondicioned Conjugate Gradient technique which reduces the storage requirements. Finally, both methods are applied to simulate the response of Ciudadela harbour, giving similar results.