Identification de paramètres hydrogéologiques dans un milieu poreux

Abstract : We identify simultaneously storage and hydraulic transmissivity coefficients in groundwater flow governed by a linear parabolic equation. Both parameters are assumed to be functions piecewise constant in space. The unknowns are the coefficient values as well as the geometry of the zones where these coefficients are constant. This problem is formulated as minimizing a least-square function calculating the difference between measurements and the corresponding quantities computed with the current parameters values. The main point of this work is to construct an adaptative parameterization technique guided by refinement indicators. Using refinement indicators, we build the parameterization iteratively, going from a one zone parametrization to a parametrization with $m$ zones where $m$ is an optimal value to identify. We distinguish the cases where the two parameters have the same parameterization and different parameterizations.\\ To improve the resolution of the inverse problem, we incorporate a posteriori error estimations.
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Mohamed Hédi Riahi. Identification de paramètres hydrogéologiques dans un milieu poreux. Physique mathématique [math-ph]. Université Pierre et Marie Curie - Paris VI; École nationale d'ingénieurs de Tunis (Tunisie), 2016. Français. ⟨NNT : 2016PA066741⟩. ⟨tel-01810506⟩

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