Nouvelles approximations numériques pour les équations de Stokes et l'équation Level Set

Abstract : This thesis work is devoted to two research topics in Scientific Computing related to the numerical approximation of problems in fluids mechanics. The first topic relates to the numerical approximation of Stokes equations, modelling the "slow" flows of incompressible fluids. It considers the approximation by a method of projection for the discretization in time. The discretization in space uses the finite element method mixed hybrids making it possible to impose in an exact way the incompressibility constraint. This approach is original since it allows to couple the hybrid mixed finite elements with a method standard finite element while preserving the order of convergence of the two methods. The second topic relates to the development of finite volume schemes for the resolution of the Level Set equation. These equations intervene in an essential way in the resolution of problems of propagation of interfaces. ln this part, we developed a new second order method of MUSCL type to solve the hyperbolic system resulting from the Level Set equation. We illustrate these properties by numerical applications. In particular we looked at the case of the problem of the two half-planes for whieh our scheme gives an approximation for the gradient of the level set function. ln addition, the expected order of accuracy is reached for the standard $L_1$ and $L_{\infty}$ norms for regular functions. Finally, it should be noted that our method can easily be extended to Hamilton-Jacobi problems of first and second orders.
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Contributor : Malcom Djenno Ngomanda <>
Submitted on : Thursday, January 7, 2010 - 5:49:30 PM
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Djenno Ngomanda Malcom. Nouvelles approximations numériques pour les équations de Stokes et l'équation Level Set. Mathématiques [math]. Université Blaise Pascal - Clermont-Ferrand II, 2007. Français. ⟨tel-00445189⟩

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