Weighted Interior Penalty discretization of fully nonlinear and weakly dispersive free surface shallow water flows - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Journal of Computational Physics Année : 2018

Weighted Interior Penalty discretization of fully nonlinear and weakly dispersive free surface shallow water flows

Résumé

In this paper, we further investigate the use of a fully discontinuous Finite Element discrete formulation for the study of shallow water free surface flows in the fully nonlinear and weakly dis-persive flow regime. We consider a decoupling strategy in which we approximate the solutions of the classical shallow water equations supplemented with a source term globally accounting for the non-hydrostatic effects. This source term can be computed through the resolution of elliptic second-order linear sub-problems, which only involve second order partial derivatives in space. We then introduce an associated Symmetric Weighted Internal Penalty discrete bilinear form, allowing to deal with the discontinuous nature of the elliptic problem's coefficients in a stable and consistant way. Similar discrete formulations are also introduced for several recent optimized fully nonlinear and weakly dis-persive models. These formulations are validated again several benchmarks involving h-convergence, p-convergence and comparisons with experimental data, showing optimal convergence properties.
Fichier principal
Vignette du fichier
swip_dg_Green_Naghdi.pdf (983.49 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01566446 , version 1 (21-07-2017)
hal-01566446 , version 2 (09-11-2017)

Identifiants

Citer

Daniele Di Pietro, Fabien A Marche. Weighted Interior Penalty discretization of fully nonlinear and weakly dispersive free surface shallow water flows. Journal of Computational Physics, 2018, 355, pp.285-309. ⟨10.1016/j.jcp.2017.11.009⟩. ⟨hal-01566446v2⟩
345 Consultations
331 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More