Cemracs project: A composite finite volume scheme for the Euler equations with source term on unstructured meshes
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...
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| Published in: | ESAIM. Proceedings and surveys Vol. 77; pp. 123 - 144 |
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| Main Authors: | , , , , , |
| Format: | Journal Article |
| Language: | English |
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EDP Sciences
2024
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| Abstract | 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 We combine this extension with the ideas developed by Alouges, Ghidaglia and Tajchman in an unpublished work [2] – focused mainly on the 1D case – and we propose two attempts at discretizing the source term of the Euler equations in order to better preserve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. |
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| AbstractList | 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 We combine this extension with the ideas developed by Alouges, Ghidaglia and Tajchman in an unpublished work [2] – focused mainly on the 1D case – and we propose two attempts at discretizing the source term of the Euler equations in order to better preserve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. |
| Author | Hoch, Philippe Boujoudar, Mohammed Paragot, Paul Lasuen, Clément Le Hénaff, Yoan Franck, Emmanuel |
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| ContentType | Journal Article |
| Copyright | 2024. This work is licensed under https://creativecommons.org/licenses/by/4.0 (the “License”). Notwithstanding the ProQuest Terms and conditions, you may use this content in accordance with the terms of the License. |
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| DOI | 10.1051/proc/202477123 |
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| Editor | Franck, Emmanuel Mehrenberger, Michel Maury, Bertrand Latu, Guillaume Hivert, Hélène Navoret, Laurent Leman, Hélène |
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| Title | Cemracs project: A composite finite volume scheme for the Euler equations with source term on unstructured meshes |
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