Malgré l'efficacité informatique et la faible dissipation numérique de la méthode de Boltzmann sur réseau (LBM) classique reposant sur un algorithme de propagation-collision, cette méthode est limitée aux maillages cartésiens uniformes. L'adaptation de l'étape de discrétisation à différentes échelles de la mécanique des fluides est généralement réalisée par des schémas LBM à échelles multiples, dans lesquels le domaine de calcul est décomposé en plusieurs sous-domaines uniformes avec différentes résolutions spatiales et temporelles. Pour des raisons de connectivité, le facteur de résolution des sous-domaines adjacents doit être un multiple de deux, introduisant un changement abrupt des échelles spatio-temporelles aux interfaces. Cette spécificité peut déclencher des instabilités numériques et produire des sources de bruit parasite rendant l'exploitation de simulations à finalités aéroacoustiques impossible. Dans la présente thèse, nous avons d'abord élucidé le sujet du raffinement de maillage dans la LBM classique en soulignant les défis et les sources potentielles d'erreur. Par la suite, une méthode de Boltzmann sur réseau hybride (HLBM) est proposée, combinant l'algorithme de propagation-collision avec un algorithme de flux au sens eulérien obtenu à partir d'une discrétisation en volumes finis des équations de Boltzmann à vitesse discrète. La HLBM combine à la fois les avantages de la LBM classique et une flexibilité géométrique accrue. La HLBM permet d'utiliser des maillages cartésiens non-uniformes. La validation de la méthode hybride sur des cas tests 2D à finalité aéroacoustique montre qu'une telle approche constitue une alternative viable aux schémas Boltzmann sur réseau à échelles multiples, permettant de réaliser des raffinements locaux en H. Enfin, un couplage original, basé sur l'algorithme de propagation-collision et une formulation isotherme des équations de Navier-Stokes en volumes finis, est proposé. Une telle tentative présente l'avantage de réduire le nombre d'équations du solveur volumes finis tout en augmentant la stabilité numérique de celui-ci, en raison d'une condition CFL plus favorable. Les deux solveurs sont couplés dans l'espace des moments, où la solution macroscopique du solveur Navier-Stokes est injectée dans l'algorithme de propagation-collision à l'aide de la collision des moments centrés. La faisabilité d'un tel couplage est démontrée sur des cas tests 2D, et les résultas obtenus sont comparés avec la HLBM. / Despite the inherent efficiency and low dissipative behaviour of the standard lattice Boltzmann method (LBM) relying on a two step stream and collide algorithm, a major drawback of this approach is the restriction to uniform Cartesian grids. The adaptation of the discretization step to varying fluid dynamic scales is usually achieved by multi-scale lattice Boltzmann schemes, in which the computational domain is decomposed into multiple uniform subdomains with different spatial resolutions. For the sake of connectivity, the resolution factor of adjacent subdomains has to be a multiple of two, introducing an abrupt change of the space-time discretization step at the interface that is prone to trigger instabilites and generate spurious noise sources that contaminate the expected physical pressure signal. In the present PhD thesis, we first elucidate the subject of mesh refinement in the standard lattice Boltzmann method and point out challenges and potential sources of error. Subsequently, we propose a novel hybrid lattice Boltzmann method (HLBM) that combines the stream and collide algorithm with an Eulerian flux-balance algorithm that is obtained from a finite-volume discretization of the discrete velocity Boltzmann equations. The interest of a hybrid lattice Boltzmann method is the pairing of efficiency and low numerical dissipation with an increase in geometrical flexibility. The HLBM allows for non-uniform grids. In the scope of 2D periodic test cases, it is shown that such an approach constitutes a valuable alternative to multi-scale lattice Boltzmann schemes by allowing local mesh refinement of type H. The HLBM properly resolves aerodynamics and aeroacoustics in the interface regions. A further part of the presented work examines the coupling of the stream and collide algorithm with a finite-volume formulation of the isothermal Navier-Stokes equations. Such an attempt bears the advantages that the number of equations of the finite-volume solver is reduced. In addition, the stability is increased due to a more favorable CFL condition. A major difference to the pairing of two kinetic schemes is the coupling in moment space. Here, a novel technique is presented to inject the macroscopic solution of the Navier-Stokes solver into the stream and collide algorithm using a central moment collision. First results on 2D tests cases show that such an algorithm is stable and feasible. Numerical results are compared with those of the previous HLBM.

[pt] O objetivo deste trabalho é desenvolver uma solução completa para o traçado de raios de cenas dinâmicas utilizando a GPU. Para que este algoritmo atinja desempenho interativo, é necessário utilizar uma estrutura espacial para reduzir os testes de interseção entre raios e triângulos da cena. Observa-se que, quando há movimento na cena, é necessário atualizar esta estrutura de aceleração, seja alterando-a parcialmente ou reconstruindo-a inteiramente. Adotamos a segunda estratégia por ser capaz de tratar o caso geral de movimento não-estruturado. Como a construção da estrutura deve ser feita da forma mais eficiente possível, escolhemos utilizar uma Grade Uniforme como foco de nossa pesquisa. Suas vantagens incluem um algoritmo de construção simples e um percurso de raios eficiente. Para explorar o poder de processamento em paralelo de uma GPU, é necessário manter os dados da cena e da estrutura de aceleração dentro da placa gráfica, evitando transferências custosas de memória entre a GPU e a CPU. Propomos neste trabalho uma técnica para construir uma grade uniforme inteiramente na GPU. Usando nosso método, é possível reconstruir toda a estrutura em poucos milissegundos, enquanto mantém-se a alta qualidade da grade obtida. Além disso, propomos uma implementaçoes do algoritmo de traçado de raios de forma a aproveitar o processamento em paralelo da GPU. Nosso procedimento é implementado inteiramente dentro da placa gráfica, onde há acesso direto para os dados dos triângulos da cena, bem como as informações da grade uniforme construída. Utilizando a solução proposta, somos capazes de obter taxas de visualização interativas mesmo para cenas com movimentos não-estruturados, incluindo texturas, sombras e até mesmo reflexões. / [en] We present a technique for ray tracing dynamic scenes using the GPU. In order to achieve interactive rendering rates, it is necessary to use a spatial structure to reduce the number of ray-triangle intersections performed. Whenever there is movement in the scene, this structure is entirely rebuilt. This way, it is possible to handle general unstructured motion. For this purpose, we have developed an algorithm for reconstructing Uniform Grids entirely inside the graphics hardware. In addition, we present ray-traversal and shading algorithms fully implemented on the GPU, including textures, shadows and reections. Combining these techniques, we demonstrate interactive ray tracing performance for dynamic scenes, even with unstructured motion and advanced shading effects.