22 research outputs found
A novel approach makes higher order wavelets really efficient for radiosity
(Eurographics 2000 proceedings). Article dans revue scientifique avec comité de lecture.International audienceSince wavelets were introduced in the radiosity algorithm, surprisingly little research has been devoted to higher order wavelets and their use in radiosity algorithms. A previous study has shown that wavelet radiosity, and especially higher order wavelet radiosity was not bringing significant improvements over hierarchical radiosity and was having a very important extra memory cost, thus prohibiting any effective computation. In this paper, we present a new implementation of wavelets in the radiosity algorithm, that is substantially different from previous implementations in several key areas (refinement oracle, link storage, resolution algorithm). We show that, with this implementation, higher order wavelets are actually bringing an improvement over standard hierarchical radiosity and lower order wavelets
Space-Angle Discontinuous Galerkin Finite Element Method for Radiative Transfer Equation
Radiative transfer theory describes the interaction of radiation with scattering and absorbing media. It has applications in neutron transport, atmospheric physics, heat transfer, molecular imaging, and others. In steady state, the radiative transfer equation is an integro-differential equation of five independent variables, which are 3 dimensions in space and 2 dimensions in the angular direction. This high dimensionality and the presence of the integral term present serious challenges when solving the equation numerically. Over the past 50 years, several techniques for solving the radiative transfer equation (RTE) have been introduced. These include, but are certainly not limited to, Monte Carlo methods, discrete-ordinate methods, spherical harmonics methods, spectral methods, finite difference methods, and finite element methods. Methods involving discrete ordinates and spherical harmonics have received particular attention in the literature.
This work introduces a parallel space-angle discontinuous Galerkin (saDG) method to solve the steady-state RTEs. The objective-oriented design of the software allowed us to apply the saDG approach to a variety of RTEs with considerable ease, including 1x1s, 1x2s, and 2x2s. The direct solver can achieve high-order accuracy solutions for low-dimensional problems. However, for high-dimensional problems, the direct solver is time-consuming and requires significant memory usage that may exceed the computer\u27s RAM capacity. To address this issue, we employed the Angular Decomposition (AD) method in the iterative solver, which improves runtime efficiency and reduces memory usage. To handle large-scale problems, we developed a parallel solver based on AD and Domain Decomposition (DD) methods. Finally, we applied Reflective Boundary Conditions to 2-D Cartesian radiative transfer problems
Innovative Ray Tracing Algorithms for Space Thermal Analysis
Pour mettre au point le systĂšme de contrĂŽle thermique dâun engin spatial (satellite, sonde ou vĂ©hicule habitĂ©), lâingĂ©nieur thermicien utilise des logiciels adaptĂ©s, tels quâESARAD et ESATAN, commercialisĂ©s par ALSTOM. Comme la composante radiative peut jouer un rĂŽle prĂ©dominant, les logiciels utilisĂ©s contiennent frĂ©quemment un algorithme de lancer de rayons pour calculer les facteurs de vue et facteurs dâĂ©change radiatif entre des surfaces de dimensions finies, supposĂ©es isothermes. Les flux externes (solaires, albĂ©do et infrarouge terrestres) sont Ă©galement calculĂ©s par lancer de rayons. Enfin, les couplages conductifs sont habituellement encodĂ©s manuellement par lâutilisateur.Comme le lancer de rayons est basĂ© sur un processus alĂ©atoire, la prĂ©cision atteinte est dĂ©terminĂ©e par le nombre de rayons lancĂ©s. En gĂ©nĂ©ral, le choix de ce nombre de rayons est laissĂ© Ă la discrĂ©tion de lâingĂ©nieur, ce qui peut conduire Ă des erreurs. Un autre inconvĂ©nient du lancer de rayons est sa faible convergence. Une mĂ©thode dâaccĂ©lĂ©ration du lancer de rayons est nĂ©cessaire.Dans le cadre de la thĂšse, nous avons dĂ©veloppĂ© une mĂ©thode de lancer de rayons plus performante, que nous avons appelĂ©e hĂ©misphĂšre stratifiĂ©, caractĂ©risĂ©e par une meilleure convergence. Un contrĂŽle statistique dâerreur a Ă©tĂ© dĂ©veloppĂ© : lâutilisateur spĂ©cifie la prĂ©cision souhaitĂ©e (dĂ©finie par une erreur relative maximale et un intervalle de confiance) et lâalgorithme adapte automatiquement le nombre de rayons en fonction de la configuration gĂ©omĂ©trique. Sur base de cette erreur gĂ©omĂ©trique, un systĂšme dâĂ©quations adjointes est utilisĂ© pour obtenir une erreur Ă©nergĂ©tique, caractĂ©risant les transferts de chaleur entre les surfaces.LâhĂ©misphĂšre stratifiĂ© est Ă©tendu de maniĂšre Ă inclure des fonctions de rĂ©flexion plus complexes. Lâapplication des relations de rĂ©ciprocitĂ© et de fermeture est Ă©galement considĂ©rĂ©e. La mĂ©thode matricielle de Gebhart, qui permet de dĂ©river les facteurs dâĂ©change radiatifs des facteurs de vue, est Ă©tendue de maniĂšre Ă inclure des surfaces non-diffuses et non-isothermes.Pour accĂ©lĂ©rer le lancer de rayons, les intersections rayons-surfaces ont Ă©tĂ© soigneusement Ă©tudiĂ©es. Nous avons Ă©galement dĂ©veloppĂ© une mĂ©thode qui combine les primitives gĂ©omĂ©triques avec des maillages Ă©lĂ©ments finis. La reprĂ©sentation tri-dimensionnelle du modĂšle gĂ©omĂ©trique est plus adaptĂ©e au calcul de la composante radiative du transfert thermique tandis que les maillages Ă©lĂ©ments finis sont plus adaptĂ©s au calcul de la conduction. Cette mĂ©thode fournit Ă©galement une accĂ©lĂ©ration du lancer de rayons. De plus, le lancer de rayons est effectuĂ© sur la gĂ©omĂ©trie exacte, ce qui est nĂ©cessaire si des rĂ©flexions spĂ©culaires sont modĂ©lisĂ©es. Nous expliquons comment le lancer de rayons peut ĂȘtre effectuĂ© sur la gĂ©omĂ©trie exacte et comment les facteurs de vue rĂ©sultants peuvent ĂȘtre projetĂ©s sur les Ă©lĂ©ments finis. Nous dĂ©finissons la notion de facteur de vue Ă©lĂ©ment fini en calculant les facteurs de vue aux noeuds et en les interpolant sur lâĂ©lĂ©ment fini au moyen des fonctions de forme. Ces facteurs de vue Ă©lĂ©ment fini sont utilisĂ©s pour lier radiativement les noeuds du modĂšle. Comme le champ de tempĂ©rature est projetĂ© sur les fonctions de forme, nous obtenons des Ă©lĂ©ments non-isothermes, contrairement aux rĂ©sultats de la mĂ©thode Thermal Lumped Parameter (diffĂ©rences finies) utilisĂ©e habituellement en thermique spatiale.Les liens conductifs sont calculĂ©s automatiquement sur base du maillage Ă©lĂ©ments finis.Toutes ces amĂ©liorations rĂ©sultent dans un algorithme plus rapide que le programme de rĂ©fĂ©rence ESARAD (pour une prĂ©cision Ă©quivalente) et qui fonctionne avec un petit nombre de paramĂštres dĂ©finis par lâutilisateur.Pour valider lâalgorithme proposĂ©, le modĂšle du vaisseau XEUS, de lâESA, a Ă©tĂ© implĂ©mentĂ©. Des comparaisons ont Ă©tĂ© effectuĂ©es avec ESARAD et le code Ă©lĂ©ments finis SAMCEF
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Development of a hybrid ïŹnite element-transfer matrix methodology for the modeling of vibroacoustic systems with attached noise control treatments
RĂ©sumĂ© : Les vĂ©hicules aĂ©riens et terrestres sont constituĂ©s de systĂšmes bĂątis complexes. La structure principale est gĂ©nĂ©ralement composĂ©e de panneaux lĂ©gers renforcĂ©s par des Ă©lĂ©ments rigides. Cette solution de conception est rĂ©pandue parce quâelle allie la force et un faible poids. Cependant, on sait quâelle offre des rĂ©sultats vibroacoustiques mĂ©diocres, câest Ă dire que lâeffet des perturbations externes qui touchent le systĂšme peut gĂ©nĂ©rer un niveau de bruit excessif Ă lâintĂ©rieur de la cabine des passagers. Câest une prĂ©occupation majeure chez les fabricants, parce que ce niveau de bruit nuit sensiblement au confort ressenti par les clients et peut causer de la fatigue chez les conducteurs et les pilotes. Pour cette raison, les composants passifs constituĂ©s de matĂ©riaux dissipatifs assemblĂ©s en mode multicouche sont gĂ©nĂ©ralement intĂ©grĂ©s Ă la structure. Ces assemblĂ©es bordĂ©es intĂšgrent surtout des matĂ©riaux poroĂ©lastiques, qui sont plutĂŽt rĂ©pandus, grĂące Ă lâagencement intĂ©ressant de bonnes propriĂ©tĂ©s dâisolation sonore et de faible poids.
LâintĂ©gration en amont des traitements de contrĂŽle du bruit au processus de conception
est la clĂ© de succĂšs dâun produit. Pour ce faire, des outils pratiques numĂ©riques en mesure de capter le comportement dynamique des systĂšmes vibroacoustiques impliquant les structures, les cavitĂ©s et les matĂ©riaux dâinsonorisation sont requis. Dâune part, la modĂ©lisation de ces systĂšmes couplĂ©s en utilisant des procĂ©dĂ©s Ă base dâĂ©lĂ©ments finis peut ĂȘtre, bien que prĂ©cis, irrĂ©alisable pour des applications pratiques. Dâautre part, les approches analytiques telles que la mĂ©thode de matrice de transfert sont souvent prĂ©fĂ©rĂ©es grĂące Ă leur facilitĂ© dâutilisation, mĂȘme si elles manquent de prĂ©cision en raison des hypothĂšses rigoureuses inhĂ©rentes au cadre analytique. Dans ce contexte, les procĂ©dures de structuration hybrides sont rĂ©cemment devenues trĂšs populaires. En effet, les diffĂ©rentes techniques de modĂ©lisation sont gĂ©nĂ©ralement recherchĂ©es pour dĂ©crire les systĂšmes vibroacoustiques complexes arbitraires sur la plus large gamme de frĂ©quences possible.
Lâobjectif du projet proposĂ© est de mettre au point un cadre hybride offrant une mĂ©-
thodologie simple pour tenir compte des traitements de contrĂŽle du bruit dans lâanalyse
vibroacoustique par Ă©lĂ©ments finis. A savoir, le modĂšle de calcul qui en dĂ©coule conserve la souplesse et la prĂ©cision de la mĂ©thode des Ă©lĂ©ments finis en bĂ©nĂ©ficiant de la simplicitĂ© et de lâefficacitĂ© de la mĂ©thode de matrice de transfert pour obtenir une rĂ©duction de la charge de calcul pour la modĂ©lisation de composants acoustiques passifs. La performance de la mĂ©thode pour prĂ©dire la rĂ©ponse vibroacoustique de structures planes homogĂšnes avec des traitements acoustiques attachĂ©es est Ă©valuĂ©e. Les rĂ©sultats dĂ©montrent que la mĂ©thode hybride proposĂ©e est trĂšs prometteuse, parce quâelle permet une rĂ©duction de lâeffort de calcul tout en conservant suffisamment de prĂ©cision par rapport Ă lâanalyse complĂšte par Ă©lĂ©ments finis. En outre, la mĂ©thode de matrice de transfert proposĂ©e de modĂ©lisation des traitements de contrĂŽle des bruits est gĂ©nĂ©rale, comme on peut lâappliquer dans dâautres cadres outre lâapplication de lâĂ©lĂ©ment fini considĂ©rĂ© dans ce travail. // Abstract : Aerial and terrestrial vehicles consist of complex built-up systems. The main structure is typically made of light panels strengthened by stiffer components. Such design solution is widely used as it combines strength and low weight. However, it is known to give poor vibroacoustic performances, i.e. the effect of external disturbances acting on the system may generate an excessive noise level inside the passengers cabin. This is a main concern for the manufacturers, as it significantly affects the comfort experienced by the costumers and may fatigue drivers and pilots. For this reason, passive components consisting of dissipative materials assembled in a multilayer fashion are typically integrated within the structure. These lined assemblies mainly involve poroelastic materials, which are commonly used thanks to the appealing combination of good noise insulation properties and low weight.
The early integration of noise control treatments in the design process is the key to a successful product. For this purpose, practical numerical tools able to capture the dynamic behavior of vibroacoustic systems involving structures, cavities and noise proofing materials are demanded. On the one hand, modeling such coupled systems using finite element based methods can be, albeit accurate, time consuming for practical applications. On the other hand, analytical approaches such as the transfer matrix method are often preferred thanks to their ease of use, although they suffer from a lack of accuracy due to the stringent assumptions inherent within the analytical framework. In this context, hybrid substructuring procedures have recently become quite popular. Indeed, different modeling techniques are typically sought to describe arbitrarily complex vibroacoustic systems over the widest possible frequency range.
The aim of this thesis is to devise a hybrid framework providing a simple methodology to
account for noise control treatments in vibroacoustic finite element analysis. Namely, the
resulting computational model retains the flexibility and accuracy of the finite element
method while taking advantage from the simplicity and efficiency of the transfer matrix
method to obtain a reduction of the computational burden in the modeling of passive
acoustic components. The performance of the method in predicting the vibroacoustic
response of flat structures with attached homogeneous acoustic treatments is assessed.
The results prove that the proposed hybrid methodology is very promising, as it allows for a reduction of the computational effort while preserving enough accuracy with respect to full finite element analysis. Furthermore, the proposed transfer matrix based methodology for noise control treatments modeling is general, as it can be used in alternative frameworks besides the finite element application considered in this work