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Boussinesq-Peregrine water wave models and their numerical approximation

journal contribution
posted on 17.06.2020 by T Katsaounis, Dimitrios Mitsotakis, G Sadaka
© 2020 Elsevier Inc. In this paper we consider the numerical solution of Boussinesq-Peregrine type systems by the application of the Galerkin finite element method. The structure of the Boussinesq systems is explained and certain alternative nonlinear and dispersive terms are compared. A detailed study of the convergence properties of the standard Galerkin method, using various finite element spaces on unstructured triangular grids, is presented. Along with the study of the Peregrine system, a new Boussinesq system of BBM-BBM type is derived. The new system has the same structure in its momentum equation but differs slightly in the mass conservation equation compared to the Peregrine system. Further, the finite element method applied to the new system has better convergence properties, when used for its numerical approximation. Due to the lack of analytical formulas for solitary wave solutions for the systems under consideration, a Galerkin finite element method combined with the Petviashvili iteration is proposed for the numerical generation of accurate approximations of line solitary waves. Various numerical experiments related to the propagation of solitary and periodic waves over variable bottom topography and their interaction with the boundaries of the domains are presented. We conclude that both systems have similar accuracy when approximate long waves of small amplitude while the Galerkin finite element method is more efficient when applied to BBM-BBM type systems.

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Preferred citation

Katsaounis, T., Mitsotakis, D. & Sadaka, G. (2020). Boussinesq-Peregrine water wave models and their numerical approximation. Journal of Computational Physics, 417, 109579-109579. https://doi.org/10.1016/j.jcp.2020.109579

Journal title

Journal of Computational Physics

Volume

417

Publication date

15/09/2020

Pagination

109579-109579

Publisher

Elsevier BV

Publication status

Accepted

ISSN

0021-9991

eISSN

1090-2716

Article number

109579

Language

en

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