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Couplage de méthodes numériques pour les lois de conservation. Application au cas de l'injection.

Abstract : This thesis deals with numerical methods for solving systems of conservative partial differential equations. When the flow is a complex one, we need many physical models without known boundaries. We can use different numerical schemes for different domains, with some overlap of the domains. We present here a new and efficient algorithm to compute the solution on these overlaps. It needs a conservative projection of the numerical solution from one scheme to the other one. There is no artificial condition on the boundary of the coupling domain. To do so we use a regularization of the Heaviside function on this domain. Thus the whole algorithm is conservative and is adapted for Conservative Laws. The mathematical analysis has been done for scalar hyperbolic equations in any dimension. It is based on the convergence of Finite Volume Methods. We prove the convergence of the measure solution with Diperna?s theorem, and then we give an error estimation in order of h¼. We did so by using a new estimation of the type weak H1 to deal with the new coupling error terms. A lot of numerical applications in Fluid Mechanics such as shock tube show that the method is stable and conservative. We use also the meshless method called Smooth Particle Hydrodynamics, in its renormalized form, to compute the birth of a jet by coupling a Finite Volumes with a Particle Method. It shows the stiffness of the algorithm and its efficiency with complex flows. This study was done in collaboration with the team of Pr. D. Kröner from the Institute Applied Mathematics of Frieburg University of Germany.
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Contributor : Martial Mancip <>
Submitted on : Thursday, April 3, 2003 - 12:42:24 PM
Last modification on : Friday, January 10, 2020 - 9:08:06 PM
Long-term archiving on: : Wednesday, November 23, 2016 - 3:34:09 PM


  • HAL Id : tel-00001960, version 2


Martial Mancip. Couplage de méthodes numériques pour les lois de conservation. Application au cas de l'injection.. Mathématiques [math]. INSA de Toulouse, 2001. Français. ⟨tel-00001960v2⟩



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