Adaptation de maillage anisotrope 3D multi-échelles et ciblée à une fonctionnelle pour la mécanique des fluides.
Application à la prédiction haute-fidélité du bang sonique.

Abstract : Hessian based unstructured mesh adaptation has already proved its efficiency to improve the ratio between solution accuracy and the number of degrees of freedom. However, when dealing with flows with shocks, several problematics occur : (i) a loss of convergence order generally due to the presence of steep gradients or genuine discontinuities in the flow, even if a provably spatially high order method is employed, (ii) error estimates may prescribe a size converging to zero in the discontinuity vicinity. These problems lead to the loss of anisotropy. We show that these problems can be solved by using a particular multi-scales mesh adaptation procedure based on a continuous mesh model. With this approach, prescribing a minimal size is not required and anisotropy is fully preserved. Global second order mesh convergence is numerically observed even with flows with shocks. When more information is given (as the EDP or a functional output), hessian based mesh adaptation is no more optimal in the distribution of degrees of freedom in the computational domain. We address this issue by considering an a priori error estimate to control approximation error on functionals when the flow is governed by the Euler equations. This estimate allows us to derive an anisotropic mesh prescription. Finally, all adaptive strategies are applied to predict high-fidelity sonic boom signature of complex aircrafts.
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https://tel.archives-ouvertes.fr/tel-00361961
Contributor : Adrien Loseille <>
Submitted on : Friday, February 20, 2009 - 5:11:53 PM
Last modification on : Thursday, February 7, 2019 - 1:33:12 AM
Long-term archiving on : Wednesday, March 29, 2017 - 3:54:21 PM

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  • HAL Id : tel-00361961, version 2

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Adrien Loseille. Adaptation de maillage anisotrope 3D multi-échelles et ciblée à une fonctionnelle pour la mécanique des fluides.
Application à la prédiction haute-fidélité du bang sonique.. Mathématiques [math]. Université Pierre et Marie Curie - Paris VI, 2008. Français. ⟨tel-00361961v2⟩

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