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Surface waves propagation in shallow water: A finite element model
Author(s) -
Do Carmo J. S. Antunes,
Santos F. J. Seabra,
Barthélemy E.
Publication year - 1993
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1650160602
Subject(s) - discretization , boussinesq approximation (buoyancy) , shallow water equations , finite element method , partial differential equation , mathematical analysis , wave propagation , mathematics , waves and shallow water , method of mean weighted residuals , plane (geometry) , free surface , plane wave , extended finite element method , finite difference method , finite difference , mixed finite element method , mechanics , geometry , physics , optics , convection , natural convection , galerkin method , rayleigh number , thermodynamics
A two‐dimensional (in‐plane) numerical model for surface waves propagation based on the non‐linear dispersive wave approach described by Boussinesq‐type equations, which provide an attractive theory for predicting the depth‐averaged velocity field resulting from that wave‐type propagation in shallow water, is presented. The numerical solution of the corresponding partial differential equations by finite‐difference methods has been the subject of several scientific works. In the present work we propose a new approach to the problem: the spatial discretization of the system composed by the Boussinesq equations is made by a finite element method, making use of the weighted residual technique for the solution approach within each element. The model is validated by comparing numerical results with theoretical solutions and with results obtained experimentally.