Finite volume schemes and Lax–Wendroff consistency
We present a (partial) historical summary of the mathematical analysis of finite difference and finite volume methods, paying special attention to the Lax–Richtmyer and Lax–Wendroff theorems. We then state a Lax–Wendroff consistency result for convection operators on staggered grids (often used in f...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2022-10-01
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| Series: | Comptes Rendus. Mécanique |
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| Online Access: | https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.132/ |
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| author | Eymard, Robert Gallouët, Thierry Herbin, Raphaele Latché, Jean-Claude |
| author_facet | Eymard, Robert Gallouët, Thierry Herbin, Raphaele Latché, Jean-Claude |
| author_sort | Eymard, Robert |
| collection | DOAJ |
| description | We present a (partial) historical summary of the mathematical analysis of finite difference and finite volume methods, paying special attention to the Lax–Richtmyer and Lax–Wendroff theorems. We then state a Lax–Wendroff consistency result for convection operators on staggered grids (often used in fluid flow simulations), which illustrates a recent generalization of the flux consistency notion designed to cope with general discrete functions. |
| format | Article |
| id | doaj-art-153d774364fc4063b4b60134348f443c |
| institution | Kabale University |
| issn | 1873-7234 |
| language | English |
| publishDate | 2022-10-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mécanique |
| spelling | doaj-art-153d774364fc4063b4b60134348f443c2025-02-07T13:45:36ZengAcadémie des sciencesComptes Rendus. Mécanique1873-72342022-10-01350S111712910.5802/crmeca.13210.5802/crmeca.132Finite volume schemes and Lax–Wendroff consistencyEymard, Robert0https://orcid.org/0000-0002-6035-0104Gallouët, Thierry1Herbin, Raphaele2https://orcid.org/0000-0003-0937-1900Latché, Jean-Claude3LAMA, Université Gustave Eiffel, Marne la Vallée, FranceI2M UMR 7373 CNRS & Aix-Marseille Université, FranceI2M UMR 7373 CNRS & Aix-Marseille Université, FranceIRSN Cadarache, FranceWe present a (partial) historical summary of the mathematical analysis of finite difference and finite volume methods, paying special attention to the Lax–Richtmyer and Lax–Wendroff theorems. We then state a Lax–Wendroff consistency result for convection operators on staggered grids (often used in fluid flow simulations), which illustrates a recent generalization of the flux consistency notion designed to cope with general discrete functions.https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.132/Finite differenceLax–Wendroff consistencyStabilityCompactnessConvergence |
| spellingShingle | Eymard, Robert Gallouët, Thierry Herbin, Raphaele Latché, Jean-Claude Finite volume schemes and Lax–Wendroff consistency Comptes Rendus. Mécanique Finite difference Lax–Wendroff consistency Stability Compactness Convergence |
| title | Finite volume schemes and Lax–Wendroff consistency |
| title_full | Finite volume schemes and Lax–Wendroff consistency |
| title_fullStr | Finite volume schemes and Lax–Wendroff consistency |
| title_full_unstemmed | Finite volume schemes and Lax–Wendroff consistency |
| title_short | Finite volume schemes and Lax–Wendroff consistency |
| title_sort | finite volume schemes and lax wendroff consistency |
| topic | Finite difference Lax–Wendroff consistency Stability Compactness Convergence |
| url | https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.132/ |
| work_keys_str_mv | AT eymardrobert finitevolumeschemesandlaxwendroffconsistency AT gallouetthierry finitevolumeschemesandlaxwendroffconsistency AT herbinraphaele finitevolumeschemesandlaxwendroffconsistency AT latchejeanclaude finitevolumeschemesandlaxwendroffconsistency |