Les écoulements instationnaires au-dessus de surfaces discontinues produisent d'important bruit aérodynamique. L'objectif de ce travail de thèse est l'étude aéroacoustique d'écoulement au-dessus de cavités bidimensionnelles rectangulaires, et de trouver des stratégies de réduction du bruit. Des simulations numériques directes des équations bidimensionnelles de Navier-Stokes compressibles ont été réalisées afin d'étudier l'influence des conditions initiales sur le mode d'oscillation de l'écoulement pour des cavités profonde et peu profonde. Les résultats montrent que dans le cas de cavités profondes, l'écoulement oscille selon un régime de couche de cisaillement suivant le second mode de Rossiter, et ce quelle que soit la condition initiale choisie. En revanche, dans le cas de cavités peu profondes, le régime d'oscillation observé peut être en couche de cisaillement ou bien en mode de sillage suivant la condition initiale choisie. Une analyse de sensibilité d'écoulement dans le cas de cavités profondes a été réalisé en utilisant une méthode adjointe. Les équations adjointes ont été forcées par une perturbation localisée sinusoïdale soit de la quantité de mouvement suivant x adjointe (au voisinage de la couche de cisaillement), soit de la densité adjointe (loin de la cavité). Les résultats désignent une région de l'écoulement très sensible à l'ajout de masse, et localisée au voisinage du coin supérieur amont de la cavité. Par conséquent, un actionneur de type soufflage/aspiration placé au bord d'attaque de la cavité agira sur les fluctuations de quantité de mouvement suivant x au voisinage de la couche de cisaillement et sur les fluctuations de pression au loin. / The unsteady flow over surface discontinuities produces high aerodynamic noise. The aim of this thesis is to study the aeroacoustics of two-dimensional rectangular cavities and to find strategies for noise reduction. Direct Numerical Simulation of the compressible Navier-Stokes equations is performed to investigate the influence of the initial condition on the oscillation modes in deep and shallow cavities. Results show that the deep cavity oscillates in shear layer regime at the second Rossiter mode regardless of the initial condition. On the other hand different initial conditions lead to a shear layer or wake mode in the shallow cavity case. A sensitivity analysis of the deep cavity is done by the use of adjoint methods. Local sinusoidal perturbations of x-momentum and density are applied to the adjoint equations. The results show a high sensitivity region to mass injection at the upstream corner. Therefore an actuator placed at the leading edge will modify the velocity fluctuations reaching the trailing edge and hence the pressure fluctuations in the far-field.

Numerical solutions obtained through the use of Computational Fluid Dynamics (CFD) are subject to discretization error, which is locally generated by truncation error. The discretization error is extremely difficult to properly estimate and this in turn leads to uncertainty over the quality of the numerical solutions obtained via CFD methods and the engineering functionals computed using these solutions. Adjoint error estimation techniques specifically seek to estimate the error in functionals, but are dependent upon accurate truncation error estimates. This work examines the application of new, single-grid, truncation error estimation procedures to the problem of adjoint error estimation for both the quasi-1D and 2D Euler equations. The new truncation error estimation techniques are based on local reconstructions of the computed solutions and comparisons are made for the quasi-1D study in order to determine the most appropriate solution variables to reconstruct as well as the most appropriate reconstruction method. In addition, comparisons are made between the single-grid truncation error estimates and methods based on uniformally refining or coarsening the underlying numerical mesh on which the computed solutions are obtained. A method based on an refined grid error estimate is shown to work well for a non-isentropic flow for the quasi-1D Euler equations, but all truncation error estimations methods ultimately result in over prediction of functional discretization error in the presence of a shock in 2D. Alternatives to adjoint methods, which can only estimate the error in a single functional for each adjoint solution obtained, are examined for the 2D Euler equations. The defection correction method and error transport equations are capable of locally improving the entire computed solution, allowing for error estimates in multiple functionals. It is found that all three functional discretization error estimates perform similarly for the same truncation error estimate, although the defect correction method is the most costly from a computational viewpoint. Comparisons are made between truncation error and adjoint weighted truncation error based adaptive indicators. For the quasi-1D Euler equations it is found that both methods are competitive, however the truncation error based method is cheaper as a separate adjoint solve is avoided. For the 2D Euler equations, the truncation error estimates on the adapted meshes suffer due to a lack of smooth grid transformations which are used in reconstructing the computed solutions. In order to complete this work, a new CFD code incorporating a variety of best practices from the field of Computer Science is developed as well as a new method of performing code verification using the method of manufactured solutions which is significantly easier to implement than traditional manufactured solution techniques. / Ph. D.

Computational fluid dynamics (CFD) simulations can provide tremendous insight into complex physical processes and are often faster and more cost-effective to execute than experiments. However, each CFD result inherently contains numerical errors that can significantly degrade the accuracy of a simulation. Discretization error is typically the largest contributor to the overall numerical error in a given simulation. Discretization error can be very difficult to estimate since the generation, transport, and diffusion of these errors is a highly nonlinear function of the computational grid and discretization scheme. As CFD is increasingly used in engineering design and analysis, it is imperative that CFD practitioners be able to accurately quantify discretization errors to minimize risk and improve the performance of engineering systems. In this work, improvements are made to the accuracy and efficiency of existing error estimation techniques. Discretization error is estimated by deriving and solving an error transport equation (ETE) for the local discretization error everywhere in the computational domain. Truncation error is shown to act as the local source for discretization error in numerical solutions. An equivalence between adjoint methods and ETE methods for functional error estimation is presented. This adjoint/ETE equivalence is exploited to efficiently obtain error estimates for multiple output functionals and to extend the higher-order properties of adjoint methods to ETE methods. Higher-order discretization error estimates are obtained when truncation error estimates are sufficiently accurate. Truncation error estimates are demonstrated to deteriorate on grids with a non-smooth variation in grid metrics (e.g., unstructured grids) regardless of how smooth the underlying exact solution may be. The loss of accuracy is shown to stem from noise in the discrete solution on the order of discretization error. When using conventional least-squares reconstruction techniques, this noise is exactly captured and introduces a lower-order error into the truncation error estimate. A novel reconstruction method based on polyharmonic smoothing splines is developed to smoothly reconstruct the discrete solution and improve the accuracy of error estimates. Furthermore, a method for iteratively improving discretization error estimates is devised. Efficiency and robustness considerations are discussed. Results are presented for several inviscid and viscous flow problems. To facilitate the study of discretization error estimation, a new, higher-order finite-volume solver is developed. A detailed description of the code base is provided along with a discussion of best practices for CFD code design. / Ph. D. / Computational fluid dynamics (CFD) is a branch of computational physics at the intersection of fluid mechanics and scientific computing in which the governing equations of fluid motion, such as the Euler and Navier-Stokes equations, are solved numerically on a computer. CFD is utilized in numerous fields including biomedical engineering, meteorology, oceanography, and aerospace engineering. CFD simulations can provide tremendous insight into physical processes and are often preferred over experiments because they can be performed more quickly, are typically more cost-effective, and can provide data in regions where it may be difficult to measure. While CFD can be an extremely powerful tool, CFD simulations are inherently subject to numerical errors. These errors, which are generated when the governing equations of fluid motion are solved on a computer, can have a significant impact on the accuracy of a CFD solution. If numerical errors are not accurately quantified, ill-informed decision-making can lead to poor system performance, increased risk of injury, or even system failure. In this work, research efforts are focused on numerical error estimation for the finite -volume method, arguably the most widely used numerical algorithm for solving CFD problems. The error estimation techniques provided herein target discretization error, the largest contributor to the overall numerical error in a given simulation. Discretization error can be very difficult to estimate since these errors are generated, convected, and diffused by the same physical processes embedded in the governing equations. In this work, improvements are made to the accuracy and efficiency of existing discretization error estimation techniques. Results are presented for several inviscid and viscous flow problems. To facilitate the study of these error estimators, a new, higher-order finite -volume solver is developed. A detailed description of the code base is provided along with a discussion of best practices for CFD code design.

In this thesis, I apply the adjoint for the Community Multiscale Air Quality model (hereafter CMAQ-ADJ) in a high spatial resolution study of the sensitivity of ozone to several of its precursors in the regions surrounding the Great Lakes. CMAQ-ADJ was originally developed for low spatial resolution applications. In order to use it in high spatial resolution (12 km) studies, it was necessary to resolve a conflict between the pre-set fixed output time step interval in CMAQ-ADJ and the CMAQ-calculated irregular synchronization time-step and also to modify the meteorological interface for the backward model integrations. To increase computation efficiency, the chemistry time-step in the modified CMAQ-ADJ is checkpointed instead of being re-calculated in the backward part of the model as before. I used the modified model to analyze the sensitivity of ozone to precursor species for cases of assumed high ozone episode in two target locations in southwestern and east-central Ontario. The studies examined the influence of pre-existing ozone, NO, CO, anthropogenic volatile organic compounds (VOCs) and isoprene on ozone level changes for the 69 hours immediately preceding the assumed high ozone event. The results are dominated by the long-distance advection, local meteorology (lake breezes), air temperature, the underlying surface features, and emissions in the pollutant pathway. Both production and titration of ozone by NOx is evident at different times and locations in the simulations. The industrial Midwest U.S. and Ohio Valley have been shown to be an important source of anthropogenic emission of NO and most VOCs that contribute to high ozone events in southwestern and east-central Ontario. Isoprene from the northern forest suppresses ozone in both target regions, with a greater magnitude in east-central Ontario. The response of ozone level in the two selected receptor regions in Ontario to different VOCs depends on the type of VOC, the time and location they are emitted, and the air temperature. Increasing VOC emissions in urban areas such as Toronto and Ottawa in the morning can enhance the ozone level by late afternoon. Increasing VOCs except ethylene and formaldehyde in regions with large VOC/NOx ratio in the morning tends to suppress the ozone level by late afternoon. Among all the species examined, NO has the largest impact on the target ozone level changes. CO is very unlikely to significantly influence the ozone level changes in southwestern or east-central Ontario.

In this thesis, I apply the adjoint for the Community Multiscale Air Quality model (hereafter CMAQ-ADJ) in a high spatial resolution study of the sensitivity of ozone to several of its precursors in the regions surrounding the Great Lakes. CMAQ-ADJ was originally developed for low spatial resolution applications. In order to use it in high spatial resolution (12 km) studies, it was necessary to resolve a conflict between the pre-set fixed output time step interval in CMAQ-ADJ and the CMAQ-calculated irregular synchronization time-step and also to modify the meteorological interface for the backward model integrations. To increase computation efficiency, the chemistry time-step in the modified CMAQ-ADJ is checkpointed instead of being re-calculated in the backward part of the model as before. I used the modified model to analyze the sensitivity of ozone to precursor species for cases of assumed high ozone episode in two target locations in southwestern and east-central Ontario. The studies examined the influence of pre-existing ozone, NO, CO, anthropogenic volatile organic compounds (VOCs) and isoprene on ozone level changes for the 69 hours immediately preceding the assumed high ozone event. The results are dominated by the long-distance advection, local meteorology (lake breezes), air temperature, the underlying surface features, and emissions in the pollutant pathway. Both production and titration of ozone by NOx is evident at different times and locations in the simulations. The industrial Midwest U.S. and Ohio Valley have been shown to be an important source of anthropogenic emission of NO and most VOCs that contribute to high ozone events in southwestern and east-central Ontario. Isoprene from the northern forest suppresses ozone in both target regions, with a greater magnitude in east-central Ontario. The response of ozone level in the two selected receptor regions in Ontario to different VOCs depends on the type of VOC, the time and location they are emitted, and the air temperature. Increasing VOC emissions in urban areas such as Toronto and Ottawa in the morning can enhance the ozone level by late afternoon. Increasing VOCs except ethylene and formaldehyde in regions with large VOC/NOx ratio in the morning tends to suppress the ozone level by late afternoon. Among all the species examined, NO has the largest impact on the target ozone level changes. CO is very unlikely to significantly influence the ozone level changes in southwestern or east-central Ontario.

Strides in modern computational fluid dynamics and leaps in high-power computing have led to unprecedented capabilities for handling large aerodynamic problem. In particular, the emergence of adjoint design methods has been a break-through in the field of aerodynamic shape optimization. It enables expensive, high-dimensional optimization problems to be tackled efficiently using gradient-based methods in CFD; a task that was previously inconceivable. However, adjoint design methods are intended for gradient-based optimization; the curse of dimensionality is still very much alive when it comes to design space exploration, where gradient-free methods cannot be avoided. This research describes a novel approach for reducing dimensionality in large, computationally expensive design problems to a point where gradient-free methods become possible. This is done using an innovative application of Principal Component Analysis (PCA), where the latter is applied to the gradient distribution of the objective function; something that had not been done before. This yields a linear transformation that maps a high-dimensional problem onto an equivalent low-dimensional subspace. None of the original variables are discarded; they are simply linearly combined into a new set of variables that are fewer in number. The method is tested on a range of analytical functions, a two-dimensional staggered airfoil test problem and a three-dimensional Over-Wing Nacelle (OWN) integration problem. In all cases, the method performed as expected and was found to be cost effective, requiring only a relatively small number of samples to achieve large dimensionality reduction.

Coupled systems are ubiquitous in modern engineering and science. Such systems can encompass fluid dynamics, structural mechanics, chemical species transport and electrostatic effects among other components, all of which can be coupled in many different ways. In addition, such models are usually multiscale, making their numerical simulation challenging, and necessitating the use of adaptive modeling techniques. The multiscale, multiphysics models of electrosomotic flow (EOF) constitute a particularly challenging coupled flow system. A special feature of such models is that the coupling between the electric physics and hydrodynamics is via the boundary. Numerical simulations of coupled systems are typically targeted towards specific Quantities of Interest (QoIs). Adjoint-based approaches offer the possibility of QoI targeted adaptive mesh refinement and efficient parameter sensitivity analysis. The formulation of appropriate adjoint problems for EOF models is particularly challenging, due to the coupling of physics via the boundary as opposed to the interior of the domain. The well-posedness of the adjoint problem for such models is also non-trivial. One contribution of this dissertation is the derivation of an appropriate adjoint problem for slip EOF models, and the development of penalty-based, adjoint-consistent variational formulations of these models. We demonstrate the use of these formulations in the simulation of EOF flows in straight and T-shaped microchannels, in conjunction with goal-oriented mesh refinement and adjoint sensitivity analysis. Complex computational models may exhibit uncertain behavior due to various reasons, ranging from uncertainty in experimentally measured model parameters to imperfections in device geometry. The last decade has seen a growing interest in the field of Uncertainty Quantification (UQ), which seeks to determine the effect of input uncertainties on the system QoIs. Monte Carlo methods remain a popular computational approach for UQ due to their ease of use and "embarassingly parallel" nature. However, a major drawback of such methods is their slow convergence rate. The second contribution of this work is the introduction of a new Monte Carlo method which utilizes local sensitivity information to build accurate surrogate models. This new method, called the Local Sensitivity Derivative Enhanced Monte Carlo (LSDEMC) method can converge at a faster rate than plain Monte Carlo, especially for problems with a low to moderate number of uncertain parameters. Adjoint-based sensitivity analysis methods enable the computation of sensitivity derivatives at virtually no extra cost after the forward solve. Thus, the LSDEMC method, in conjuction with adjoint sensitivity derivative techniques can offer a robust and efficient alternative for UQ of complex systems. The efficiency of Monte Carlo methods can be further enhanced by using stratified sampling schemes such as Latin Hypercube Sampling (LHS). However, the non-incremental nature of LHS has been identified as one of the main obstacles in its application to certain classes of complex physical systems. Current incremental LHS strategies restrict the user to at least doubling the size of an existing LHS set to retain the convergence properties of LHS. The third contribution of this research is the development of a new Hierachical LHS algorithm, that creates designs which can be used to perform LHS studies in a more flexibly incremental setting, taking a step towards adaptive LHS methods. / text

Le mode adjoint de la Différentiation Algorithmique (DA) est particulièrement intéressant pour le calcul des gradients. Cependant, ce mode utilise les valeurs intermédiaires de la simulation d'origine dans l'ordre inverse à un coût qui augmente avec la longueur de la simulation. La DA cherche des stratégies pour réduire ce coût, par exemple en profitant de la structure du programme donné. Dans ce travail, nous considérons d'une part le cas des boucles à point-fixe pour lesquels plusieurs auteurs ont proposé des stratégies adjointes adaptées. Parmi ces stratégies, nous choisissons celle de B. Christianson. Nous spécifions la méthode choisie et nous décrivons la manière dont nous l'avons implémentée dans l'outil de DA Tapenade. Les expériences sur une application de taille moyenne montrent une réduction importante de la consommation de mémoire. D'autre part, nous étudions le checkpointing dans le cas de programmes parallèles MPI avec des communications point-à-point. Nous proposons des techniques pour appliquer le checkpointing à ces programmes. Nous fournissons des éléments de preuve de correction de nos techniques et nous les expérimentons sur des codes représentatifs. Ce travail a été effectué dans le cadre du projet européen ``AboutFlow'' / The adjoint mode of Algorithmic Differentiation (AD) is particularly attractive for computing gradients. However, this mode needs to use the intermediate values of the original simulation in reverse order at a cost that increases with the length of the simulation. AD research looks for strategies to reduce this cost, for instance by taking advantage of the structure of the given program. In this work, we consider on one hand the frequent case of Fixed-Point loops for which several authors have proposed adapted adjoint strategies. Among these strategies, we select the one introduced by B. Christianson. We specify further the selected method and we describe the way we implemented it inside the AD tool Tapenade. Experiments on a medium-size application shows a major reduction of the memory needed to store trajectories. On the other hand, we study checkpointing in the case of MPI parallel programs with point-to-point communications. We propose techniques to apply checkpointing to these programs. We provide proof of correctness of our techniques and we experiment them on representative CFD codes

O objetivo desse trabalho consiste no estudo de métodos de identificação de parâmetros em problemas envolvendo a equação de advecção-difusão 2D. Essa equação é resolvida utilizando o método dos volumes finitos, sendo empregada métodos de reconstrução de alta ordem em malhas não-estruturadas de triângulos para calcular os fluxos nas faces dos volumes de controle. Como ferramenta de busca dos parâmetros é empregada a técnica baseadas em gradientes, sendo os mesmos calculados utilizando processos baseados em métodos adjuntos. / The aim of this work concern to study parameter identification methods on problems involving the advection-diffusion equation in two dimensions. This equation is solved employing the finite volume methods, and high-order reconstruction methods, on triangle unstructured meshes to solve the fluxes across the faces of control volumes. As parameter searching tool is employed technicals based on gradients. The gradients are solved using processes based on adjoint methods.

O objetivo desse trabalho consiste no estudo de métodos de identificação de parâmetros em problemas envolvendo a equação de advecção-difusão 2D. Essa equação é resolvida utilizando o método dos volumes finitos, sendo empregada métodos de reconstrução de alta ordem em malhas não-estruturadas de triângulos para calcular os fluxos nas faces dos volumes de controle. Como ferramenta de busca dos parâmetros é empregada a técnica baseadas em gradientes, sendo os mesmos calculados utilizando processos baseados em métodos adjuntos. / The aim of this work concern to study parameter identification methods on problems involving the advection-diffusion equation in two dimensions. This equation is solved employing the finite volume methods, and high-order reconstruction methods, on triangle unstructured meshes to solve the fluxes across the faces of control volumes. As parameter searching tool is employed technicals based on gradients. The gradients are solved using processes based on adjoint methods.