Stability of finite difference schemes for the hyperbolic initial boundary value problem by winding number computations - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Annales de la Faculté des Sciences de Toulouse. Mathématiques. Année : 2023

Stability of finite difference schemes for the hyperbolic initial boundary value problem by winding number computations

Résumé

In this paper, we present a numerical strategy to check the strong stability (or GKS-stability) of one-step explicit finite difference schemes for the one-dimensional advection equation with an inflow boundary condition. The strong stability is studied using the Kreiss-Lopatinskii theory. We introduce a new tool, the intrinsic Kreiss-Lopatinskii determinant, which possesses the same regularity as the vector bundle of discrete stable solutions. By applying standard results of complex analysis to this determinant, we are able to relate the strong stability of numerical schemes to the computation of a winding number, which is robust and cheap. The study is illustrated with the O3 scheme and the fifth-order Lax-Wendroff (LW5) scheme together with a reconstruction procedure at the boundary.
Fichier principal
Vignette du fichier
BLBS23.pdf (939.79 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03970775 , version 1 (02-02-2023)

Licence

Paternité - Partage selon les Conditions Initiales

Identifiants

Citer

Benjamin Boutin, Pierre Le Barbenchon, Nicolas Seguin. Stability of finite difference schemes for the hyperbolic initial boundary value problem by winding number computations. Annales de la Faculté des Sciences de Toulouse. Mathématiques., In press. ⟨hal-03970775⟩
68 Consultations
31 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More