Publications internationales
Résumé: In this paper, we introduce a numerical study of the hydrocarbon system used for petroleum reservoir simulations. This system is a simplified model which describes a two-phase flow (oil and gas) with mass transfer in a porous medium, which leads to fluid compressibility. This kind of flow is modeled by a system of parabolic degenerated non-linear convection-diffusion equations. Under certain hypotheses, such as the validity of Darcy’s law, incompressibility of the porous medium, compressibility of the fluids, mass transfer between the oil and the gas, and negligible gravity, the global pressure formulation of Chavent (Mathematical Models and Finite Elements for Reservoir Simulation: Single Phase, Multiphase and Multicomponent Flows Through Porous Media, 1986) is formulated. This formulation allows the establishment of theoretical results on the existence and uniqueness of the solution (Gasmi and Nouri in Appl. Math. Sci. 7(42):2055-2064, 2013). Furthermore, different numerical schemes have been considered by many authors, among others we can refer the reader to (Chen in Finite element methods for the black oil model in petroleum reservoirs, 1994; Chen in Reservoir Simulation: Mathematical Techniques in Oil Recovery, 2007) and (Gagneux et al. in Rev. Mat. Univ. Complut. Madr. 2(1):119-148, 1989). Here we make use of a scheme based on the finite volume method and present numerical results for this simplified system.
Résumé: Our aim in this paper is to study the interaction between surface and subsurface flows. The model considered is a system coupling Navier–Stokes and Darcy equations.We make use of a discontinuous Galerkin finite element method for the discretisation of this problem. Then we develop a posteriori error analysis for the resulting discrete problem. Numerical experimentations confirm our analytical results.
Résumé: Image inpainting is a fundamental problem in image processing and has many applications [1] and [2], motivated by the recent tight frame based method on image restoration in either the image or the domain transformation. In this work, we present an inpainting model based on tixotrop non-Newtonian fluids for damaged wavelet coefficients. The advantage of this model is to make a benefit from the smoothing model and correct the lying out of the contours by putting them more clearly. Experimental results using our model show that better inpainting quality can be achieved with much less computing time.
Publications nationales
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