Réduction de modèles cinétiques et applications à l'acoustique du bâtiment

Abstract : In this PhD thesis we are interested in the study of different numerical methods for the simulation of high-frequency acoustic problems taking place on the scale of the building. In the high-frequency approximation the sound propagation can be modeled through a kinetic transport equation paired with the boundary conditions that describe the specular or diffuse nature of the reflections with the boundaries of the domain. In the first part of this paper we will tackle the resolution of this model, posed in a seven-dimensional space, by the application of the discrete ordinates method. This method consists in the discretisation of the velocity space into a finite number of allowable directions and leads to a system of coupled transport equations having lost all velocity dependence. Secondly, we will apply the method of moments with entropic closure. The resulting system, of a hyperbolic nature, allows the macroscopic dynamics to be described by only two conservative variables. In two dimensions, the resolution of these models is performed through a finite volume scheme implemented on GPU. In three dimensions, a discontinuous Galerkin method is used which can be executed on a hybrid GPU/CPU architecture. For comparative purposes, a particle method has also been implemented and solved using a fully GPU-parallelised ray-tracing algorithm. Finally, we will apply and compare the developed methods on several test cases specific to room acoustics.
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Submitted on : Thursday, February 13, 2020 - 3:35:34 PM
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Pierre Gerhard. Réduction de modèles cinétiques et applications à l'acoustique du bâtiment. Mathématiques [math]. Université de Strasbourg, 2020. Français. ⟨tel-02445322v2⟩

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