Structure preservation in high-order hybrid discretisations of advection-diffusion equations: linear and nonlinear approaches

Lemaire, Simon; Moatti, Julien

Type de document :

Pré-publication ou Document de travail

URL permanente :

http://hdl.handle.net/20.500.12210/98375

Titre :

Structure preservation in high-order hybrid discretisations of advection-diffusion equations: linear and nonlinear approaches

Auteur(s) :

Lemaire, Simon [Auteur]

Reliable numerical approximations of dissipative systems [RAPSODI]
Moatti, Julien [Auteur]
Reliable numerical approximations of dissipative systems [RAPSODI]

Date de publication :

2023-10-19

Mot(s)-clé(s) en anglais :

High-order methods
Hybrid methods
Polytopal meshes
Structure-preserving schemes
Advection-diffusion equations
Long-time behaviour
Entropy methods

Discipline(s) HAL :

Mathématiques [math]/Analyse numérique [math.NA]

Résumé en anglais : [en]

We are interested in the high-order approximation of anisotropic advection-diffusion problems on general polytopal partitions. We study two hybrid schemes, both built upon the Hybrid High-Order technology. The first one ...
Lire la suite >We are interested in the high-order approximation of anisotropic advection-diffusion problems on general polytopal partitions. We study two hybrid schemes, both built upon the Hybrid High-Order technology. The first one hinges on exponential fitting and is linear, whereas the second is nonlinear. The existence of solutions is established for both schemes. Both schemes are also shown to enjoy a discrete entropy structure, ensuring that the discrete long-time behaviour of solutions mimics the PDE one. The nonlinear scheme is designed so as to enforce the positivity of discrete solutions. On the contrary, we display numerical evidence indicating that the linear scheme violates positivity, whatever the order. Finally, we verify numerically that the nonlinear scheme has optimal order of convergence, expected long-time behaviour, and that raising the polynomial degree results, also in the nonlinear case, in an efficiency gain.Lire moins >

Langue :

Anglais

Projet ANR :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :