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Couplage d'un schéma aux résidus distribués à l'analyse isogéométrique : méthode numérique et outils de génération et adaptation de maillage

Algiane Froehly 1
1 BACCHUS - Parallel tools for Numerical Algorithms and Resolution of essentially Hyperbolic problems
Inria Bordeaux - Sud-Ouest, UB - Université de Bordeaux, CNRS - Centre National de la Recherche Scientifique : UMR5800
Abstract : During high order simulations, the approximation error may be dominated by the errors linked to the sub-parametric discretization used for the geometry representation. Many works propose to use an isogeometric analysis approach to better represent the geometry and hence solve this problem. In this work, we will present the coupling between the limited stabilized Lax-Friedrichs residual distributed scheme and the isogeometric analysis. Especially, we will build a family of basis functions defined on both triangular and quadrangular elements and allowing the exact representation of conics : the rational Bernstein basis functions. We will then focus in how to generate accurate meshes for isogeometric analysis. Our idea is to create a curved mesh from a classical piecewise-linear mesh of the geometry. We obtain a conforming unstructured mesh which ensures the continuity of the basis functions over the entire mesh. Last, we will detail the curved mesh adaptation methods developed : the order elevation and the isotropic mesh refinement. Of course, the adaptation processes preserve the exact geometry of the initial curved mesh.
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https://tel.archives-ouvertes.fr/tel-00765918
Contributor : Algiane Froehly <>
Submitted on : Monday, December 17, 2012 - 10:58:41 AM
Last modification on : Thursday, February 11, 2021 - 2:56:43 PM
Long-term archiving on: : Sunday, December 18, 2016 - 3:02:09 AM

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  • HAL Id : tel-00765918, version 1

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Algiane Froehly. Couplage d'un schéma aux résidus distribués à l'analyse isogéométrique : méthode numérique et outils de génération et adaptation de maillage. Mécanique des fluides [physics.class-ph]. Université Sciences et Technologies - Bordeaux I, 2012. Français. ⟨NNT : 2012BOR14563⟩. ⟨tel-00765918⟩

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