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| HAL : hal-00544506, version 3 |
| DOI : 10.1016/j.apm.2012.01.031 |
| Fiche détaillée |  Récupérer au format |
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| Applied Mathematical Modelling 36, 12 (2012) 5936-5951 |
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| Versions disponibles : | v1 (08-12-2010) | v2 (23-02-2011) | v3 (13-01-2012) |
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| Numerical resolution of a mono-disperse model of bubble growth in magmas |
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| Louis Forestier-Coste 1Simona Mancini 1 |
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| (2012) |
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| Growth of gas bubbles in magmas may be modeled by a system of differential equations that account for the evolution of bubble radius and internal pressure and that are coupled with an advection-diffusion equation defining the gas flux going from magma to bubble. This system of equations is characterized by two relaxation parameters linked to the viscosity of the magma and to the diffusivity of the dissolved gas, respectively. Here, we propose a numerical scheme preserving, by construction, the total mass of water of the system. We also study the asymptotic behavior of the system of equations by letting the relaxation parameters vary from 0 to infinity, and show the numerical convergence of the solutions obtained by means of the general numerical scheme to the simplified asymptotic limits. Finally, we validate and compare our numerical results with those obtained in experiments. |
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| 1 : | Mathématiques - Analyse, Probabilités, Modélisation - Orléans (MAPMO) |
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Université d'Orléans – CNRS : UMR7349 |
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| 2 : | Institut des Sciences de la Terre d'Orléans (ISTO) |
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Université d'Orléans – CNRS : UMR6113 – Université François Rabelais - Tours – INSU |
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| Domaine | : | Mathématiques/Analyse numérique Planète et Univers/Sciences de la Terre/Volcanologie Sciences de l'environnement/Milieux et Changements globaux |
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| Coupled ode system and diffusion equation Mass preserving scheme Bubble growth |
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| Liste des fichiers attachés à ce document : | |||||
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| hal-00544506, version 3 | |
| http://hal.archives-ouvertes.fr/hal-00544506 | |
| oai:hal.archives-ouvertes.fr:hal-00544506 | |
| Contributeur : Simona Mancini | |
| Soumis le : Vendredi 13 Janvier 2012, 12:23:35 | |
| Dernière modification le : Jeudi 9 Août 2012, 15:26:46 | |
