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| HAL: hal-00697727, version 1 |
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| XXXVI Latin American Conference on Informatics (CLEI 2010), Asunción : Paraguay (2010) |
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| New Resolution Strategies for Multi-scale Reaction Waves: Optimal Time Operator Splitting and Space Adaptive Multiresolution |
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Max Duarte 1Marc Massot 1 |
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| (2011-04) |
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| We tackle the numerical simulation of reaction-diffusion equations modeling multi-scale reaction waves. This type of problems induces peculiar difficulties and potentially large stiffness which stem from the broad spectrum of temporal scales in the nonlinear chemical source term as well as from the presence of large spatial gradients in the reaction fronts, spatially very localized. In this paper, we introduce a new resolution strategy based on time operator splitting and space adaptive multiresolution in the context of very localized and stiff reaction fronts. Based on recent theoretical studies of numerical analysis, such a strategy leads to a splitting time step which is not restricted neither by the fastest scales in the source term nor by restrictive diffusive step stability limits, but only by the physics of the phenomenon. We thus aim at solving accurately complete models including all time and space scales of the phenomenon, considering large simulation domains with conventional computing resources. The efficiency is evaluated through the numerical simulation of configurations which were so far out of reach of standard methods in the field of nonlinear chemical dynamics for 2D spiral waves and 3D scroll waves as an illustration. Future extensions of the proposed strategy are finally discussed. |
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| 1: | Laboratoire d'Énergétique Moléculaire et Macroscopique, Combustion (EM2C) |
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CNRS : UPR288 – Ecole Centrale Paris |
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| 2: | Laboratoire Jean Alexandre Dieudonné (JAD) |
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CNRS : UMR6621 – Université Nice Sophia Antipolis [UNS] |
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| 3: | Laboratoire d'Informatique pour la Mécanique et les Sciences de l'Ingénieur [Orsay] (LIMSI) |
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CNRS : UPR3251 – Université Pierre et Marie Curie [UPMC] - Paris VI – Université Paris XI - Paris Sud |
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| 4: | Institut Camille Jordan (ICJ) |
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CNRS : UMR5208 – Université Claude Bernard - Lyon I – Ecole Centrale de Lyon – Institut National des Sciences Appliquées (INSA) - Lyon |
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| 5: | NUMED (ENS Lyon / UCB Lyon / Inria Grenoble Rhône-Alpes) |
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Université Claude Bernard - Lyon I – INRIA – École Normale Supérieure - Lyon – CNRS : UMR5669 – Unité de Mathématiques Pures et Appliquées |
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| Subject | : | Computer Science/Data Structures and Algorithms Mathematics/Analysis of PDEs Engineering Sciences/Reactive fluid environment |
| hal-00697727, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00697727 | |
| oai:hal.archives-ouvertes.fr:hal-00697727 | |
| From: Max Duarte | |
| Submitted on: Wednesday, 16 May 2012 02:12:40 | |
| Updated on: Tuesday, 22 January 2013 16:48:20 | |
