The proper orthogonal decomposition (POD) has been widely used in fluid dynamic applications for extracting dominant flow features. The “gappy” POD is an extension to this method that allows the consideration of incomplete data sets. In this paper, the gappy POD is extended to handle unsteady flow reconstruction problems, such as those encountered when limited flow measurement data is available. In addition, a systematic approach for effective sensor placement is formulated within the gappy framework. Two applications are considered. The first aims to reconstruct the unsteady flow field using a small number of surface pressure measurements for a subsonic airfoil undergoing plunging motion. The second considers estimation of POD modal content of a cylinder wake flow for active control purposes. In both cases, using the dominant POD basis vectors and a small number of sensor signals, the gappy approach is found to yield accurate flow reconstruction results. / Singapore-MIT Alliance (SMA)

L'assimilation de données en tant qu'outil pour la mécanique des fluides a connu une croissance exponentielle au cours des dernières décennies. La possibilité de combiner des mesures précises mais partielles avec un modèle dynamique complet est précieuse et a de nombreuses applications dans des domaines allant de l'aérodynamique, à la géophysique et à l’aéraulique. Cependant, son utilité reste limitée en raison des contraintes imposées par l'assimilation de données notamment en termes de puissance de calcul, de besoins en mémoire et en informations préalables. Cette thèse tente de remédier aux différentes limites de la procédure d'assimilation pour faciliter plus largement son utilisation en mécanique des fluides. Un obstacle majeur à l'assimilation des données est un coût de calcul prohibitif pour les écoulements complexes. Une modélisation de la turbulence à grande échelle est intégrée à la procédure d'assimilation afin de réduire considérablement la coût de calcul et le temps requis. La nécessité d'une information volumétrique préalable pour l'assimilation est abordée à l'aide d'une nouvelle méthodologie de reconstruction développée et évaluée dans cette thèse. L'algorithme d'optimisation reconstruit les champs 3D à partir d'observations dans deux plans orthogonaux en exploitant l'homogénéité directionnelle. La méthode et ses variantes fonctionnent bien avec des ensembles de données synthétiques et expérimentaux fournissant des reconstructions précises. La méthodologie de reconstruction permet également d’estimer la matrice de covariance d’ébauche indispensable à un algorithme d’assimilation efficace. Tous les ingrédients sont combinés pour effectuer avec succès l'assimilation de données variationnelles d'un écoulement turbulent dans le sillage d'un cylindre à un nombre de Reynolds transitoire. L'algorithme d'assimilation est validé pour des observations volumétriques synthétiques et est évalué sur des observations expérimentales dans deux plans orthogonaux. / Data assimilation as a tool for fluid mechanics has grown exponentially over the last few decades. The ability to combine accurate but partial measurements with a complete dynamical model is invaluable and has numerous applications to fields ranging from aerodynamics, geophysics, and internal ventilation. However, its utility remains limited due to the restrictive requirements for performing data assimilation in the form of computing power, memory, and prior information. This thesis attempts at redressing various limitations of the assimilation procedure in order to facilitate its wider use in fluid mechanics. A major roadblock for data assimilation is the computational cost which is restrictive for all but the simplest of flows. Following along the lines of Joseph Smagorinsky, turbulence modelling through large-eddy simulation is incorporated in to the assimilation procedure to significantly reduce computing power and time required. The requirement for prior volumetric information for assimilation is tackled using a novel reconstruction methodology developed and assessed in this thesis. The snapshot optimisation algorithm reconstructs 3D fields from 2D cross- planar observations by exploiting directional homogeneity. The method and its variants work well with synthetic and experimental data-sets providing accurate reconstructions. The reconstruction methodology also provides the means to estimate the background covariance matrix which is essential for an efficient assimilation algorithm. All the ingredients are combined to perform variational data assimilation of a turbulent wake flow around a cylinder successfully at a transitional Reynolds number. The assimilation algorithm is validated with synthetic volumetric observation and assessed on 2D cross-planar observations emulating experimental data.

<p>    </p> <p>Cerebral aneurysms are presented in 3-5% of the population and account for approximately 10% of all strokes. The clinical decision on treating unruptured aneurysms should not be taken lightly because a majority of the asymptomatic cerebral aneurysm will not rupture, while both endovascular and microsurgical treatments carry the risk of morbidity and mortality. Thus, there is a need for objective risk assessment to reliably predict the high-risk aneurysms to intervene. Recent studies have found that the blood flow hemodynamic metrics such as pressure and wall shear stress (WSS) are related to the growth and rupture of the aneurysms. 4D flow magnetic resonance imaging (MRI) measures time-resolved three-dimensional velocity fields in the aneurysms <em>in vivo</em>, allowing for the evaluation of hemodynamic parameters. This work presents the developments of flow-physics constrained data enhancement and augmentation methods for 4D flow MRI to assist the risk stratification of cerebral aneurysms. First, a phase unwrapping and denoising method is introduced to enhance the dynamic range and accuracy of 4D flow MRI velocity measurement by incorporating the divergence-free constraint of incompressible flow. Moreover, methods are developed to improve the estimation of hemodynamic parameters from 4D flow data including pressure and WSS. The pressure reconstruction method is also applied to the flow data acquired using particle imaging velocimetry (PIV) and particle tracking velocimetry (PTV) and shows superior performance as compared to the existing methods by solving the pressure Poisson equation. We also proposed a framework to estimate the uncertainty of the PIV/PTV based pressure estimation by propagating the velocity uncertainty. In addition, a multi-modality approach is introduced to enhances the resolution and accuracy of 4D flow data with sparse representation, which improves the reliability of the hemodynamic evaluation. Finally, we present a method to measure the left ventricular flow propagation velocity from cardiac imaging to help in assessing the diastolic function. </p>

In this thesis we address the problem of control flow reconstruction in the presence of indirect jumps. We introduce an alternating approach which combines both overand under-approximation to increase the precision of the reconstructed control flow automaton compared to pure over-approximation. More specifically, the abstract interpretation based tool, Jakstab, from earlier work by Kinder, is used for the over-approximation. Furthermore, directed symbolic execution is applied to under-approximate successors of instructions when these can not be over-approximated precisely. The results of our experiments show that our approach can improve the precision of the reconstructed CFA compared to only using Jakstab. However, they reveal that our approach consumes a large amount of memory since it requires extraction and temporary storage of a large number of possible paths to the unresolved locations. As such, its usability is limited to control flow automatas of limited complexity. Further, the results show that strided interval analysis suffers in performance when encountering particularly challenging loops in the control flow automaton. / I detta examensarbete studeras hur rekonstruktion av kontrollflöde kan utföras i närvaro av indirekta hoppinstruktioner. I examensarbetet introduceras ett alternerande tillvägagångssätt som kombinerar både överoch underapproximation för att öka precisionen av den rekonstruerade kontrollflödesautomaten jämfört med endast överapproximation. Mer specifikt används det abstrakta tolknings-baserade verktyget, Jakstab, tidigare utvecklat av Kinder, för överapproximation. Vidare nyttjas riktad symbolisk exekvering för att underapproximera efterträdare till instruktioner när dessa inte kunnat överapproximeras med hög precision. Resultaten av våra experiment visar att vårt tillvägagångssätt kan förbättra precisionen hos den rekonstruerade kontrollflödesautomaten jämfört med att endast använda Jakstab. Dock visar de att vårt tillvägagångssätt kan fordra en stor mängd minne då det kräver extraktion och tillfällig lagring av ett stort antal möjliga vandringar från programmets ingång till de olösta programpositionerna. Därmed är dess användbarhet limiterad till kontrollflödesautomater av begränsad complexitet. Vidare visar resultaten av våra experiment även att analyser baserade på klivande intervaller tappar i prestanda när de möter en vis typ av loopar i kontrollflödesautomaten.

No description available.