Motivée par les contraintes économiques et les exigences environnementales, l'industrie du transport tente de réduire ses dépenses énergétiques. Elle concentre notamment ses efforts sur la traînée de frottement. Bien que d'origine visqueuse, celle-ci est fortement amplifiée par les mouvements turbulents. La capacité à manipuler les fluctuations turbulentes, complexes et chaotiques, offre alors des perspectives de gain énergétique substantiel, mais nécessite une bonne compréhension des phénomènes physiques. Parmi les stratégies de contrôle les plus prometteuses, l'utilisation de revêtements rainurés, nommés riblets, est étudiée dans ce mémoire. Bien que leur capacité de réduction de frottement soit connue depuis plusieurs décennies, les mécanismes par lesquels ils interagissent avec la turbulence restent à préciser. À ces fins, une méthode pour leur simulation numérique est mise au point. En redéfinissant la position de l'origine virtuelle, c'est-à-dire de la paroi plane équivalente, une forte similitude est établie entre les écoulements contrôlé et canonique. D'un point de vue applicatif, cela permet notamment de quantifier les performances de réduction de traînée atteignables à haut nombre de Reynolds. Enfin, le potentiel a priori prometteur des riblets tridimensionnels est exploré. En s'appuyant sur les rares résultats précurseurs de la littérature, il s'agit de proposer une géométrie industriellement réalisable optimale en termes de réduction de traînée. Pour chacune des géométries novatrices testées, les simulations révèlent avec finesse que les éventuels bénéfices sur le frottement sont systématiquement surpassés par l'influence délétère des efforts de pression. / Economical constrains and environmental requirements lead the transportation industry to progress towards energy expenditure reduction. Efforts are especially focused on the skin-friction drag. Friction drag, while due to viscosity, is greatly amplified by turbulent motions. The ability to manipulate the complex and chaotic near-wall turbulent fluctuations thus offers prospects for substantial energy saving, but also requires a solid understanding of the physical phenomena.Among the most promising control strategies, the present manuscript focuses on riblet-covered surfaces. Even though their drag-reducing capability has been observed from decades, the mechanisms by which they interact with the near-wall turbulent motions still need to be clarified. Towards these ends, a numerical method for ensuring their proper simulation is developed. The virtual origin—interpreted as the equivalent flat wall location—is redefined, which highlights a strong similarity between the controlled and the canonical flows. As a practical interest, this similarity enables an improved evaluation of the drag reduction capabilities achievable at high Reynolds numbers.Additionally, the promising potential for three-dimensional riblets is examined. Based on the scattered precursory results of the literature, we intend to come up with a design which demonstrates optimal drag reduction capabilities under the constraint of industrial feasibility. For each of the prospected innovative designs, the numerical simulations accurately reveal that the potential profit on skin-friction is consistently exceeded by the harmful influence of pressure stresses.

The aim of this thesis is to develop a numerical method to find approximations to solutions of the double-slip and double-spin model for the deformation and flow of granular materials. The model incorporates the physical and kinematic concepts of yield, shearing motion on slip lines, dilatation and average grain rotation. The equations governing the model comprise a set of five first order partial differential equations for the five dependent variables comprising two stress variables, two velocity components and the density. For steady state flows, the model is hyperbolic and the characteristic directions and relations along the characteristics are presented. The numerical approximation for the rate of working of the stresses are also presented. The model is then applied to a number of granular flow problems using the numerical method.

Le procédé de soudage par friction et malaxage est un procédé récent qui a été développé au sein de l'institut de soudure britannique "The Welding Institute" au début des années 90. Ce procédé, utilisé généralement en aéronautique, est sans apport de matière et permet de souder principalement des alliages d'aluminium difficilement soudables par les procédés classiques de soudage. Il consiste à malaxer le matériau de base à l'aide d'un outil constitué d'un pion et d'un épaulement frottant sur les faces supérieures des tôles à souder. La modélisation de ce procédé est très complexe puisque ce dernier implique des couplages entre des phénomènes mécaniques, thermiques et métallurgiques. Le malaxage dans le procédé de soudage FSW est difficile à simuler à l'aide de la méthode des éléments finis (en lagrangien) puisque la zone proche de l'outil de soudage est le siège de grandes déformations. Donc le remaillage est nécessaire. Cependant, le remaillage est cher et très difficile pour les problèmes tridimensionnels. Par ailleurs, après un remaillage, il est nécessaire d'interpoler les champs (vitesses, contraintes,...) correspondant à la solution courante, ce qui peut introduire des erreurs supplémentaires dans le calcul (on parle de diffusion numérique). Nous proposons dans ce travail des modèles basés sur la méthode sans maillage dite "Smoothed Particle Hydrodynamics SPH" et la méthode des moindres carrés mobiles (Moving Least Square MLS) pour la simulation de ce procédé. Ces modèles sont formulés dans le cadre lagrangien et utilisent la forme forte des équations aux dérivées partielles. Le premier modèle basé sur SPH considère la zone de soudure comme un fluide non newtonien faiblement compressible et dont la viscosité dépend de la température. Ce modèle est proposé pour la simulation numérique du comportement thermomécanique d'un matériau soudé par le procédé FSW. Dans le deuxième modèle, un algorithme itératif implicite de premier ordre a été proposé, pour simuler le malaxage de la matière dans le cas d'un matériau viscoplastique, en utilisant la méthode MLS et la technique de collocation. Le troisième modèle est un algorithme implicite d'ordre élevé basée sur le couplage de la méthode MLS et la Méthode Asymptotique Numérique MAN. Cet algorithme permet de réduire le temps de calcul par rapport à l'algorithme itératif implicite de premier ordre. La validation de ces trois modèles proposés a été faite par le code industriel Fluent / Friction stir welding is a recent process that has been developed by the British Welding Institute TWI "The Welding Institute" since 1990s. This process, generally used in aerospace, does not need additional material and allows mainly joining plates of aluminum alloys which are difficult to weld by the classical welding processes. It consists in mixing the base material using a tool comprising a pin and a shoulder which heats the plates to be welded by friction. The modeling of this process is very complex since it involves the coupling between mechanical, thermal and metallurgical phenomena. The mixing in welding process FSW is difficult to simulate using finite element method in lagrangian framework since the area near the welding tool is submitted to large deformations. So remeshing procedure is often required. However, remeshing can be very expensive and difficult to perform for three-dimensional problems. Moreover, after remeshing step, it is necessary to interpolate the fields (velocities, constraints ...) corresponding to the current solution, which may lead to additional errors in the calculation (called numerical diffusion). We propose in this work models based on meshless methods called "Smoothed Particle Hydrodynamics SPH" and Moving Least Square method for the simulation of this welding process. These models are formulated in lagrangian framework and use the strong form of partial differential equations. The first model based on SPH considers the welding zone as a weakly compressible non-newtonian fluid and whose viscosity depends on the temperature. This model is proposed for the numerical simulation of thermo-mechanical behavior of a welded material by FSW process. The second model is a first order implicit iterative algorithm proposed to simulate material mixing in the case a visco-plastic behavior using the MLS method and the collocation technique. The third model is a high order implicit algorithm based on the coupling of MLS method and Asymptotic Numerical Method (ANM). This algorithm allows reducing the computation time by comparison with the first order implicit iterative algorithm. The validation of these three proposed models was done by the industrial code Fluent

Décrit comme l'un des algorithmes les plus prometteurs du 20ème siècle, le formalisme multipolaire appliqué à la méthode des éléments de frontière, permet de nos jours de traiter de larges problèmes encore inconcevables il y a quelques années. La motivation de ce travail de thèse est d'évaluer la capacité, ainsi que les avantages concernant les ressources numériques, de ce formalisme pour apporter une solution de référence aux problèmes de propagation sonore tri-dimensionnels en environnement urbain, dans l'objectif d'améliorer les algorithmes plus rapides déjà existants. Nous présentons la théorie nécessaire à l'obtention de l'équation intégrale de frontière pour la résolution de problèmes non bornés. Nous discutons également de l'équation intégrale de frontière conventionnelle et hyper-singulière pour traiter les artefacts numériques liés aux fréquences fictives, lorsque l'on résout des problèmes extérieurs. Nous présentons par la suite un bref aperçu historique et technique du formalisme multipolaire rapide et des outils mathématiques requis pour représenter la solution élémentaire de l'équation de Helmholtz. Nous décrivons les principales étapes, d'un point de vue numérique, du calcul multipolaire. Un problème de propagation sonore dans un quartier, composé de 5 bâtiments, nous a permis de mettre en évidence des problèmes d'instabilités dans le calcul par récursion des matrices de translations, se traduisant par des discontinuités sur le champs de pression de surface et une non convergence du solveur. Ceci nous a conduits à considérer le travail très récent de Gumerov et Duraiswamy en lien avec un processus récursif stable pour le calcul des coefficients des matrices de rotation. Cette version améliorée a ensuite été testée avec succès sur un cas de multi diffraction jusqu'à une taille dimensionnelle de problème de 207 longueur d'ondes. Nous effectuons finalement une comparaison entre un algorithme d'élément de frontière, Micado3D, un algorithme multipolaire et un algorithme basé sur le tir de rayons, Icare, pour le calcul de niveaux de pression moyennés dans une cour ouverte et fermée. L'algorithme multipolaire permet de valider les résultats obtenus par tir de rayons dans la cour ouverte jusqu'à 300 Hz (i.e. 100 longueur d'ondes), tandis que concernant la cour fermée, zone très sensible par l'absence de contribution directes ou réfléchies, des études complémentaires sur le préconditionnement de la matrice semblent requises afin de s'assurer de la pertinence des résultats obtenus à l'aide de solveurs itératifs / Described as one of the best ten algorithms of the 20th century, the fast multipole formalism applied to the boundary element method allows to handle large problems which were inconceivable only a few years ago. Thus, the motivation of the present work is to assess the ability, as well as the benefits in term of computational resources provided by the application of this formalism to the boundary element method, for solving sound propagation problems and providing reference solutions, in three dimensional dense urban environments, in the aim of assessing or improving fast engineering tools. We first introduce the mathematical background required for the derivation of the boundary integral equation, for solving sound propagation problems in unbounded domains. We discuss the conventional and hyper-singular boundary integral equation to overcome the numerical artifact of fictitious eigen-frequencies, when solving exterior problems. We then make a brief historical and technical overview of the fast multipole principle and introduce the mathematical tools required to expand the elementary solution of the Helmholtz equation and describe the main steps, from a numerical viewpoint, of fast multipole calculations. A sound propagation problem in a city block made of 5 buildings allows us to highlight instabilities in the recursive computation of translation matrices, resulting in discontinuities of the surface pressure and a no convergence of the iterative solver. This observation leads us to consider the very recent work of Gumerov & Duraiswamy, related to a ``stable'' recursive computation of rotation matrices coefficients in the RCR decomposition. This new improved algorithm has been subsequently assessed successfully on a multi scattering problem up to a dimensionless domain size equal to 207 wavelengths. We finally performed comparisons between a BEM algorithm, extit{Micado3D}, the FMBEM algorithm and a ray tracing algorithm, Icare, for the calculation of averaged pressure levels in an opened and closed court yards. The fast multipole algorithm allowed to validate the results computed with Icare in the opened court yard up to 300 Hz corresponding, (i.e. 100 wavelengths), while in the closed court yard, a very sensitive area without direct or reflective fields, further investigations related to the preconditioning seem required to ensure reliable solutions provided by iterative solver based algorithms

Master’s thesis deals with numerical finding the global minimum. A theoretical part of project presents a problem of global optimization, her basic division and shows basic examples the specific problems of global optimization. Further, the reader is familiar with the basics of some numerical methods and with description of their strengths and weaknesses. A practical part shows concrete algorithm of global optimization, its use on data of specified function. Data refer to the issue of radiative heat transfer.

The main object of this diploma thesis is solving problems concerning heat transfer in disposal cannister for spent nuclear fuel. In forepart possibilities of conceptual solving according of disposal cannister to particular states are reviwed. On the basis of this a variant of possible protect of a nuclear fuel repository in the Czech republic has been chosen for calculationof a simplified model. Second part is computational solving that was divided into two parts. The first deals with calculation of heat transfer in disposal canister and is done by an analytical method. In the second part is calculation is done by numerical model. In this way region in near surroundings of this model of disposal cannister is analysed. Last part those diploma thesis deals with design of the storage of spacing among disposal canisters as well as optimum placing in underground part of nuclear fuel repository.

This thesis deals with a procedure for determining the complete processing of aerodynamic flow instabilities (rotating stall and surge) in a centrifugal compressor. At small flows the performance of a compressor system is limited by the surge line, which is caused by flow instabilities. Numerical solution is obtained using the method of transfer matrix. This system is simulated through several models with local resistances that represent the dissipation of pressure energy. Pulses are excitated in these models by the pressure jump placed before the centrifugal compressor. From the frequency-amplitude characteristics for the selected range of frequencies and flow the impedance characteristic of the compressor system is determined. We are looking for problematic frequencies in this characteristic that cause flow instabilities in the compressor system.

This thesis presents a numerical approach based on generalized fractional-order Chebyshev wavelets for solving fractional-order optimal control problems. The exact value of the Riemann– Liouville fractional integral operator of the generalized fractional-order Chebyshev wavelets is computed by applying the regularized beta function. We apply the given wavelets, the exact formula, and the collocation method to transform the studied problem into a new optimization problem. The convergence analysis of the proposed method is provided. The present method is extended for solving fractional-order, distributed-order, and variable-order optimal control problems. Illustrative examples are considered to show the advantage of this method in comparison with the existing methods in the literature.

No description available.

In order to elucidate the progression mechanism of cavitation erosion, the behaviors of a single cavitation bubble collapse near a pit on a wall and both the resulting pressure wave in fluid and stress wave in material are investigated in detail. To find out the mechanism of cavitation erosion, many experimental studies on the bubble collapse behavior near a flat rigid wall and the resulting material damage have been conducted so far. A lot of numerical studies using only fluid analysis have been also carried out. In recent years, a few studies on the bubble collapse near a more complex geometry were made and it is reported that more complex geometry has an effect on the bubble collapse behavior, jet formation and subsequent wave dynamics. It is, however, very challenging to introduce a material analysis and investigate detailed stress wave propagation in the material and its effect on the material damage i.e. cavitation erosion. This study tackles this problem using an in-house fluid/material two-way coupled numerical analysis method which considers reflection and transmission of plane waves with acoustic impedance at the fluid/material boundary. In the fluid domain, the locally homogeneous model of compressible gas-liquid two-phase medium is used for capturing the gas-liquid interface. The compressibility of two-phase flow is also considered in this model so that the propagation of pressure wave can be also be taken into account. The governing equations are the 3D compressible gas-liquid two-phase Navier-Stokes equations. In the material domain, the governing equations are composed of the motion equations and the time-differential constitutive equations assuming that the material is a homogeneous isotropic elastic medium, which can simulate the stress wave propagation in the material. Results show that the stress waves are concentrated at the bottom of the pit regardless of the initial bubble position. It is also found that the surface pressure in the fluid side does not necessarily correlate with the stresses in the material, suggesting the importance of material analysis. Moreover, under high pressure conditions, a rapid bubble collapse causes a gas phase generation at the bottom of the pit and its gas phase is contracted and collapsed by the pressure wave, which leads to pressure and stress peaks at the bottom of the pit. Furthermore, through the study of the effect of initial bubble position on its collapse behavior, it is confirmed that, when the initial bubble position is shifted horizontally, bubble collapses asymmetrically and the pressure waves tend to be directed away from a pit. This research numerically reveals that a single bubble collapse near a pit on a wall results in high strain energy concentration at the bottom of the pit, which gives rise to deeper erosion progression at the bottom of the pit. / För att klargöra framstegsmekanismen för kavitationserosion kollapsar beteendet hos en enda kavitationsbubbla nära en grop på en vägg och både den resulterande tryckvågen i vätska och stressvåg i material undersöks i detalj. För att ta reda på mekanismen för kavitationserosion har många experimentella studier av bubblans kollapsbeteende nära en platt styv vägg och den resulterande materialskada genomförts hittills. Många numeriska studier med endast vätskeanalys har också genomförts. Under de senaste åren gjordes några studier om bubblans kollaps nära en mer komplex geometri och det rapporteras att mer komplex geometri har en effekt på bubblans kollapsbeteende, strålbildning och efterföljande vågdynamik. Det är dock mycket utmanande att införa en materialanalys och undersöka detaljerad spänningsvågförökning i materialet och dess inverkan på materialskadorna, dvs. kavitationserosion. Denna studie hanterar detta problem med hjälp av en inbyggd tvåvägs kopplad numerisk analysmetod som tar hänsyn till reflektion och överföring av plana vågor med akustisk impedans vid vätska / materialgränsen. I fluiddomänen används den lokalt homogena modellen av tvåfasmedium för komprimerbar gas-vätska för att fånga gas-vätskegränssnittet. Komprimerbarheten av tvåfasflöde beaktas också i denna modell så att utbredningen av tryckvågen också kan beaktas. De styrande ekvationerna är de 3D-komprimerbara tvåfasiga gasvätska Navier-Stokes-ekvationerna. I materialdomänen är de styrande ekvationerna sammansatta av rörelseekvationer och tidsdifferentialkonstitutiva ekvationer förutsatt att materialet är ett homogent isotropiskt elastiskt medium, vilket kan simulera spänningsvågutbredningen i materialet. Resultaten visar att stressvågorna är koncentrerade längst ner i gropen oavsett den ursprungliga bubbelpositionen. Man har också funnit att yttrycket i vätskesidan inte nödvändigtvis korrelerar med spänningarna i materialet, vilket tyder på vikten av materialanalys. Vidare orsakar en snabb bubbelskollaps under högtrycksförhållanden en gasfasgenerering vid botten av gropen och dess gasfas dras samman och kollapsas av tryckvågen, vilket leder till tryck och spänningstoppar vid botten av gropen. Vidare bekräftas det genom studien av effekten av den ursprungliga bubbelpositionen på dess kollapsbeteende att när den ursprungliga bubbelpositionen förskjuts horisontellt kollapsar bubblan asymmetriskt och tryckvågorna tenderar att riktas bort från en grop. Denna undersökning avslöjar numeriskt att en enda bubbla kollapsar nära en grop på en vägg resulterar i hög spänningsenergikoncentration längst ner i gropen, vilket ger upphov till djupare erosionsprogression längst ner i gropen.