A CONTINUOUS FINITE ELEMENT APPROACH TO THE WELL-BALANCED SHALLOW WATER EQUATIONS

Túlio Ligneul Santos¹; Alvaro Luiz Gayoso de Azeredo Coutinho¹

¹ Federal University of Rio de Janeiro

doi:10.20906/CPS/CILAMCE2017-0712

Resumo

It is presented a well-balanced two-dimensional single layer shallow water model which considers viscous, wind and Coriolis forces, as well as bed friction. It is outlined how each term can be defined and the whole model is brought out as a generalized convection-diffusion equation. The inherent non-linear system is solved by a continuous finite element approach. Also, two SUPG and three shock capturing operators are applied and compared. Time integration is performed with a predictor-multicorretor algorithm. Additionally, mesh refinement/coarsening and time stepping are employed in an adaptive fashion. Finally, numerical results are presented for some test problems and comparisons with analytical or literature available solutions are made.

Palavras-chave: Well-balanced equations; Shallow water model; Finite element