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Pré-Publication, Document De Travail Année : 2024

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

Résumé

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.
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Dates et versions

hal-04593726 , version 1 (30-05-2024)

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  • HAL Id : hal-04593726 , version 1

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