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| HAL: hal-00653113, version 2 |
| DOI: 10.3934/dcdsb.2012.17.1383 |
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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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| Available versions: | v1 (2011-12-18) | v2 (2012-02-20) |
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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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| (2012-07) |
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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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| Subject | : | Mathematics/Analysis of PDEs Mathematics/Numerical Analysis Physics/Physics/Fluid Dynamics Engineering Sciences/Mechanics/Fluids mechanics Physics/Mechanics/Mechanics of the fluids |
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| Artificial compressibility – Navier-Stokes equations – Vector penalty-projection – Pseudo-compressibility – Penalty method |
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| hal-00653113, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00653113 | |
| oai:hal.archives-ouvertes.fr:hal-00653113 | |
| From: Philippe Angot | |
| Submitted on: Sunday, 19 February 2012 22:53:06 | |
| Updated on: Sunday, 22 April 2012 17:18:05 | |
