Non-dispersive conservative regularisation of nonlinear shallow water and isothermal Euler equations
Résumé
A new regularisation of the shallow water (and isentropic Euler) equations is proposed. The regularised equations are non-dissipative, non-dispersive and possess a variational structure. Thus, the mass, the momentum and the energy are conserved. Hence, for instance, regularised hydraulic jumps are smooth and non-oscillatory. Another particularly interesting feature of this regularisation is that smoothed `shocks' propagates at exactly the same speed as the original discontinuous ones. The performance of the new model is illustrated numerically on some dam-break test cases, which are classical in the hyperbolic realm.
Domaines
Mécanique des fluides [physics.class-ph] Physique Atmosphérique et Océanique [physics.ao-ph] Dynamique des Fluides [physics.flu-dyn] Physique Numérique [physics.comp-ph] Systèmes Solubles et Intégrables [nlin.SI] Formation de Structures et Solitons [nlin.PS] Equations aux dérivées partielles [math.AP] Analyse classique [math.CA] Analyse numérique [math.NA]| Origine | Fichiers produits par l'(les) auteur(s) |
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