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Adaptive finite volume method based on a posteriori error estimators for solving two-phase flow in porous media

Abstract : In Chapter 2, this thesis presents Darcy's compositional model and some discrete Finite Volume methods used by IFPEn. This problem couples partial differential equations, stating the balance of mass, momentum, and energy, with algebraic constraints enforcing conservation of volume in the pores, partition of unity of molar fractions, and chemical equilibrium of each component. In order to respect the approach of IFPEN's applications, we base this formulation on the balance of mass and momentum for each component. The main difficulty of this model arises from the fact that the set of unknowns varies at each point of the domain. The problem is discretized by FV methods with flux upwinding in space and backward Euler implicit discretization in time. Chapter 3 is devoted to the simpler case of immiscible two-phase flow. The performance of the numerical computation depends strongly on the choice of discretizations and of algorithms for solving the nonlinear and linear systems. This part describes the implementation of resolution strategies based on a posteriori error indicators. Its main object is the optimization of stopping criteria of the nonlinear and linear solvers that preserve the quality of the numerical output, in particular the accuracy of the displacement of the interface between the two phases and the accuracy of the momentum in the domain. Chapter 4 is devoted to the elaboration of a prototype that solves the main features of Darcy's compositional model.
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Carole Widmer. Adaptive finite volume method based on a posteriori error estimators for solving two-phase flow in porous media. Numerical Analysis [math.NA]. Université Pierre et Marie Curie (Paris 6), 2013. English. ⟨tel-01900433⟩

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