On the stability of totally upwind schemes for the hyperbolic initial boundary value problem

Benjamin Boutin (1) , Pierre Le Barbenchon (1) , Nicolas Seguin (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

In this paper, we present a numerical strategy to check the strong stability (or GKS-stability) of one-step explicit totally upwind scheme in 1D with numerical boundary conditions. The underlying approximated continuous problem is a hyperbolic partial differential equation. Our approach is based on the Uniform Kreiss-Lopatinskii Condition, using linear algebra and complex analysis to count the number of zeros of the associated determinant. The study is illustrated with the Beam-Warming scheme together with the simplified inverse Lax-Wendroff procedure at the boundary.

Mots clés: boundary conditions; Kreiss-Lopatinskii determinant; GKS stability; finite-difference methods; inverse Lax-Wendroff

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Benjamin Boutin, Pierre Le Barbenchon, Nicolas Seguin. On the stability of totally upwind schemes for the hyperbolic initial boundary value problem. 2022. ⟨hal-03732720v1⟩