The conduit equation : hyperbolic approximation and generalized Riemann problem - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2024

The conduit equation : hyperbolic approximation and generalized Riemann problem

Résumé

The conduit equation is a dispersive non-integrable scalar equation modeling the flow of a low-viscous buoyant fluid embedded in a highly viscous fluid matrix. This equation can be written in a special form reminiscent of the famous Godunov form proposed in 1961 for the Euler equations of compressible fluids. We propose a hyperbolic approximation of the conduit equation by retaining the Godunov-type structure. The comparison of solutions to the conduit equation and those to the approximate hyperbolic system is performed : the wave fission of a large initial perturbation of a rectangular or of gaussian form. The results are in good agreement. New generalized solutions to the conduit equation are discovered composed of a finite set of waves of the same period and linked with a constant solution by generalized Rankine-Hugoniot relations. Such multi-hump structures interact which each other almost as solitary waves : they collide, merge and reconstruct after the interaction. This partly indicates the stability of such multi-hump solutions under small perturbations. Both the exact and approximate hyperbolic system describe such an interaction with good accuracy.
Fichier principal
Vignette du fichier
Conduit_equation_SG_BN_KMS.pdf (6.94 Mo) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-04377682 , version 1 (07-01-2024)

Identifiants

  • HAL Id : hal-04377682 , version 1

Citer

Sergey Gavrilyuk, Boniface Nkonga, Keh-Ming Shyue. The conduit equation : hyperbolic approximation and generalized Riemann problem. 2024. ⟨hal-04377682⟩
25 Consultations
22 Téléchargements

Partager

Gmail Facebook X LinkedIn More