General boundary conditions for a Boussinesq model with varying bathymetry
Résumé
This paper is devoted to the theoretical and numerical investigation of the initial boundary value problem for a system of equations used for the description of waves in coastal areas, namely, the Boussinesq-Abbott system in the presence of topography. We propose a procedure that allows one to handle very general linear or nonlinear boundary conditions. It consists in reducing the problem to a system of conservation laws with nonlocal fluxes and coupled to an ODE. This reformulation is used to propose two hybrid finite volumes/finite differences schemes of first and second order respectively. The possibility to use many kinds of boundary conditions is used to investigate numerically the asymptotic stability of the boundary conditions, which is an issue of practical relevance in coastal oceanography since asymptotically stable boundary conditions would allow one to reconstruct a wave field from the knowledge of the boundary data only, even if the initial data is not known.
Fichier principal
BNDconditions_BoussinesqAbbott.pdf (1.6 Mo)
Télécharger le fichier
gaussian_init_setup.pdf (62.34 Ko)
Télécharger le fichier
gaussian_over_bump_LF_MC_RR_T15_dx2p3em2.pdf (38.48 Ko)
Télécharger le fichier
incoming_soliton.pdf (17.07 Ko)
Télécharger le fichier
outgoing_soliton.pdf (16.55 Ko)
Télécharger le fichier
sine_over_bump_N768_NN1536_mu0p01_compare_1.pdf (83.69 Ko)
Télécharger le fichier
sine_over_bump_N768_NN1536_mu0p01_compare_4.pdf (59.38 Ko)
Télécharger le fichier
sine_over_bump_N768_NN1536_mu0p1_compare_1.pdf (120.54 Ko)
Télécharger le fichier
sine_over_bump_N768_NN1536_mu0p1_compare_3.pdf (72.11 Ko)
Télécharger le fichier
sine_over_bump_N768_NN1536_mu0p1_compare_4.pdf (273.79 Ko)
Télécharger le fichier
sine_over_bump_N768_NN1536_mu1_T0.pdf (49.49 Ko)
Télécharger le fichier
sine_over_bump_N768_NN1536_mu1_compare_1.pdf (75.03 Ko)
Télécharger le fichier
sine_over_bump_N768_NN1536_mu1_compare_3.pdf (43.99 Ko)
Télécharger le fichier
sine_over_bump_N768_NN1536_mu1_compare_4.pdf (209.33 Ko)
Télécharger le fichier
Origine | Fichiers produits par l'(les) auteur(s) |
---|---|
Licence |
Origine | Fichiers produits par l'(les) auteur(s) |
---|---|
Licence |