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- ItemNumerical methods for the simulation of a corrosion model in a nuclear waste deep repository(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Batallion, Christian; Bouchon, Francois; Chainais-Hillairet, Claire; Fuhrmann, Jürgen; Hoarau, Emma; Touzani, RachidLiteraturverz. In this paper, we design numerical methods for a PDE system arising in corrosion modelling. This system describes the evolution of a dense oxide layer. It is based on a drift-diffusion system and includes moving boundary equations. The choice of the numerical methods is justified by a stability analysis and by the study of their numerical performance. Finally, numerical experiments with real-life data shows the efficiency of the developed methods.
- ItemA numerical analysis focused comparison of several finite volume schemes for an unipolar degenerated drift-diffusion model(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2019) Cancès, Clément; Chainais-Hillairet, Claire; Fuhrmann, Jürgen; Gaudeul, BenoîtIn this paper, we consider an unipolar degenerated drift-diffusion system where the relation between the concentration of the charged species c and the chemical potential h is h(c) = log c/1-c. We design four different finite volume schemes based on four different formulations of the fluxes. We provide a stability analysis and existence results for the four schemes. The convergence proof with respect to the discretization parameters is established for two of them. Numerical experiments illustrate the behaviour of the different schemes.