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| HAL : hal-00653113, version 2 |
| DOI : 10.3934/dcdsb.2012.17.1383 |
| Fiche détaillée |  Récupérer au format |
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| Discrete and Continuous Dynamical Systems - Series B 17, 5 (2012) pp. 1383--1405, communicated by Roger Temam |
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| Versions disponibles : | v1 (18-12-2011) | v2 (20-02-2012) |
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| Convergence results for the vector penalty-projection and two-step artificial compressibility methods |
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Philippe Angot 1Pierre Fabrie 2 |
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| (07/2012) |
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| In this paper, we propose and analyze a new artificial compressibility splitting method which is issued from the recent vector penalty-projection method for the numerical solution of unsteady incompressible viscous flows introduced in [1], [2] and [3]. This method may be viewed as an hybrid two-step prediction-correction method combining an artificial compressibility method and an augmented Lagrangian method without inner iteration. The perturbed system can be viewed as a new approximation to the incompressible Navier-Stokes equations. In the main result, we establish the convergence of solutions to the weak solutions of the Navier-Stokes equations when the penalty parameter tends to zero. |
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| 1 : | Laboratoire d'Analyse, Topologie, Probabilités (LATP) |
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CNRS : UMR6632 – Université de Provence - Aix-Marseille I – Université Paul Cézanne - Aix-Marseille III |
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| 2 : | Institut de Mathématiques de Bordeaux (IMB) |
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CNRS : UMR5251 – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II |
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| Analyse Appliquée EDP |
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| Domaine | : | Mathématiques/Equations aux dérivées partielles Mathématiques/Analyse numérique Physique/Physique/Dynamique des Fluides Sciences de l'ingénieur/Mécanique/Mécanique des fluides Physique/Mécanique/Mécanique des fluides |
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| Artificial compressibility – Navier-Stokes equations – Vector penalty-projection – Pseudo-compressibility – Penalty method |
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| Liste des fichiers attachés à ce document : | |||||
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| hal-00653113, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00653113 | |
| oai:hal.archives-ouvertes.fr:hal-00653113 | |
| Contributeur : Philippe Angot | |
| Soumis le : Dimanche 19 Février 2012, 22:53:06 | |
| Dernière modification le : Dimanche 22 Avril 2012, 17:18:05 | |
