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Méthodes en maillages mobiles auto-adaptatifs pour des systèmes hyperboliques en une et deux dimensions d'espace

Abstract : the present work is a contribution to the development of dynamic meshes methods for solving partial differential equations in fluid mechanics. More precisely, we devise a finite-volume scheme, on non-structured dynamic meshes with a potentially variable topology, based on the Godunov' method. the node addition and substraction are based on a generalization of dynamic meshes methods to inflating or fading volumes. First, we study this scheme for one-dimensional hyperbolic equations. We prove for linear advection that it meets the classical properties of finite-volume methods (maximum principle, decreasing of the global variation, L² stability) under CFL-type constraints. To avoid these restrictions, the temporal integratioin is realized bay an implicite formulation. In the second part of this work, we extend our method to the two space-dimensionnal case. the flow is described by a mathematical momdel given by the Euler equations. Furthermore, we implement this scheme in a way that enables meshes to adapt easily and automatically. For this porpose, we introduce a spring distribution between the mesh nodes, which can be either attractive or repulsive. Node moves result from the achievment of the equilibrium state. Refinement and unrefinement are based on a local criteria, such as the gradient. Finally, we focus on the numerical simulation of fluid-structure interaction phenomena, in the aim of validating our works. the concrete application handled is a compressible flow around in-flight aircraft wing profile.
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https://pastel.archives-ouvertes.fr/pastel-00001053
Contributor : Ecole Des Ponts Paristech <>
Submitted on : Friday, September 10, 2010 - 4:41:11 PM
Last modification on : Friday, September 24, 2010 - 5:41:53 PM
Long-term archiving on: : Saturday, December 11, 2010 - 2:30:10 AM

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  • HAL Id : pastel-00001053, version 1

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Maud Poret. Méthodes en maillages mobiles auto-adaptatifs pour des systèmes hyperboliques en une et deux dimensions d'espace. Mathématiques [math]. Ecole des Ponts ParisTech, 2005. Français. ⟨NNT : 2005ENPC0001⟩. ⟨pastel-00001053⟩

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