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# Modélisation et simulation numérique de la vitesse de propagation d'une piqûre de corrosion

Abstract : Steel corrosion plays a central role in different technological fields. The prediction of long term corrosion behavior of stainless steel is needed to ensure that its physical integrity will not be affected during its expected life time. In this study, we focus on pitting corrosion of steels in contact with a solution of sodium chloride (NaCl). The scientific objectives of this thesis are related to the physico-chemical modeling of pitting corrosion, by means of mathematical analysis and numerical simulations. First, we studied a simple case of a corrosion phenomenon which describes a pure iron dissolution in sodium chloride. We proved that under rather general hypotheses on the initial data, the solution of this iron dissolution model converges to a self-similar profile as t→+∞. This result is proved for an equivalent one-dimensional formulation of the physical model known as a one-phase Stefan problem. In order to prove the convergence result, we applied a comparison principle together with suitable upper and lower solutions. Then, we gradually derived a more complicated anodic-dissolution model in one-space dimension. It is a strongly coupled mathematical model of partial differential equations which represents the propagation of a pit in pure iron steel. It involves an anodic reaction of dissolution, the transport of aqueous chemical species by diffusion and migration and the moving of the iron interface. Then, we proposed an efficient numerical solution method for this system. To that purpose, we have developed an implicit in time numerical scheme based on the ALE method together with a Newton procedure. Through many simulations, we have examined the behavior of our system with respect to the variations of certain physical parameters. In the last step, we have integrated the hydrolysis reactions of iron cations in the system. This final model developed in this thesis is a diffusion-migration-reaction model with a moving interface for five-species. Finally, we derived a reduced system for our diffusion-migration model. Then, by means of two approximations, we analytically found an approximating solution for this reduced system, which turns out to be a very good approximation of the solution of our strongly coupled diffusion-migration model.The major advantage of developing such a nearly exact solution is to allow the validation of our numerical scheme.
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Submitted on : Tuesday, November 30, 2021 - 10:34:07 AM
Last modification on : Wednesday, April 20, 2022 - 3:44:13 AM
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Meriem Bouguezzi. Modélisation et simulation numérique de la vitesse de propagation d'une piqûre de corrosion. Equations aux dérivées partielles [math.AP]. Université Paris-Saclay, 2021. Français. ⟨NNT : 2021UPASM027⟩. ⟨tel-03456588⟩

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