Cemracs project: A composite finite volume scheme for the Euler equations with source term on unstructured meshes
ESAIM. Proceedings, Tome 77 (2024), pp. 123-144
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In this work we focus on an adaptation of the method described in [1] in order to deal with source term in the 2D Euler equations. This method extends classical 1D solvers (such as VFFC, Roe, Rusanov) to the two-dimensional case on unstructured meshes. The resulting schemes are said to be composite as they can be written as a convex combination of a purely node-based scheme and a purely edge-based scheme. We combine this extension with the ideas developed by Alouges, Ghidaglia and Tajchman in an unpublished work [2] – focused mainly on the 1D case – and we propose two attempts at discretizing the source term of the Euler equations in order to better preserve stationary solutions. We compare these discretizations with the “usual” centered discretization on several numerical examples.
Affiliations des auteurs :
Mohammed Boujoudar 1 ; Emmanuel Franck 2 ; Philippe Hoch 3 ; Clément Lasuen 3 ; Yoan Le Hénaff 4 ; Paul Paragot 5
@article{EP_2024_77_a6,
author = {Mohammed Boujoudar and Emmanuel Franck and Philippe Hoch and Cl\'ement Lasuen and Yoan Le H\'enaff and Paul Paragot},
title = {Cemracs project: {A} composite finite volume scheme for the {Euler} equations with source term on unstructured meshes},
journal = {ESAIM. Proceedings},
pages = {123--144},
year = {2024},
volume = {77},
doi = {10.1051/proc/202477123},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/202477123/}
}
TY - JOUR AU - Mohammed Boujoudar AU - Emmanuel Franck AU - Philippe Hoch AU - Clément Lasuen AU - Yoan Le Hénaff AU - Paul Paragot TI - Cemracs project: A composite finite volume scheme for the Euler equations with source term on unstructured meshes JO - ESAIM. Proceedings PY - 2024 SP - 123 EP - 144 VL - 77 UR - http://geodesic.mathdoc.fr/articles/10.1051/proc/202477123/ DO - 10.1051/proc/202477123 LA - en ID - EP_2024_77_a6 ER -
%0 Journal Article %A Mohammed Boujoudar %A Emmanuel Franck %A Philippe Hoch %A Clément Lasuen %A Yoan Le Hénaff %A Paul Paragot %T Cemracs project: A composite finite volume scheme for the Euler equations with source term on unstructured meshes %J ESAIM. Proceedings %D 2024 %P 123-144 %V 77 %U http://geodesic.mathdoc.fr/articles/10.1051/proc/202477123/ %R 10.1051/proc/202477123 %G en %F EP_2024_77_a6
Mohammed Boujoudar; Emmanuel Franck; Philippe Hoch; Clément Lasuen; Yoan Le Hénaff; Paul Paragot. Cemracs project: A composite finite volume scheme for the Euler equations with source term on unstructured meshes. ESAIM. Proceedings, Tome 77 (2024), pp. 123-144. doi: 10.1051/proc/202477123
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