Approche mixte interface nette/diffuse pour les problèmes d'intrusion saline en sous-sol : Modélisation, analyse mathématique et illustrations numériques

Abstract : The context of the subject is the management of aquifers, especially the control of their operations and their possible pollution. A critical case is the saltwater intrusion problem in costal aquifers. The goal is to obtain efficient and accurate models to simulate the displacement of fresh and salt water fronts for the optimal exploitation of groundwater. More generally, the work applies for miscible and stratified displacements in slightly deformable porous media. In this work we propose an original model mixing abrupt interfaces/diffuse interfaces approaches. The advantage is to adopt the (numerical) simplicity of a sharp interface approach, and to take into account the existence of diffuse interfaces. The model is based on the conservation laws written in the saltwater zone and in the freshwater zone, these two free boundary problems being coupled through an intermediate phase field model. An upscaling procedure let us reduce the problem to a two-dimensional setting. The theoretical analysis of the new model is performed. We also present numerical simulations comparing our 2D model with the classical 3D model for miscible displacement in a confined aquifer. Physical predictions from our new model are also given for an unconfined setting.
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Submitted on : Monday, February 22, 2016 - 10:24:11 PM
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Moussa Mory Diédhiou. Approche mixte interface nette/diffuse pour les problèmes d'intrusion saline en sous-sol : Modélisation, analyse mathématique et illustrations numériques. Equations aux dérivées partielles [math.AP]. Université de La Rochelle; Laboratoire de Mathématiques, Images et Applications de l'Université de La Rochelle, 2015. Français. ⟨tel-01277655⟩

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