Dans cet article, nous nous intéressons au -schéma centré en espace pour la résolution approchée de l’équation de transport à vitesse constante dans un segment en dimension 1, avec données de Neumann homogènes aux deux bords du domaine. De manière très surprenante, la solution numérique présente un caractère périodique, comme si la donnée initiale était périodique sur avec une période égale à deux fois ou quatre fois, suivant les cas, la longueur du segment. Nous énonçons précisément ce résultat et le démontrons, puis évoquons un comportement similaire dans le cas où les deux conditions de bord sont de type Dirichlet.
This paper is devoted to the space-centered -scheme for the transport equation with constant velocity on an interval, with homogeneous Neumann boundary data on each side. The numerical solution presents a weird behavior, as if the initial datum was periodical over , with a period that would be twice or four times (depending on the case) the length of the considered interval. We precisely formulate this statement and prove it. We also study a similar behavior in the case of Dirichlet boundary conditions.
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@article{AFST_2020_6_29_4_927_0,
author = {Inglard, M\'elanie and Lagouti\`ere, Fr\'ed\'eric and Rugh, Hans Henrik},
title = {Ghost solutions with centered schemes for one-dimensional transport equations with {Neumann} boundary conditions},
journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
pages = {927--950},
publisher = {Universit\'e Paul Sabatier, Toulouse},
volume = {Ser. 6, 29},
number = {4},
year = {2020},
doi = {10.5802/afst.1650},
language = {en},
url = {http://www.numdam.org/articles/10.5802/afst.1650/}
}
TY - JOUR AU - Inglard, Mélanie AU - Lagoutière, Frédéric AU - Rugh, Hans Henrik TI - Ghost solutions with centered schemes for one-dimensional transport equations with Neumann boundary conditions JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2020 SP - 927 EP - 950 VL - 29 IS - 4 PB - Université Paul Sabatier, Toulouse UR - http://www.numdam.org/articles/10.5802/afst.1650/ DO - 10.5802/afst.1650 LA - en ID - AFST_2020_6_29_4_927_0 ER -
%0 Journal Article %A Inglard, Mélanie %A Lagoutière, Frédéric %A Rugh, Hans Henrik %T Ghost solutions with centered schemes for one-dimensional transport equations with Neumann boundary conditions %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2020 %P 927-950 %V 29 %N 4 %I Université Paul Sabatier, Toulouse %U http://www.numdam.org/articles/10.5802/afst.1650/ %R 10.5802/afst.1650 %G en %F AFST_2020_6_29_4_927_0
Inglard, Mélanie; Lagoutière, Frédéric; Rugh, Hans Henrik. Ghost solutions with centered schemes for one-dimensional transport equations with Neumann boundary conditions. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 29 (2020) no. 4, pp. 927-950. doi : 10.5802/afst.1650. http://www.numdam.org/articles/10.5802/afst.1650/
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