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Applied Mathematical Modelling 36, 12 (2012) 5936-5951
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Numerical resolution of a mono-disperse model of bubble growth in magmas
Louis Forestier-Coste 1, Simona Mancini 1, Alain Burgisser 2, François James 1

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.
1 :  Mathématiques - Analyse, Probabilités, Modélisation - Orléans (MAPMO)
Université d'Orléans – CNRS : UMR7349
2 :  Institut des Sciences de la Terre d'Orléans (ISTO)
CNRS : UMR6113 – INSU – Université d'Orléans – Université François Rabelais - Tours
Mathématiques/Analyse numérique

Planète et Univers/Sciences de la Terre/Volcanologie

Sciences de l'environnement/Milieux et Changements globaux
Coupled ode system and diffusion equation Mass preserving scheme Bubble growth
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