The flow of blood in the human body is a very important component in un-derstanding a number of different ailments such as atherosclerosis and a falseaneurysm. In this thesis, we have utilized Poiseuille’s solution to Navier-Stokesequations with a Newtonian, incompressible fluid flowing laminar with zero ac-celeration in a pipe with non-flexible walls in order to study blood flow in anarterial tree. In order to study and simulate a larger arterial tree we have uti-lized a primitive building block, a bifurcation with one inlet and two outlets,joined together forming a tree. By prescribing an inlet flow and the pressureat every outlet at the bottom of the tree we have shown that we may solvethe system by fixed-point iteration, the Matlab functionfsolve, and Newton’smethod. This way of using primitive building blocks offers a flexible way to doanalysis as it makes it possible to easily change the shape of the tree as well asadding new building blocks such as a block that represents arteriosclerosis.

We present a novel approach for deriving analytical solutions to transport equations expressedin similarity variables. We apply a fixed-point iteration procedure to these transformedequations by formally solving for the highest derivative term and then integrating to obtainan expression for the solution in terms of a previous estimate. We are able to analyticallyobtain the Lipschitz condition for this iteration procedure and, from this (via requirements forconvergence given by the contraction mapping principle), deduce a range of values for the outerlimit of the solution domain, for which the fixed-point iteration is guaranteed to converge.

Dans cette thèse, une nouvelle méthode de frontières immergées a été développée pour la simulation d'interaction fluide-structure, appelée la méthode de frontières immergées mobiles (en langage anglo-saxon: MIBM). L'objectif principal de cette nouvelle méthode est de déplacer arbitrairement les solides à géométrie complexe dans un fluide visqueux incompressible, sans remailler le domaine fluide. Cette nouvelle méthode a l'avantage d'imposer la condition de non-glissement à l'interface d'une manière exacte via une force sans introduire des constantes artificielles modélisant la structure rigide. Cet avantage conduit également à la satisfaction de la condition CFL avec un pas de temps plus grand. Pour un calcul précis de la force induite par les frontières mobiles, un système linéaire a été introduit et résolu par la méthode de gradient conjugué. La méthode proposée peut être intégrée facilement dans des solveurs résolvant les équations de Navier-Stokes. Dans ce travail la MIBM a été mise en œuvre en couplage avec un solveur fluide utilisant une méthode de projection adaptée pour obtenir des solutions d'ordre deux en temps et en espace. Le champ de pression a été obtenu par l'équation de Poisson qui a été résolue à l'aide de la méthode du gradient conjugué préconditionné par la méthode multi-grille. La combinaison de ces deux méthodes a permis un gain de temps considérable par rapport aux méthodes classiques de la résolution des systèmes linéaires. De plus le code de calcul développé a été parallélisé sur l'unité graphique GPU équipée de la bibliothèque CUDA pour aboutir à des hautes performances de calcul. Enfin, comme application de nos travaux sur la MIBM, nous avons étudié le couplage "fort" d'interaction fluide-structure (IFS). Pour ce type de couplage, un schéma implicite partitionné a été adopté dans lequel les conditions à l'interface sont satisfaites via un schéma de type "point fixe". Pour réduire le temps de calcul inhérent à cette application, un nouveau schéma de couplage a été proposé pour éviter la résolution de l'équation de Poisson durant les itérations du "point fixe". Cette nouvelle façon de résoudre les problèmes IFS a montré des performances prometteuses pour des systèmes en IFS complexe. / In this thesis a novel non-body conforming mesh formulation is developed, called the moving immersed boundary method (MIBM), for the numerical simulation of fluid-structure interaction (FSI). The primary goal is to enable solids of complex shape to move arbitrarily in an incompressible viscous fluid, without fitting the solid boundary motion with dynamic meshes. This novel method enforces the no-slip boundary condition exactly at the fluid-solid interface with a boundary force, without introducing any artificial constants to the rigid body formulation. As a result, large time step can be used in current method. To determine the boundary force more efficiently in case of moving boundaries, an additional moving force equation is derived and the resulting system is solved by the conjugate gradient method. The proposed method is highly portable and can be integrated into any fluid solver as a plug-in. In the present thesis, the MIBM is implemented in the fluid solver based on the projection method. In order to obtain results of high accuracy, the rotational incremental pressure correction projection method is adopted, which is free of numerical boundary layer and is second order accurate. To accelerate the calculation of the pressure Poisson equation, the multi-grid method is employed as a preconditioner together with the conjugate gradient method as a solver. The code is further parallelized on the graphics processing unit (GPU) with the CUDA library to enjoy high performance computing. At last, the proposed MIBM is applied to the study of two-way FSI problem. For stability and modularity reasons, a partitioned implicit scheme is selected for this strongly coupled problem. The interface matching of fluid and solid variables is realized through a fixed point iteration. To reduce the computational cost, a novel efficient coupling scheme is proposed by removing the time-consuming pressure Poisson equation from this fixed point interaction. The proposed method has shown a promising performance in modeling complex FSI system.

Distributed optimization over multi-agent networks has become an increasingly popular research topic as it incorporates many applications from various areas such as consensus optimization, distributed control, network resource allocation, large scale machine learning, etc. Parallel distributed solution algorithms are highly desirable as they are more scalable, more robust against agent failure, align more naturally with either underlying agent network topology or big-data parallel computing framework. In this dissertation, we consider a multi-agent optimization formulation where the global objective function is the summation of individual local objective functions with respect to local agents' decision variables of different dimensions, and the constraints include both local private constraints and shared coupling constraints. Employing and extending tools from the monotone operator theory (including resolvent operator, operator splitting, etc.) and fixed point iteration of nonexpansive, averaged operators, a series of distributed solution approaches are proposed, which are all iterative algorithms that rely on parallel agent level local updates and inter-agent coordination. Some of the algorithms require synchronizations across all agents for information exchange during each iteration while others allow asynchrony and delays. The algorithms' convergence to an optimal solution if one exists are established by first characterizing them as fixed point iterations of certain averaged operators under certain carefully designed norms, then showing that the fixed point sets of these averaged operators are exactly the optimal solution set of the original multi-agent optimization problem. The effectiveness and performances of the proposed algorithms are demonstrated and compared through several numerical examples.<br>

A formal framework is developed and implemented in this research for preliminary rotorcraft design using IPPD methodology. All the technical aspects of design are considered including the vehicle engineering, dynamic analysis, stability and control, aerodynamic performance, propulsion, transmission design, weight and balance, noise analysis and economic analysis. The design loop starts with a detailed analysis of requirements. A baseline is selected and upgrade targets are identified depending on the mission requirements. An Overall Evaluation Criterion (OEC) is developed that is used to measure the goodness of the design or to compare the design with competitors. The requirements analysis and baseline upgrade targets lead to the initial sizing and performance estimation of the new design. The digital information is then passed to disciplinary experts. This is where the detailed disciplinary analyses are performed. Information is transferred from one discipline to another as the design loop is iterated. To coordinate all the disciplines in the product development cycle, Multidisciplinary Design Optimization (MDO) techniques e.g. All At Once (AAO) and Collaborative Optimization (CO) are suggested. The methodology is implemented on a Light Turbine Training Helicopter (LTTH) design. Detailed disciplinary analyses are integrated through a common platform for efficient and centralized transfer of design information from one discipline to another in a collaborative manner. Several disciplinary and system level optimization problems are solved. After all the constraints of a multidisciplinary problem have been satisfied and an optimal design has been obtained, it is compared with the initial baseline, using the earlier developed OEC, to measure the level of improvement achieved. Finally a digital preliminary design is proposed. The proposed design methodology provides an automated design framework, facilitates parallel design by removing disciplinary interdependency, current and updated information is made available to all disciplines at all times of the design through a central collaborative repository, overall design time is reduced and an optimized design is achieved.