Structure preservation in high-order hybrid discretisations of advection-diffusion equations: linear and nonlinear approaches - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2023

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

Résumé

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.
Fichier principal
Vignette du fichier
sphho.pdf (727.37 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-04250412 , version 1 (19-10-2023)
hal-04250412 , version 2 (12-01-2024)

Identifiants

Citer

Simon Lemaire, Julien Moatti. Structure preservation in high-order hybrid discretisations of advection-diffusion equations: linear and nonlinear approaches. 2023. ⟨hal-04250412v1⟩
208 Consultations
109 Téléchargements

Altmetric

Partager

More