An Efficient Coupled-Mode/FEM Numerical Method for Linear Wave Propagation Over 3D Variable Bathymetry Domains

摘要

A robust numerical algorithm for the simulation of linear water wavepropagation over uneven bottom topography is developed. The solutionstrategy is based on a highly efficient reduction of the 3D problem to asystem of partial differential equations by means of a consistentcoupled mode series expansion for water wave propagation overvariable seabed. The main feature of the proposed series representationis 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, withrespect to the expansion coefficients (functions of the horizontal planespatial coordinates), of a suitably chosen energy functional. Theresulting model is a variable coefficient system of second order, withrespect to the spatial coordinates, Partial Differential Equations (PDEs).Linear triangular finite elements are employed for the solution of thisPDE system offering flexibility in the discretization of complex 2Ddomains. The numerical method developed has been applied to severaltest cases yielding accurate representations of the wave field atrelatively low computational cost and small execution times.