Geodesic
High order numerical schemes for transport equations on bounded domains
B. Boutin1 ; T.H.T. Nguyen1 ; A. Sylla2 ; S. Tran-Tien3 ; J.-F. Coulombel4
1IRMAR (UMR CNRS 6625), Université de Rennes, Campus de Beaulieu, 35042 Rennes Cedex, France
2Institut Denis Poisson CNRS UMR 7013, Université de Tours, Faculté des Sciences et Techniques, Bâtiment E2, Parc de Grandmont, 37200 Tours, France
3École Normale Supérieure de Lyon, 15 parvis René Descartes, BP 7000, 69342 Lyon Cedex 07, France
4Institut de Mathématiques de Toulouse; UMR5219, Université de Toulouse; CNRS, F-31062 Toulouse Cedex 9, France
ESAIM. Proceedings, Tome 70 (2021), pp. 84-106
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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.
DOI : 10.1051/proc/202107006

B. Boutin  1   ; T.H.T. Nguyen  1   ; A. Sylla  2   ; S. Tran-Tien  3   ; J.-F. Coulombel  4

1 IRMAR (UMR CNRS 6625), Université de Rennes, Campus de Beaulieu, 35042 Rennes Cedex, France
2 Institut Denis Poisson CNRS UMR 7013, Université de Tours, Faculté des Sciences et Techniques, Bâtiment E2, Parc de Grandmont, 37200 Tours, France
3 École Normale Supérieure de Lyon, 15 parvis René Descartes, BP 7000, 69342 Lyon Cedex 07, France
4 Institut de Mathématiques de Toulouse; UMR5219, Université de Toulouse; CNRS, F-31062 Toulouse Cedex 9, France 
@article{EP_2021_70_a6,
     author = {B. Boutin and T.H.T. Nguyen and A. Sylla and S. Tran-Tien and J.-F. Coulombel},
     title = {High order numerical schemes for transport equations on bounded domains},
     journal = {ESAIM. Proceedings},
     pages = {84--106},
     year = {2021},
     volume = {70},
     doi = {10.1051/proc/202107006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/202107006/}
}
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B. Boutin; T.H.T. Nguyen; A. Sylla; S. Tran-Tien; J.-F. Coulombel. High order numerical schemes for transport equations on bounded domains. ESAIM. Proceedings, Tome 70 (2021), pp. 84-106. doi: 10.1051/proc/202107006

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