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

• Type: Article in International Scientific Journal
• Date: 2009

Authors

Paulo Avilez-Valente (Author) FEUP; Fernando J. Seabra-Santos (Author) Other

Journal

Title: International Journal for Numerical Methods in Fluids

Vol. 59 No. 9

Pages: 969-1010

ISSN: 0271-2091

Publisher: Wiley-Blackwell

Indexing

ISI Web of Knowledge - 8 Citations

ISI Web of Science

Scopus - 11 Citations

INSPEC

COMPENDEX

Scientific classification

FOS: Engineering and technology > Electrical engineering, Electronic engineering, Information engineering

CORDIS: Physical sciences > Mathematics

Other information

Authenticus ID: 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.

Language: English

Type (Professor's evaluation): Scientific