The Neumann boundary condition for the two-dimensional Lax-Wendroff scheme. II

La condition au bord de Neumann pour le schéma de Lax-Wendroff bi-dimensionnel. II

Antoine Benoit (1) , Jean-François Coulombel (2)

1 LMPA - Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville
2 IMT - Institut de Mathématiques de Toulouse UMR5219

We study the stability of a two-dimensional Lax-Wendroff scheme in a quarter-plane. Following our previous work, we aim here at adapting the energy method in order to study second order extrapolation boundary conditions. We first show on the one-dimensional problem why modifying the energy is a necessity in order to obtain stability estimates. We then study the two-dimensional case and propose a modified energy as well as second order extrapolation boundary and corner conditions in order to maintain second order accuracy and stability of the whole scheme, including near the corner.

Mots clés: transport equations; numerical schemes; domains with corners; boundary conditions; stability

Domaines: Analyse numérique [math.NA]

Antoine Benoit, Jean-François Coulombel. The Neumann boundary condition for the two-dimensional Lax-Wendroff scheme. II. 2024. ⟨hal-04593726⟩