An EBE finite element method for the shallow water wave equation

A numerical model for the solution of the linear shallow water wave equation is presented. The spatial discretisation uses the finite element method while the time-stepping scheme is an implicit finite difference one. The problem is formulated for the vertical free-surface acceleration. Free-surface displacement is obtained by a double time-integration. The assembly of global matrices is avoided due to storage at element level. The equations are solved by a pre-conditioned conjugate gradient (PCG) method. The horizontal velocity field is computed a posteriori, using a weighted residual statement. Some results of refraction, diffraction and resonance problems, including a performance analysis of a Tapchan wave power plant collector, are presented and discussed.