A finite element method for 1D and 2D shallow water

Abstract

The finite dement method has been used to develop two numerical tools for a Boussinesq shallow water equation, 2DH and 1DH. In both models, an automatic unstructured mesh generator has been employed to assure the convergence and stability of the numerical solution through the assumption of a Courant number close to one in the whole domain. Partially reflecting- absorbing boundary conditions has been carried out to model the open seaward contour and other contour types. In the 1DH numerical model has been carried out the finite element version of the Deigaard et al break wave model and it is valid for spilling breaks. A new intuitive and numerical break rule has been developed to simulate the plunging break mode. The results obtained with both models had been compared with the equivalent results of others numerical methods and experimental data for the same problem type such as pure diffraction and step varying bottoms.