An efficient coupled-mode/FEM numerical method for linear wave propagation over 3D variable bathymetry domains

A robust numerical algorithm for the simulation of linear water wave propagation over uneven bottom topography is developed. The solution strategy is based on a highly efficient reduction of the 3D problem to a system of partial differential equations by means of a consistent coupled mode series expansion for water wave propagation over variable seabed. The main feature of the proposed series representation is the incorporation of special terms in the vertical expansion basis, accounting for the bottom boundary condition of the varying seabed. The formulation of the 2D system follows from the variations, with respect to the expansion coefficients (functions of the horizontal plane spatial coordinates), of a suitably chosen energy functional. The resulting model is a variable coefficient system of second order, with respect to the spatial coordinates, Partial Differential Equations (PDEs). Linear triangular finite elements are employed for the solution of this PDE system offering flexibility in the discretization of complex 2D domains. The numerical method developed has been applied to several test cases yielding accurate representations of the wave field at relatively low computational cost and small execution times.