Description en espaces de chemins et méthode de Monte Carlo pour les transferts thermiques couplés dans les structures fluides et solides, une approche compatible avec l'informatique graphique

The present manuscript deals with the coupling of thermal heat transfers. More precisely, it adresses this coupling by making use of the Monte Carlo method and the sampling of random paths. This choice was made in the perspective of building algorithms that do not present constraints regarding the complexity of the studied geometry. Indeed, the combined use of this kind of statistical approaches, and acceleration tools coming from the image synthesis community, already allowed for an exact resolution of radiative transfer in arbitrary geometries. Regarding diffusive heat transfers, exact results using random paths are only achievable in academic configurations. Thus, approximate random paths are commonly used to account for this kind of thermal transport. Among the possible choices, we will use random paths built on ray tracing, therefore allowing to benefit once again from all the advantages of the tools developed in computer graphics. A proof of concept of the insensitivity of the computation time of the resolution of thermal transfers in porous exchangers to the number of pores by making use of conducto-convecto-radiative random paths will be presented. Beyond this result, an analysis of the behaviour of this method in ducts heat exchangers will allow to clarify when this kind of insensitivity can indeed be observed. This analysis will induce the concept of thermal thickness, by analogy with optical thickness for radiative transfer.Les travaux présentés dans ce manuscrit abordent la thématique du couplage des transferts thermiques. En particulier, ils s’inscrivent dans une réflexion actuelle autour de l’échantillonnage de chemins aléatoires par la méthode de Monte Carlo. Ce choix est justifié par un souhait d’obtenir des algorithmes ne présentant pas de contraintes sur la complexité des géométries étudiées. En effet, l’utilisation conjointe de ce type d’approches statistiques et des outils d’accélération de la synthèse d’image (grilles accélératrices) permet d’ores et déjà une résolution exacte du transfert radiatif en géométrie quelconque. Pour les transferts thermiques de type diffusif, l’exactitude des approches en espaces de chemins n’est atteignable que pour des configurations simples. On choisit donc d’utiliser des chemins statistiques approchés pour rendre compte de ce type de phénomènes thermiques dans des géométries quelconques. Parmi les choix disponibles, on retiendra des espaces de chemins construits autour du lancer de rayon, qui permettront donc de bénéficier de l’ensemble des avantages des outils développés par la communauté de l’informatique graphique. Une preuve de concept de l’insensibilité du temps de calcul au nombre de pores de la résolution thermique d’un échangeur poreux par l’utilisation de marches aléatoires conducto-convecto-radiatives sera ainsi présentée. Au-delà de ce résultat, une analyse du comportement de la méthode sur des échangeurs à canaux permettra de classifier des situations d’insensibilité, ou pas, à la complexité des milieux poreux étudiés. La capacité à expliquer les limites de cette insensibilité et le comportement de ce temps de calcul fera alors émerger un concept d’épaisseur thermique homologue à la problématique de l’épaisseur optique en transfert radiatif

Paths description and Monte Carlo method for coupled heat transfer in fluid and solid structures, a computer graphics' compatible approach

Les travaux présentés dans ce manuscrit abordent la thématique du couplage des transferts thermiques. En particulier, ils s’inscrivent dans une réflexion actuelle autour de l’échantillonnage de chemins aléatoires par la méthode de Monte Carlo. Ce choix est justifié par un souhait d’obtenir des algorithmes ne présentant pas de contraintes sur la complexité des géométries étudiées. En effet, l’utilisation conjointe de ce type d’approches statistiques et des outils d’accélération de la synthèse d’image (grilles accélératrices) permet d’ores et déjà une résolution exacte du transfert radiatif en géométrie quelconque. Pour les transferts thermiques de type diffusif, l’exactitude des approches en espaces de chemins n’est atteignable que pour des configurations simples. On choisit donc d’utiliser des chemins statistiques approchés pour rendre compte de ce type de phénomènes thermiques dans des géométries quelconques. Parmi les choix disponibles, on retiendra des espaces de chemins construits autour du lancer de rayon, qui permettront donc de bénéficier de l’ensemble des avantages des outils développés par la communauté de l’informatique graphique. Une preuve de concept de l’insensibilité du temps de calcul au nombre de pores de la résolution thermique d’un échangeur poreux par l’utilisation de marches aléatoires conducto-convecto-radiatives sera ainsi présentée. Au-delà de ce résultat, une analyse du comportement de la méthode sur des échangeurs à canaux permettra de classifier des situations d’insensibilité, ou pas, à la complexité des milieux poreux étudiés. La capacité à expliquer les limites de cette insensibilité et le comportement de ce temps de calcul fera alors émerger un concept d’épaisseur thermique homologue à la problématique de l’épaisseur optique en transfert radiatif.The present manuscript deals with the coupling of thermal heat transfers. More precisely, it adresses this coupling by making use of the Monte Carlo method and the sampling of random paths. This choice was made in the perspective of building algorithms that do not present constraints regarding the complexity of the studied geometry. Indeed, the combined use of this kind of statistical approaches, and acceleration tools coming from the image synthesis community, already allowed for an exact resolution of radiative transfer in arbitrary geometries. Regarding diffusive heat transfers, exact results using random paths are only achievable in academic configurations. Thus, approximate random paths are commonly used to account for this kind of thermal transport. Among the possible choices, we will use random paths built on ray tracing, therefore allowing to benefit once again from all the advantages of the tools developed in computer graphics. A proof of concept of the insensitivity of the computation time of the resolution of thermal transfers in porous exchangers to the number of pores by making use of conducto-convecto-radiative random paths will be presented. Beyond this result, an analysis of the behaviour of this method in ducts heat exchangers will allow to clarify when this kind of insensitivity can indeed be observed. This analysis will induce the concept of thermal thickness, by analogy with optical thickness for radiative transfer

Couplage conducto-convecto-radiatif par échantillonnage de chemins : un parallèle avec les chemins de multi-diffusions en transfert radiatif

International audienceLa méthode de Monte Carlo est largement utilisée pour la simulation du transfert radiatif. De récents travaux proposent d’utiliser des algorithmes similaires pour la résolution des transferts thermiques conducto-convecto-radiatif couplés. Ces approches statistiques ont pour principal avantage d’être résilients à la complexité géométrique, y compris en présence de grands rapports d’échelle en temps et en espace, grâce aux outils de la synthèse d’image. Cependant, certaines difficultés sont apparues à certaines limites paramétriques au niveau des temps de calcul. Cette étude s’efforce de faire un parallèle entre ces difficultés et celles rencontrées pour les fortes épaisseurs optiques dans la résolution du transfert radiatif par Monte Carlo

Three viewpoints on null-collision Monte Carlo algorithms

International audienceIn 2013, Galtier et al. [1] theoretically revisited a numerical trick that had been used since the very beginning of linear-transport Monte-Carlo simulation: introducing “null” scatterers into a heterogeneous field to make it virtually homogeneous.The rigorous connection between null-collision algorithms and integral formulations of the radiative transfer equation led to null-collision algorithms being used in distinct contexts, from atmospheric or combustion sciences to computer graphics, addressing questions that may strongly depart from the initial objective of handling heterogeneous fields (handling large spectroscopic databases, non-linearly coupling radiation with other physics).We briefly describe here some of this research and we classify it by proposing three alternative viewpoints on the very same null-collision concept: an intuitive, physical point of view, called similitude; a viewpoint built on the probability theory, where the null-collision method is seen as rejection sampling; and a more formal writing where the nonlinear exponential function is expanded into an infinite sum of linear terms.By formulating the null-collision concept under three distinct formalisms, our intention is to increase the reader’s awareness of its flexibility.The idea defended and illustrated in this paper is that the ability to explore null-collision algorithms under their different forms has often led to a broadening of the solution space when facing difficult problems, including ones where the Monte Carlo method was consensually considered inapplicable

Toward the use of Symbolic Monte Carlo for Conduction-Radiation Coupling in Complex Geometries

International audienceWe address the interest of using Symbolic Monte Carlo to obtain a reduced model for conduction-radiation coupling in complex geometries. Symbolic Monte Carlo was successfully used for radiative transfer in a decoupled manner, but no attempt has yet been reported to extend its use to radiation coupled with other modes. Here we show that from a unique Monte Carlo simulation of radiation coupled with conduction in a semi-transparent solid surrounded by a convective flow, it is possible to build a formulation of the local temperature as function of the convective heat trans- fer coefficient, for instance, including the evaluation of uncertainty. This reduced model (a transfer function) enables to decrease the computation time when the function needs to be evaluated plenty of times for different values of the parameters as in optimization or control algorithms

Combined conductive-convective-radiative heat transfer in complex geometry using the Monte Carlo method: application to solar receivers

International audienceDeterministic methods are commonly used to solve coupled conductive-convective-radiative systems in threedimensional geometries (3D). With the increasing amount and accuracy of data available, and growing complexity of systems studied, these methods have to deal with endless increases in computation times. This article presents a stochastic method for the simulation of the heat balance equation in solids and fluids with known velocity fields, as well as coupled surface to surface radiative transfers. The construction of the corresponding algorithm is comprehensively detailed and results are compared to deterministic simulations. The presented method uses a Monte Carlo approach and is shown to preserve short computation times for complex geometries

Advection, diffusion and linear transport in a single path-sampling Monte-Carlo algorithm : getting insensitive to geometrical refinement

We address the question of numerically simulating the coupling of diffusion, advection and one-speed linear transport with the specific objective of handling increases of the amount, the geometrical refinement and the accuracy level of input data. The computer graphics research community has succeeded in designing Monte Carlo algorithms simulating linear radiation transport in physically realistic scenes with numerical costs that are insensitive to geometrical refinement: adding more details to the scene description does not affect the computation time. The corresponding benefits in terms of engineering flexibility are already fully integrated in the cinema industry and are gradually inherited by the video game industry. We show here that the same insensitivity to the complexity of the geometrical description can also be achieved when considering one-speed linear transport not only alone but coupled with diffusion and advection. Pure linear-transport paths are replaced with advection-diffusion/linear-transport paths constituted of subpaths, each representing one of the three physical phenomena in a recursive manner. Illustration is made with a porous medium involving up to 10000 pores, the computation time being strictly independent of the number of pores

Advection, diffusion and linear transport in a single path-sampling Monte-Carlo algorithm : getting insensitive to geometrical refinement

We address the question of numerically simulating the coupling of diffusion, advection and one-speed linear transport with the specific objective of handling increases of the amount, the geometrical refinement and the accuracy level of input data. The computer graphics research community has succeeded in designing Monte Carlo algorithms simulating linear radiation transport in physically realistic scenes with numerical costs that are insensitive to geometrical refinement: adding more details to the scene description does not affect the computation time. The corresponding benefits in terms of engineering flexibility are already fully integrated in the cinema industry and are gradually inherited by the video game industry. We show here that the same insensitivity to the complexity of the geometrical description can also be achieved when considering one-speed linear transport not only alone but coupled with diffusion and advection. Pure linear-transport paths are replaced with advection-diffusion/linear-transport paths constituted of subpaths, each representing one of the three physical phenomena in a recursive manner. Illustration is made with a porous medium involving up to 10000 pores, the computation time being strictly independent of the number of pores

Synthèse d'images infrarouges sans calcul préalable du champ de température

International audienceNous presentons un ensemble d’algorithmes statistiques permettant d’effectuer le rendu d’une image thermique, en régime instationnaire, dans une scène quelconque. Simuler le signal reçu par chaque pixel de la camera consiste à propager les sources thermiques (conditions aux limites et initiales) par les phenomènes de conduction, convection et rayonnement. La technique ne nécessite pas un calcul préalable du champ de température en tout point de la scène et en tout temps. Un exemple en geométrie complexe est présenté, et qualitativement comparé à une prise de vue