A high-order Petrov-Galerkin finite element method for the classical Boussinesq wave model

• Tipo: Artigo em Revista Científica Internacional
• Data: 2009

Autores

Paulo Avilez-Valente (Autor) FEUP; Fernando J. Seabra-Santos (Autor) Outra

Revista

Título: International Journal for Numerical Methods in Fluids

Vol. 59 Nº 9

Páginas: 969-1010

ISSN: 0271-2091

Editora: Wiley-Blackwell

Indexação

ISI Web of Knowledge - 8 Citações

ISI Web of Science

Scopus - 11 Citações

INSPEC

COMPENDEX

Classificação Científica

FOS: Ciências da engenharia e tecnologias > Engenharia electrotécnica, electrónica e informática

CORDIS: Ciências Físicas > Matemática

Outras Informações

ID Authenticus: P-003-MEC

DOI: 10.1002/fld.1846

Abstract (EN): A high-order Petrov-Galerkin finite element scheme is presented to solve the one-dimensional depth-integrated classical Boussinesq equations for weakly non-linear and weakly dispersive waves. Finite elements are used both in the space and the time domains. The shape functions are bilinear in space-time, whereas the weighting functions are linear in space and quadratic in time, with C0-continuity. Dispersion correction and a highly selective dissipation mechanism are introduced through additional streamline upwind terms in the weighting functions. An implicit, conditionally stable, one-step predictor-corrector time integration scheme results. The accuracy and stability of the non-linear discrete equations are investigated by means of a local Taylor series expansion. A linear spectral analysis is used for the full characterization of the predictor-corrector inner iterations. Based on the order of the analytical terms of the Boussinesq model and on the order of the numerical discretization, it is concluded that the scheme is fourth-order accurate in terms of phase velocity. The dissipation term is third order only affecting the shortest wavelengths. A numerical convergence analysis showed a second-order convergence rate in terms of both element size and time step. Four numerical experiments are addressed and their results are compared with analytical solutions or experimental data available in the literature: the propagation of a solitary wave, the oscillation of a flat bottom closed basin, the oscillation of a non-flat bottom closed basin, and the propagation of a periodic wave over a submerged bar.

Idioma: Inglês

Tipo (Avaliação Docente): Científica