L'utilisation croissante de véhicules au cours des dernières décennies a causé une augmentation dans les émissions de gaz d'échappement nocifs provoquant des problèmes de santé et d'environnement. Cette problématique a conduit les gouvernements à mettre en place des limites d'émissions plus strictes. Afin de respecter ces limites, il est nécessaire de développer des systèmes de post-traitement plus performants. Parmi plusieurs solutions possibles, l'analyse et l'optimisation de l'impact de l'écoulement sur les réactions chimiques est une approche importante pour résoudre ce problème complexe. Au point de vue expérimental, il est très difficile de mesurer le champ de vitesse détaillé et la distribution de la température et de la concentration. Les simulations numériques peuvent fournir des informations supplémentaires pour comprendre l'interaction entre la distribution de l'écoulement et l'efficacité des réactions. La simulation numérique de ces systèmes est très coûteuse due aux phénomènes physiques et chimiques complexes ayant lieu simultanément dans tout le système. Afin de diminuer ce coût, on peut développer des modèles physiques et chimiques simplifiés ainsi que des techniques numériques spécifiques pour simuler le système tout en réduisant le temps de calcul. Dans cette thèse, nous développons une approche générale pour modéliser et simuler le système de post-traitement des gaz d'échappement automobile contenant les aspects physiques et chimiques. L'approche présente combine des modèles simplifiés et des techniques numériques de multi-résolutions afin de capturer correctement les caractéristiques de l'écoulement dans le système. Alors que la méthode de raffinement de maillage adaptatif (AMR) est optimisée afin de minimiser l'effort de calcul dans les régions divergente et convergente, un modèle de sous-maille est développé pour décrire l'écoulement dans les micro-canaux du substrat catalytique placé entre la région divergente et la région convergente. La performance du modèle est validée par rapport aux résultats expérimentaux obtenus par Benjamin et al. (2002). Le couplage effectif de méthode AMR et le modèle de sous-maille permet de capturer les caractéristiques de l'écoulement dans le système avec un temps de calcul réduit de manière significative. L'impact de l'écoulement pulsé et de l'écoulement en expansion sur le taux de réaction dans un canal de monolithe est étudié numériquement. La méthode AMR est montrée pour capturer les couches mince de diffusion près de la paroi à l'interface solide-liquide. Sur la base des résultats numériques, nous proposons un modèle simplifié de transport capturant les effets de l'écoulement, la diffusion et la réaction catalytiques à la paroi. Le modèle simplifié de transport peut être directement appliqué dans la forme de modèle de sous-maille pour la description complète de tous les processus physiques et chimiques ayant lieu à l'intérieur du système. Grâce aux approches de modélisation numériques physiques et chimiques développées, il est possible de simuler le système en trois dimensions avec un temps de calcul raisonnable capturant encore la physique principale du problème. / The increasing use of passenger vehicles over the past decades has caused an increase in harmful exhaust gas emissions which give rise to environmental and health problems. This problematic has led governments to establish very stringent emission limits. The emission restrictions require more performing after-treatment systems. Among many other solutions, analysing and optimising the flow impact on the conversion efficiency is an important step towards the solution of the complex engineering problem. Detailed velocity, temperature and concentration distributions are very difficult to measure experimentally. Numerical simulations can provide additional information to understand the interaction of flow distribution and conversion efficiency. The simulation of these systems is computationally very expensive due to complex physical and chemical phenomena occurring simultaneously throughout the system. To overcome this cost, one can resort to some simplified physical and chemical models together with specific numerical techniques to simulate the system with a reduced computational time. In this dissertation, we develop a general approach to model and simulate the automotive catalytic converter system including all the physical and chemical processes. The present approach combines sub-grid models and numerical multi-resolution techniques in order to correctly capture the flow characteristics inside an automotive catalytic converter. While Adaptive Mesh Refinement (AMR) techniques are optimized in order to minimise the computational effort in the divergent and convergent regions, a sub-grid model is developed to describe the flow inside the catalytic substrate placed between the convergent and divergent regions. The performance of the sub-grid model is validated against the experimental results obtained by Benjamin et al. (2002). The effective coupling of AMR techniques and the sub-grid model allows to capture the flow features with significantly reduced computational time. The impact of pulsating and expansion flow on the conversion efficiency within a single monolith channel is investigated numerically. AMR techniques are shown to capture the small boundary layers near the wall at the solid-fluid interface. Based on the numerical results, we propose a simplified transport model that captures the effects of flow, diffusion and catalytic wall reactions. The simplified transport model can be directly applied as a sub-grid model for the complete description of all the physical and chemical processes taking place inside the system. The developed physical, chemical and numerical modelling approaches make the three-dimensional simulations possible with a reasonable computational time still capturing the main physics of the problem.

abstract: Compressible fluid flows involving multiple physical states of matter occur in both nature and technical applications such as underwater explosions and implosions, cavitation-induced bubble collapse in naval applications and Richtmyer-Meshkov type instabilities in inertial confinement fusion. Of particular interest is the atomization of fuels that enable shock-induced mixing of fuel and oxidizer in supersonic combustors. Due to low residence times and varying length scales, providing insight through physical experiments is both technically challenging and sometimes unfeasible. Numerical simulations can help provide detailed insight and aid in the engineering design of devices that can harness these physical phenomena. In this research, computational methods were developed to accurately simulate phase interfaces in compressible fluid flows with a focus on targeting primary atomization. Novel numerical methods which treat the phase interface as a discontinuity, and as a smeared region were developed using low-dissipation, high-order schemes. The resulting methods account for the effects of compressibility, surface tension and viscosity. To aid with the varying length scales and high-resolution requirements found in atomization applications, an adaptive mesh refinement (AMR) framework is used to provide high-resolution only in regions of interest. The developed methods were verified with test cases involving strong shocks, high density ratios, surface tension effects and jumps in the equations of state, in one-, two- and three dimensions, obtaining good agreement with theoretical and experimental results. An application case of the primary atomization of a liquid jet injected into a Mach 2 supersonic crossflow of air is performed with the methods developed. / Dissertation/Thesis / Doctoral Dissertation Aerospace Engineering 2020

We present an Embedded Boundary with Adaptive Mesh Refinement technique for solving the compressible Navier Stokes equations in arbitrary complex domains; followed by a numerical studies for the effect of circular cylinders on the transient dynamics of the Richtmyer-Meshkov Instability. A PDE multidimensional extrapolation approach is used to reconstruct the solution in the ghost-fluid regions and imposing boundary conditions on the fluid-solid interface, coupled with a multi-dimensional algebraic interpolation for freshly cleared cells. The Navier Stokes equations are numerically solved by the second order multidimensional upwind method. Block-structured AMR, implemented with the Chombo framework, is utilized to reduce the computational cost while keeping high resolution mesh around the Embedded Boundary and regions of high gradient solutions. The versatility of the method is demonstrated via several numerical examples, in both static and moving geometry, ranging from low Mach number nearly incompressible to supersonic flows. Our simulation results are extensively verified against other numerical results and validated against available experimental results where applicable. The effects on the transient dynamics of the Richtmyer-Meshkov instability due to small scale perturbations introduced on the shock-wave or the material interface by a single or set of solid circular cylinders were computationally investigated using the developed technique. First, we discuss the RMI initiated on a flat interface by a rippled shock-wave that is disturbed by a single circular cylinder. Then, we study the effect of introducing a number of circular cylinders on the interface. The arrangement of the cylinders set mimic (in a two dimensional domain) the presence of the solid supporting grid wires used in the formation of the material interface in the experimental setup. We analyzed their effects on the mixing layer growth and the mixedness level, and qualitatively demonstrate the cylinders' perturbation effects on the mixing layer structure. We modeled the cylinders' influence based on their diameters; and showed the model ability to predict the variation of the mixing layer growth for different flow parameters.

Adaptive finite element methods for the solution of partial differential equations require effective methods of mesh refinement and coarsening, fast multilevel solvers for the systems of FE equations need a hierarchical structure of the grid. In the paper a technology is presented for the application of irregular hierarchical triangular meshes arising from refinement by only dividing elements into four congruent triangles. The paper describes the necessary data structures and data structure management, the principles and algorithms of refining and coarsening the mesh, and also a specific assembly technique for the FE equations system. Aspects of the parallel implementation on MIMD computers with a message passing communication are included.

abstract: This dissertation introduces FARCOM (Fortran Adaptive Refiner for Cartesian Orthogonal Meshes), a new general library for adaptive mesh refinement (AMR) based on an unstructured hexahedral mesh framework. As a result of the underlying unstructured formulation, the refinement and coarsening operators of the library operate on a single-cell basis and perform in-situ replacement of old mesh elements. This approach allows for h-refinement without the memory and computational expense of calculating masked coarse grid cells, as is done in traditional patch-based AMR approaches, and enables unstructured flow solvers to have access to the automated domain generation capabilities usually only found in tree AMR formulations. The library is written to let the user determine where to refine and coarsen through custom refinement selector functions for static mesh generation and dynamic mesh refinement, and can handle smooth fields (such as level sets) or localized markers (e.g. density gradients). The library was parallelized with the use of the Zoltan graph-partitioning library, which provides interfaces to both a graph partitioner (PT-Scotch) and a partitioner based on Hilbert space-filling curves. The partitioned adjacency graph, mesh data, and solution variable data is then packed and distributed across all MPI ranks in the simulation, which then regenerate the mesh, generate domain decomposition ghost cells, and create communication caches. Scalability runs were performed using a Leveque wave propagation scheme for solving the Euler equations. The results of simulations on up to 1536 cores indicate that the parallel performance is highly dependent on the graph partitioner being used, and differences between the partitioners were analyzed. FARCOM is found to have better performance if each MPI rank has more than 60,000 cells. / Dissertation/Thesis / Doctoral Dissertation Aerospace Engineering 2019

Dans le contexte de la dynamique moléculaire classique appliquée à la physique de la matière condensée, les chercheurs du CEA étudient des phénomènes physiques à une échelle atomique. Pour cela, il est primordial d'optimiser continuellement les codes de dynamique moléculaire sur les dernières architectures de supercalculateurs massivement parallèles pour permettre aux physiciens d'exploiter la puissance de calcul pour reproduire numériquement des phénomènes physiques toujours plus complexes. Cependant, les codes de simulations doivent être adaptés afin d'équilibrer la répartition de la charge de calcul entre les cœurs d'un supercalculateur.Pour ce faire, dans cette thèse nous proposons d'incorporer la méthode de raffinement de maillage adaptatif dans le code de dynamique moléculaire ExaSTAMP. L'objectif est principalement d'optimiser la boucle de calcul effectuant le calcul des interactions entre particules grâce à des structures de données multi-threading et vectorisables. La structure permet également de réduire l'empreinte mémoire de la simulation. La conception de l’AMR est guidée par le besoin d'équilibrage de charge et d'adaptabilité soulevé par des ensembles de particules se déplaçant très rapidement au cours du temps.Les résultats de cette thèse montrent que l'utilisation d'une structure AMR dans ExaSTAMP permet d'améliorer les performances de celui-ci. L'AMR permet notamment de multiplier par 1.31 la vitesse d'exécution de la simulation d'un choc violent entraînant un micro-jet d'étain de 1 milliard 249 millions d'atomes sur 256 KNLs. De plus, l'AMR permet de réaliser des simulations qui jusqu'à présent n'étaient pas concevables comme l'impact d'une nano-goutte d'étain sur une surface solide avec plus 500 millions d'atomes. / In the context of classical molecular dynamics applied to condensed matter physics, CEA researchers are studying complex phenomena at the atomic scale. To do this, it is essential to continuously optimize the molecular dynamics codes of recent massively parallel supercomputers to enable physicists to exploit their capacity to numerically reproduce more and more complex physical phenomena. Nevertheless, simulation codes must be adapted to balance the load between the cores of supercomputers.To do this, in this thesis we propose to incorporate the Adaptive Mesh Refinement method into the ExaSTAMP molecular dynamics code. The main objective is to optimize the computation loop performing the calculation of particle interactions using multi-threaded and vectorizable data structures. The structure also reduces the memory footprint of the simulation. The design of the AMR is guided by the need for load balancing and adaptability raised by sets of particles moving dynamically over time.The results of this thesis show that using an AMR structure in ExaSTAMP improves its performance. In particular, the AMR makes it possible to execute 1.31 times faster than before the simulation of a violent shock causing a tin microjet of 1 billion 249 million atoms on 256 KNLs. In addition, simulations that were not conceivable so far can be carried out thanks to AMR, such as the impact of a tin nanodroplet on a solid surface with more than 500 million atoms.

This thesis details the development of the radiation transport code torus for radiation hydrodynamic applications and its subsequent use in investigating problems regarding radiative feedback. The code couples Monte Carlo photoionization with grid-based hydrodynamics and has the advantage that all of the features available to a dedicated radiation transport code are at its disposal in RHD applications. I discuss the development of the code, including the hydrodynamics scheme, the adaptive mesh refinement (AMR) framework and the coupling of radiation transport with hydrodynamics. Extensive testing of the resulting code is also presented. The main application involves the study of radiatively driven implosion (RDI), a mechanism where the expanding ionized region about a massive star impacts nearby clumps, potentially triggering star formation. Firstly I investigate the way in which the radiation field is treated, isolating the relative impacts of polychromatic and diffuse field radiation on the evolution of radiation hydrodynamic RDI models. I also produce synthetic SEDs, radio, Hα and forbidden line images of the bright rimmed clouds (BRCs) resulting from the RDI models, on which I perform standard diagnostics that are used by observers to obtain the cloud conditions. I test the accuracy of the diagnostics and show that considering the pressure difference between the neutral cloud and surrounding ionized layer can be used to infer whether or not RDI is occurring. Finally I use more synthetic observations to investigate the accuracy of molecular line diagnostics and the nature of line profiles of BRCs. I show that the previously unexplained lack of dominant blue-asymmetry (a blue-asymmetry is the expected signature of a collapsing cloud) in the line profiles of BRCs can be explained by the shell of material, swept up by the expanding ionized region, that drives into the cloud. The work in this thesis combines to help resolve the difficulties in understanding radiative feedback, which is a non–linear process that happens on small astrophysical timescales, by improving numerical models and the way in which they are compared with observations.

Les nouveaux enjeux environnementaux motivent la recherche par les acteurs de l'industrie aéronautique de méthodes de calcul de trajectoires optimales. Les contributions de cette thèse se déclinent selon trois axes. Dans un premier temps, plusieurs techniques d'optimisation de trajectoire avion sont comparées sur un cas simple traité dans la bibliographie universitaire. Puis, un modèle réduit pour prendre en compte le niveau des nuisances sonores dans un algorithme d'optimisation de trajectoire est proposé.Enfin, un problème d'optimisation de trajectoire de montée d'un avion civil est résolu par une approche directe. Les spécificités du problème consistent en la présence de plusieurs phases au sein de la trajectoire, la formulation de contraintes égalités à vérifier par des composantes du vecteur d'état sur des intervalles de temps et enfin la difficulté d'intégration numérique du modèle de bruit. / Forthcoming environmental challenges stimulate the development of trajectory optimization methods by aeronautical actors. This contribution consists in three parts. First, several trajectory optimization techniques are compared. The comparison is based on a simple academic problem. After that, a model is proposed for considering noise nuisance level in the framework of trajectory optimization. Finally, the optimization problem of an ascent phase of a civil aircraft is solved using a direct approach. The specific issues of the problem are tackled with a general formulation. They consist in the presence of several phases along the trajectory, running state equality constraints and tough numerical integration of the noise model.

Finite amplitude perturbations in compressible media are ubiquitous in scientific and engineering applications such as gas-turbine engines, rocket propulsion systems, combustion instabilities, inhomogeneous solids, and traffic flow prediction models, to name a few. Small amplitude waves in compressible fluids propagate as sound and are very well described by linear theory. On the other hand, the theory of nonlinear acoustics, concerning high-amplitude wave propagation (Mach<2) is relatively underdeveloped. Most of the theoretical development in nonlinear acoustics has focused on wave steepening and has been centered around the Burgers' equation, which can be extended to nonlinear acoustics only for purely one-way traveling waves. In this dissertation, theoretical and computational developments are discussed with the objective of advancing the multi-fidelity modeling of nonlinear acoustics, ranging from quasi one-dimensional high-amplitude waves to combustion-induced detonation waves. <br> <br> We begin with the theoretical study of spectral energy cascade due to the propagation of high amplitude sound in the absence of thermal sources. To this end, a first-principles-based system of governing equations, correct up to second order in perturbation variables is derived. The exact energy corollary of such second-order system of equations is then formulated and used to elucidate the spectral energy dynamics of nonlinear acoustic waves. We then extend this analysis to thermoacoustically unstable waves -- i.e. amplified as a result of thermoacoustic instability. We drive such instability up until the generation of shock waves. We further study the nonlinear wave propagation in geometrically complex case of waves induced by the spark plasma between the electrodes. This case adds the geometrical complexity of a curved, three-dimensional shock, yielding vorticity production due to baroclinic torque. Finally, detonation waves are simulated by using a low-order approach, in a periodic setup subjected to high pressure inlet and exhaust of combustible gaseous mixture. An order adaptive fully compressible and unstructured Navier Stokes solver is currently under development to enable higher fidelity studies of both the spark plasma and detonation wave problem in the future. <br>

The thesis presents a comprehensive study of a posteriori error estimation in the adaptive solution to some classical elliptic partial differential equations. Several new error estimators are proposed for diffusion problems with discontinuous coefficients and for convection-reaction-diffusion problems with dominated convection/reaction. The robustness of the new estimators is justified theoretically. Extensive numerical results demonstrate the robustness of the new estimators for challenging problems and indicate that, compared to the well-known residual-type estimators, the new estimators are much more accurate.