L'analyse de sensibilité pour la simulation numérique des écoulements compressibles en aérodynamique externe par rapport à la discrétisation de maillage et aux incertitudes liées à des paramètres d'entrées du modèle a été traitée 1- par le moyen des méthodes adjointes pour le calcul de gradient et 2- par approximations stochastiques non-intrusives basées sur des grilles creuses. 1- Une méthode d'adaptation de maillages goal-oriented basée sur les dérivées totales des fonctions aérodynamiques d'intérêt par rapport aux nœuds du maillage a été introduite sous une forme améliorée. La méthode s'applique au cadre de volumes finis pour des écoulements RANS pour des maillages mono-bloc et multi-bloc structurés. Des applications 2D pour des écoulements transsoniques ainsi que subsonique détaché atour d'un profil pour l'estimation du coefficient de traînée sont présentées. L'apport de la méthode proposée est vérifié. 2- Les méthodes du polynôme de chaos généralisé sous forme pseudospectrale creuse et de la collocation stochastique construite sur des grilles creuses isotropes et anisotropes sont examinées. Les maillages anisotropes sont obtenus par le biais d'une méthode adaptive basée sur l'analyse de sensibilité globale. L'efficacité des ces approximations est testée avec des fonctions test et des écoulements aérodynamiques visqueux autour d'un profil en présence d'incertitudes géométriques et opérationnelles. L'intégration des méthodes et aboutissements 1- et 2- dans une approche couplée permettrait de contrôler de façon équilibrée l'erreur déterministe/stochastique goal-oriented. / Sensitivity analysis for the numerical simulation of external aerodynamics compressible flows with respect to the mesh discretization and to the model input parametric uncertainty has been addressed respectively 1- through adjoint-based gradient computation techniques and 2- through non-intrusive stochastic approximation methods based on sparse grids. 1- An enhanced goal-oriented mesh adaptation method based on aerodynamic functional total derivatives with respect to mesh coordinates in a RANS finite-volume mono-block and non-matching multi-block structured grid framework is introduced. Applications to 2D RANS flow about an airfoil in transonic and detached subsonic conditions for the drag coefficient estimation are presented. The asset of the proposed method is patent. 2- The generalized Polynomial Chaos in its sparse pseudospectral form and stochastic collocation methods based on both isotropic and dimension-adapted sparse grids obtained through an improved dimension-adaptivity method driven by global sensitivity analysis are considered. The stochastic approximations efficiency is assessed on multi-variate test functions and airfoil viscous aerodynamics simulation in the presence of geometrical and operational uncertainties. Integration of achievements 1- and 2- into a coupled approach in future work will pave the way for a well-balanced goal-oriented deterministic/stochastic error control.

Large-scale unsteady flow structures play an influential role in the dynamics of many practical flows, such as those found in gas turbine combustion chambers. This thesis is concerned primarily with large-scale unsteady structures that arise due to self-sustained hydrodynamic oscillations, also known as global hydrodynamic instability. Direct numerical simulation (DNS) of the Navier--Stokes equations in the low Mach number limit is used to obtain a steady base flow, and the most unstable direct and adjoint global modes. These are combined, using a structural sensitivity framework, to identify the region of the flow and the feedback mechanisms that are responsible for causing the global instability. Using a Lagrangian framework, the direct and adjoint global modes are also used to identify the regions of the flow where steady and unsteady control, such as a drag force or heat input, can suppress or promote the global instability. These tools are used to study a variety of reacting and non-reacting flows to build an understanding of the physical mechanisms that are responsible for global hydrodynamic instability in swirling diffusion flames. In a non-swirling lifted jet diffusion flame, two modes of global instability are found. The first mode is a high-frequency mode caused by the instability of the low-density jet shear layer in the premixing zone. The second mode is a low-frequency mode caused by an instability of the outer shear layer of the flame. Two types of swirling diffusion flames with vortex breakdown bubbles are considered. They show qualitatively similar behaviour to the lifted jet diffusion flames. The first type of flame is unstable to a low-frequency mode, with wavemaker located at the flame base. The second type of flame is unstable to a high-frequency mode, with wavemaker located at the upstream edge of the vortex breakdown bubble. Feedback from density perturbations is found to have a strong influence on the unstable modes in the reacting flows. The wavemaker of the high-frequency mode in the reacting flows is very similar to its non-reacting counterpart. The low-frequency mode, however, is only observed in the reacting flows. The presence of reaction increases the influence of changes in the base flow mixture fraction profiles on the eigenmode. This increased influence acts through the heat release term. These results emphasize the possibility that non-reacting simulations and experiments may not always capture the important instability mechanisms of reacting flows, and highlight the importance of including heat release terms in stability analyses of reacting flows.

Cette thèse vise à mettre en place une méthode de calcul automatique de forme optimale pour les antennes, par modification de la forme des motifs métalliques constituant les éléments rayonnants d'une antenne. La première partie propose un état de l'art des deux principales thématiques de cette thèse. Le chapitre 1 présente la simulation électromagnétique des antennes, basée sur la méthode des équations intégrales et résolue par éléments finis de frontière. Le chapitre 2 présente l'algorithme d'optimisation de forme utilisé, qui couple une analyse de sensibilité avec la méthode Level Set pour l’évolution de la géométrie. La deuxième partie s’intéresse à l'application de cet algorithme d'optimisation au problème qui a motivé cette thèse, à savoir le calcul de la forme optimale d'un motif métallique sur un élément rayonnant. Le calcul des champs électriques et magnétiques est effectué par la méthode des équations intégrales, qui renvoie notamment l’observable à minimiser : le coefficient de réflexion de l’antenne. Les chapitres 3 et 4 présentent les aspects théoriques de ce travail, dans le domaine continu et le domaine discret respectivement. La troisième partie explique la mise en œuvre numérique des résultats établis théoriquement dans la partie 2. Le chapitre 5 décrit la boucle globale de l'algorithme d'optimisation de forme. Les résultats obtenus par cet algorithme sont présentés dans le chapitre 6 : ils s’appuient sur plusieurs éléments rayonnants dont la forme de la métallisation évolue afin d’optimiser le coefficient de réflexion ainsi que d'autres critères dérivés. / This thesis aims at establishing a method which computes automatically the optimal design of an antenna, by modifying the shape of metallic patterns constituting the radiating elements of an antenna. In the first part is proposed a state of the art of the two main topics of this thesis. The electromagnetic simulation of antennas based on the integral equations method and solved by the boundary elements method is presented in Chapter 1. Chapter 2 presents the utilized shape optimization algorithm, which combines a sensitivity analysis and the Level Set method for tracking the evolution of the geometry. The second part deals with the application of this optimization algorithm to the problem that motivated this thesis, namely computing the optimal shape of a metallic pattern on a radiating element. The electric and magnetic fields computation is performed by the integral equation method which returns, among others, the observable to minimize: the reflection coefficient. Chapters 3 and 4 present the theoretical aspects of this work, in the continuous domain and the discrete domain respectively. In part 3 is explained the numerical implementation of the theoretical results established in part 2. Chapter 5 addresses the global loop of the shape optimization algorithm. The numerical results obtained by this algorithm are set out in chapter 6: they are based on several radiating elements whose shape of the metallization evolves in order to optimize the reflection coefficient as well as other derived criteria.

Cílem mé disertační práce je analyzovat a vyvinout parametrizační metodu pro 2D a 3D tvarové optimalizace v kontextu průmyslového aerodynamického návrhu letounu založeném na CFD simulacích. Aerodynamická tvarová optimalizace je efektivní nástroj, který si klade za cíl snížení nákladů na návrh letounů. Nástroj založený na automatickém hledání optimálního tvaru. Klíčovou částí úspěšného optimalizačního procesu je použití vhodné parametrizační metody, metody schopné garantovat možnost dosažení optimálního tvaru. Parametrizační metody obecně používané v oblasti aerodynamické tvarové optimalizace momentálně nejsou připravený na komplikované průmyslové aplikace vyskytující se u moderních dopravních letounů, které mají šípová zalomená křídla s winglety a motorovými gondolami, přechodové prvky spojující např. trup s křídlem atd.. Existuje tedy potřeba nalezení obecné parametrizační metody, která bude aplikovatelná na širokou škálu různých geometrických tvarů. Free-Form Deformation (FFD[1]) parametrizace může, vzhledem ke svým schopnostem při zacházení s geometrií, být odpovědí na tuto potřebu. Adaptivní parametrizace by se měla být schopna automaticky přizpůsobit danému tvaru tak, aby byly její kontrolní body vhodně rozmístěny. Což umožní dostatečnou kontrolu deformací objektu, která zaručí možnost vytvoření optimálního tvaru objektu a splnění geometrických omezení. Primární aplikací takové parametrizační metody je deformace tvaru objektu. Dalším navrhovaným cílem je modifikace FFD parametrizační metody pro současné deformace tvaru objektu a CFD výpočetní sítě, umožnující velké deformace objektu při zachování kvality výpočetní sítě.

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This thesis covers recent advances in the adjoint variable method for the sensitivity estimations through time-domain electromagnetic simulations. It considers both frequency-independent and frequency-dependent response functions, and at the same time, provides a novel adjoint treatment for addressing dispersive sensitivity parameters in the material constitutive relation. With this proposed adjoint technique, response sensitivities with respect to all N sensitivity parameters can be computed through at most one extra simulations regardless of the value of N. This thesis also extends the existing adjoint technique to estimate all N^2 second-order sensitivity entries in the response Hessian matrix through N additional simulations. All adjoint sensitivity techniques presented in this thesis are numerically validated through various practical examples. Comparison shows that our produced adjoint results agree with those produced through central finite-difference approximations or through exact analytical approaches. / Dissertation / Doctor of Engineering (DEng)

For accurate prediction of tsunami wave propagation, information on the system of PDEs modelling its evolution and full initial and/or boundary data is required. However the latter is not generally fully available, and so the primary objective becomes to find an optimal estimate of these conditions, using available information. Data Assimilation is a methodology used to optimally integrate observed measurements into a mathematical model, to generate a better estimate of some control parameter, such as the initial condition of the wave, or the sea floor bathymetry. In this study, we considered the shallow water equations in both linear and non-linear form as an approximation for ocean wave propagation, and derived a data assimilation scheme based on the calculus of variations, the purpose of which is to optimise some distorted form of the initial condition to give a prediction closer to the exact initial data. We considered two possible forms of distortion, by adding noise to our initial wave, and by rescaling the wave amplitude. Multiple cases were analysed, with observations measured at different points in our spatial domain, as well as variations in the number of observation points. We found that the error between measurements and observation data was sufficiently minimised across all cases. A relationship was found between the number of measurement points and the error, dependent on the choice of where measurements were taken. In the linear case, since the wave form simply translates a fixed form, multiple measurement points did not necessarily provide more information. In the nonlinear case, because the waveform changes shape as it translates, adding more measurement points provides more information about the dynamics and the wave shape. This is reflected in the fact that in the nonlinear case adding more points gave a bigger decrease in error, and much closer convergence of the optimised guess for our initial condition to the exact initial wave profile. / Thesis / Master of Science (MSc) / In ocean wave modelling, information on the system dynamics and full initial and/or boundary data is required. When the latter is not fully available the primary objective is to find an optimal estimate of these conditions, using available information. Data Assimilation is a methodology used to optimally integrate observed measurements into a mathematical model, to generate a better estimate of some control parameter, such as the initial condition of the wave, or the sea floor bathymetry. In this study, we considered the shallow water equations in both linear and non-linear form as an approximation for ocean wave propagation, and derived a data assimilation scheme to optimise some distorted form of the initial condition to generate predictions converging to the exact initial data. The error between measurements and observation data was sufficiently minimised across all cases. A relationship was found between the number of measurement points and the error, dependent on the choice of where measurements were taken.

We propose an efficient wideband theory for adjoint variable sensitivity analysis of problems with general anisotropic materials. The method is formulated based on the transmission line numerical modeling technique. The anisotropic material properties of potential interest are the full tensors of permittivity, permeability, electrical conductivity, magnetic resistivity, magnetoelectric coupling, and electromagnetic coupling. The tensors may contain non-diagonal elements. Our method estimates the gradients of the desired response with respect to all designable parameters using at most one extra simulation, regardless of their number. In contrast, in the conventional sensitivity analysis method using central finite differences, the number of the required simulations scales linearly with the number of designable parameters. The theory has been implemented for sensitivity analysis of the two and three-dimensional structures. The available adjoint variable method (AVM) sensitivities enable the optimization-based design of anisotropic and dispersive anisotropic structures. We apply our AVM technique to optimization-based wideband invisibility cloak design of arbitrary-shape objects. Our method optimizes the voxel-by-voxel constitutive parameters of an anisotropic cloak. This results in a large number of optimizable parameters. The associated sensitivities of a wideband cloaking objective function are efficiently estimated using our anisotropic adjoint variable method technique. A gradient-based optimization algorithm utilizes the available sensitivity information to iteratively minimize the visibility objective function and to determine the constitutive parameters of the optimal cloak. / Thesis / Doctor of Philosophy (PhD)

Optimization methods are commonly used to develop new products and are also an importantstep in more incremental design improvements. In the maritime industry, these methodsare often used to create more ecient vessels and to ful ll the environmental requirementsimposed by the IMO. In recent years, the adjoint method have been used more frequently.This method can be used to predict the inuence of some input parameters on a quantityin a Computational Fluid Dynamics (CFD) simulation.In this project, the adjoint method has been investigated and applied on a relevant case;how it can be used to reduce the drag of a twisted rudder by changing the twist angles.STAR-CCM+ has been used to perform the CFD and adjoint simulations. These resultshave been imported to CAESES, a CAD-modeler, which connects the adjoint results to thedesign parameters. The adjoint results indicate a possible change of the design parameter,the twist angle is modi ed based on these results and a new geometry of the rudder is constructedin CAESES. Furthermore, the numerical results indicates that the method can beused to reduce the drag on the rudder. One of the cases in the project achieved a reductionof the rudder drag by 3.35 % and the total drag decreased with 0.18 %. However, the othertwo cases did not achieve a reduction of the drag and hence further investigations needs tobe done.The adjoint method have the possibility to be a good optimization alternative for developmentof new products or in engineering-to-order processes. The option of connecting theadjoint results to design parameters is a great advantage. On the other hand, the method inthis project is not reliable and the reason for the contradictory results needs to be studiedfurther. / Optimeringsmetoder är vanligt förekommande när nya produkter utvecklas och är också ett viktigt steg i inkrementella designförbättringar. I sjöfartsindustrin används dessa metoder för att skapa effektivare fartyg och för att uppfylla miljökraven framtagna av IMO. På senare år har adjointmetoden börjat användas mer. Metoden kan användas för att förutspåindataparametrars inverkan på en kvantitet i en strömningsmekanisk beräkning, även kallat CFD. I det här projektet ska adjointmetoden utvärderas och hur den kan användas för att reducera motståndet på ett tvistat roder genom att ändra tvist vinklarna. STAR-CCM+ har använts för att utföra CFD- och adjointberäkningarna. Dessa resultat importerades till en CAD-modellerare, CAESES, som kopplar adjointresultaten till designvariabler. Resultaten från adjointsimuleringen indikerar en möjlig förändring av designvariabeln, som sedan ändras utefter detta resultat och en ny rodergeometri genereras av CAESES. De numeriska resultaten indikerar att adjointmetoden kan användas för att reducera motståndet på ett tvistat roder. I ett av fallen i projektet reducerades motståndet med 3,35 % och det totala motståndet för hela fartyget reducerades med 0,18 %. Däremot så påvisade två andra fall ingen förändring av rodermotståndet och anledningen till detta kräver ytterligare unders ökningar. Adjointmetoden har möjligheterna att bli ett bra alternativ i en optimeringsprocess och för utveckling av nya produkter. Möjligheten att koppla adjointresultaten till designvariabler är också en stor fördel. Däremot så är metoden i detta projekt inte så tillförlitlig och anledningen till de motsägelsefulla resultaten måste studeras ytterligare.