High order numerical schemes for transport equations on bounded domains

Benjamin Boutin (1) , Thi Hoai Thuong Nguyen (1) , Abraham Sylla (2) , Sébastien Tran-Tien (3) , Jean-François Coulombel (4)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 IDP - Institut Denis Poisson
3 ENS de Lyon - École normale supérieure de Lyon
4 IMT - Institut de Mathématiques de Toulouse UMR5219

This article is an account of the NABUCO project achieved during the summer camp CEMRACS 2019 devoted to geophysical fluids and gravity flows. The goal is to construct finite difference approximations of the transport equation with nonzero incoming boundary data that achieve the best possible convergence rate in the maximum norm. We construct, implement and analyze the so-called inverse Lax-Wendroff procedure at the incoming boundary. Optimal convergence rates are obtained by combining sharp stability estimates for extrapolation boundary conditions with numerical boundary layer expansions. We illustrate the results with the Lax-Wendroff and O3 schemes.

Domaines: Analyse numérique [math.NA]

Benjamin Boutin, Thi Hoai Thuong Nguyen, Abraham Sylla, Sébastien Tran-Tien, Jean-François Coulombel. High order numerical schemes for transport equations on bounded domains. ESAIM: Proceedings and Surveys, 2021, 70, pp.84-106. ⟨hal-02395068⟩