Convergence de schémas volumes finis pour des problèmes de convection diffusion non linéaires

Abstract : The main subject of this report is the mathematical study of finite volume schemes for problems of two phase flow in porous media. These problems are often called convection dominated problems''. The first part concerns the numerical approximation of degenerate hyperbolic parabolic equations by a finite volume method. In Chapter 1, Chapter 2 and Chapter 3, We study the convergence of the scheme and in Chapter 4, we present numerical results. The second part of this report concerns the study of two numerical methods for a simplified model of two phase flow in porous media. For the first scheme also called schéma des mathématiciens'', we transform the coupled system in an equivalent system of two equations, a parabolic equation on the saturation and an elliptic equation on the pressure coupled by the convective term. The second scheme is a phase by phase upwinding finite volume scheme which is used in petroleum industry. We study the convergence of the schemes and we make a comparison between the two methods by using numerical experiments.
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https://tel.archives-ouvertes.fr/tel-00002553
Contributor : Anthony Michel <>
Submitted on : Thursday, March 13, 2003 - 3:58:15 PM
Last modification on : Wednesday, October 10, 2018 - 1:25:44 AM
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• HAL Id : tel-00002553, version 1

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Anthony Michel. Convergence de schémas volumes finis pour des problèmes de convection diffusion non linéaires. Mathématiques [math]. Université de Provence - Aix-Marseille I, 2001. Français. ⟨tel-00002553⟩

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