Dissertations / Theses on the topic 'Numerical Synthesis'

In this thesis work the accuracy of the spherical harmonic synthesis and analysis are investigated, by simulated numerical studies.The main idea is to investigate the loss of accuracy, in the geopotential coeffcients, by the following testing method. We start with a synthesis calculation, using the coefficients(EGM2008), to calculate geoid heights on a regular grid. Those geoid heights are then used in an analysis calculation to obtain a new set of coeffcients, which are in turn used to derive a new set of geoid heights. The difference between those two sets of geoid heights will be analyzed to assess the accuracy of the synthesis and analysis calculations.The tests will be conducted with both point-values and area-means in the blocks in the grid. The area-means are constructed in some different ways and will also be compared to the mean value from 10000 point values as separate tests. Numerical results from this investigation show there are signifi…cant systematic errors in the geoid heights computed by spherical harmonic synthesis and analysis, sometimes reaching as high as several meters. Those big errors are most common at the polar regions and at the mid-latitude regions.

In questo lavoro viene presentato un modello matematico per la simulazione della formazione e crescita di nanoparticelle di Silicio nella camera di reazione di una torcia al plasma ad induzione. Le simulazioni sono state condotte adottando modelli di turbolenza diversi, per evidenziare l'impatto di questo fenomeno sulla sintesi di nanoparticelle. Le simulazioni effettuate mostrano che il modello matematico fornisce risultati coerenti con i fenomeni fisici.

This thesis introduces a new technique, and its associated tool SOAP, to automatically perform source-to-source optimization of numerical programs, specifically targeting the trade-off among numerical accuracy, latency, and resource usage as a high-level synthesis flow for FPGA implementations. A new intermediate representation, MIR, is introduced to carry out the abstraction and optimization of numerical programs. Equivalent structures in MIRs are efficiently discovered using methods based on formal semantics by taking into account axiomatic rules from real arithmetic, such as associativity, distributivity and others, in tandem with program equivalence rules that enable control-flow restructuring and eliminate redundant array accesses. For the first time, we bring rigorous approaches from software static analysis, specifically formal semantics and abstract interpretation, to bear on program transformation for high-level synthesis. New abstract semantics are developed to generate a computable subset of equivalent MIRs from an original MIR. Using formal semantics, three objectives are calculated for each MIR representing a pipelined numerical program: the accuracy of computation and an estimate of resource utilization in FPGA and the latency of program execution. The optimization of these objectives produces a Pareto frontier consisting of a set of equivalent MIRs. We thus go beyond existing literature by not only optimizing the precision requirements of an implementation, but changing the structure of the implementation itself. Using SOAP to optimize the structure of a variety of real world and artificially generated arithmetic expressions in single precision, we improve either their accuracy or the resource utilization by up to 60%. When applied to a suite of computational intensive numerical programs from PolyBench and Livermore Loops benchmarks, SOAP has generated circuits that enjoy up to a 12x speedup, with a simultaneous 7x increase in accuracy, at a cost of up to 4x more LUTs.

Thesis (M.S. in Mechanical Engineering) Naval Postgraduate School, September 1998.
"September 1998." Thesis advisor(s): Matthew D. Kelleher, C.N. Calvano. Includes bibliographical references (p. 229-230). Also available online.

The theme of this masters thesis are driven chaotic oscillators. The aim of this project is show the various types of driven chaotic oscillator and propose mathematical model solutions using numerical methods. In the first part of this thesis are shown theory of chaos, history of chaos theory, chaotic systems and chaos quantifiers. Next is numerical analysis of differential equations second order by Runge-Kutta fourth order method. Next part contains circuit blocks and synthesis of oscillators. In next part are defined all types of oscillators. Parameters of analysis, equations, circuits and simulations are defined for each type of driven chaotic oscillators. In each subchapter is design electrical circuit. This circuit is simulated and some of them realized.

The work in this thesis presents and discusses new techniques for modelling string instrument vibrations for the purpose of physics-based sound synthesis. The work focuses on coupled systems, where phenomena such as sympathetic vibrations should naturally occur. Finite difference (FD) methods are chosen for modelling string vibrations for to their flexibility both in terms of local adjustments and possible extensions to nonlinearities. The resonating body is represented using a modal formulation. Modelling the body in such a way has the advantage of scalability which can improve efficiency. This is shown to be possible without affecting the overall timbre of the sound. The models were formulated using idealised shapes such as the beam and plate, but the modal formulation is general for all linear systems. A technique for interfacing the FD model of the string to the modal formulation of the body is presented. In this way the advantages of both methods are exploited, improving the balance between accurate and efficiency. Initially, this coupling is formulated using only transverse motion but is then extended to include longitudinal motion. In simulations of a harp-like instrument where the strings are coupled to the body at an angle, results obtained with numerical experiments show that including longitudinal vibrations impacts the eigenmodes of the system and prove essential for accurately modelling sympathetic vibrations. Comparisons with previous studies validate these results. By applying the proposed method to model resembling a simplified piano, online changes to parameters such as soundboard density further demonstrate the proposed technique.

La parla és una de les formes de comunicació més naturals i directes entre éssers humans, ja que codifica un missatge i també claus paralingüístiques sobre l’estat emocional del locutor, el to o la seva intenció, esdevenint així fonamental en la consecució d’una interacció humà-màquina (HCI) més natural. En aquest context, la generació de parla expressiva pel canal de sortida d’HCI és un element clau en el desenvolupament de tecnologies assistencials o assistents personals entre altres aplicacions. La parla sintètica pot ser generada a partir de parla enregistrada utilitzant mètodes basats en corpus com la selecció d’unitats (US), que poden aconseguir resultats d’alta qualitat però d’expressivitat restringida a la pròpia del corpus. A fi de millorar la qualitat de la sortida de la síntesi, la tendència actual és construir bases de dades de veu cada cop més grans, seguint especialment l’aproximació de síntesi anomenada End-to-End basada en tècniques d’aprenentatge profund. Tanmateix, enregistrar corpus ad-hoc per cada estil expressiu desitjat pot ser extremadament costós o fins i tot inviable si el locutor no és capaç de realitzar adequadament els estils requerits per a una aplicació donada (ex: cant en el domini de la narració de contes). Alternativament, nous mètodes basats en la física de la producció de veu s’han desenvolupat a la darrera dècada gràcies a l’increment en la potència computacional. Per exemple, vocals o diftongs poden ser obtinguts utilitzant el mètode d’elements finits (FEM) per simular la propagació d’ones acústiques a través d’una geometria 3D realista del tracte vocal obtinguda a partir de ressonàncies magnètiques (MRI). Tanmateix, atès que els principals esforços en aquests mètodes de producció numèrica de veu s’han focalitzat en la millora del modelat del procés de generació de veu, fins ara s’ha prestat poca atenció a la seva expressivitat. A més, la col·lecció de dades per aquestes simulacions és molt costosa, a més de requerir un llarg postprocessament manual com el necessari per extreure geometries 3D del tracte vocal a partir de MRI. L’objectiu de la tesi és afegir expressivitat en un sistema que genera veu neutra, sense haver d’adquirir dades expressives del locutor original. Per un costat, s’afegeixen capacitats expressives a un sistema de conversió de text a parla basat en selecció d’unitats (US-TTS) dotat d’un corpus de veu neutra, per adreçar necessitats específiques i concretes en l’àmbit de la narració de contes, com són la veu cantada o situacions de suspens. A tal efecte, la veu és parametritzada utilitzant un model harmònic i transformada a l’estil expressiu desitjat d’acord amb un sistema expert. Es presenta una primera aproximació, centrada en la síntesi de suspens creixent per a la narració de contes, i es demostra la seva viabilitat pel que fa a naturalitat i qualitat de narració de contes. També s’afegeixen capacitats de cant al sistema US-TTS mitjançant la integració de mòduls de transformació de parla a veu cantada en el pipeline del TTS, i la incorporació d’un mòdul de generació de prosòdia expressiva que permet al mòdul de US seleccionar unitats més properes a la prosòdia cantada obtinguda a partir de la partitura d’entrada. Això resulta en un framework de síntesi de conversió de text a parla i veu cantada basat en selecció d’unitats (US-TTS&S) que pot generar veu parlada i cantada a partir d'un petit corpus de veu neutra (~2.6h). D’acord amb els resultats objectius, l’estratègia de US guiada per la partitura permet reduir els factors de modificació de pitch requerits per produir veu cantada a partir de les unitats de veu parlada seleccionades, però en canvi té una efectivitat limitada amb els factors de modificació de les durades degut a la curta durada de les vocals parlades neutres. Els resultats dels tests perceptius mostren que tot i òbviament obtenir una naturalitat inferior a la oferta per un sintetitzador professional de veu cantada, el framework pot adreçar necessitats puntuals de veu cantada per a la síntesis de narració de contes amb una qualitat raonable. La incorporació d’expressivitat s’investiga també en la simulació numèrica 3D de vocals basada en FEM mitjançant modificacions de les senyals d’excitació glotal utilitzant una aproximació font-filtre de producció de veu. Aquestes senyals es generen utilitzant un model Liljencrants-Fant (LF) controlat amb el paràmetre de forma del pols Rd, que permet explorar el continu de fonació lax-tens a més del rang de freqüències fonamentals, F0, de la veu parlada. S’analitza la contribució de la font glotal als modes d’alt ordre en la síntesis FEM de les vocals cardinals [a], [i] i [u] mitjançant la comparació dels valors d’energia d’alta freqüència (HFE) obtinguts amb geometries realistes i simplificades del tracte vocal. Les simulacions indiquen que els modes d’alt ordre es preveuen perceptivament rellevants d’acord amb valors de referència de la literatura, particularment per a fonacions tenses i/o F0s altes. En canvi, per a vocals amb una fonació laxa i/o F0s baixes els nivells d’HFE poden resultar inaudibles, especialment si no hi ha soroll d’aspiració en la font glotal. Després d’aquest estudi preliminar, s’han analitzat les característiques d’excitació de vocals alegres i agressives d’un corpus paral·lel de veu en castellà amb l’objectiu d’incorporar aquests estils expressius de veu tensa en la simulació numèrica de veu. Per a tal efecte, s’ha usat el vocoder GlottDNN per analitzar variacions d’F0 i pendent espectral relacionades amb l’excitació glotal en vocals [a]. Aquestes variacions es mapegen mitjançant la comparació amb vocals sintètiques en valors d’F0 i Rd per simular vocals que s’assemblin als estils alegre i agressiu. Els resultats mostren que és necessari incrementar l’F0 i disminuir l’Rd respecte la veu neutra, amb variacions majors per a alegre que per agressiu, especialment per a vocals accentuades. Els resultats aconseguits en les investigacions realitzades validen la possibilitat d’afegir expressivitat a la síntesi basada en corpus US-TTS i a la simulació numèrica de veu basada en FEM. Tanmateix, encara hi ha marge de millora. Per exemple, l’estratègia aplicada a la producció numèrica de veu es podria millorar estudiant i desenvolupant mètodes de filtratge invers així com incorporant modificacions del tracte vocal, mentre que el framework US-TTS&S es podria beneficiar dels avenços en tècniques de transformació de veu incloent transformacions de la qualitat de veu, aprofitant l’experiència adquirida en la simulació numèrica de vocals expressives.
El habla es una de las formas de comunicación más naturales y directas entre seres humanos, ya que codifica un mensaje y también claves paralingüísticas sobre el estado emocional del locutor, el tono o su intención, convirtiéndose así en fundamental en la consecución de una interacción humano-máquina (HCI) más natural. En este contexto, la generación de habla expresiva para el canal de salida de HCI es un elemento clave en el desarrollo de tecnologías asistenciales o asistentes personales entre otras aplicaciones. El habla sintética puede ser generada a partir de habla gravada utilizando métodos basados en corpus como la selección de unidades (US), que pueden conseguir resultados de alta calidad, pero de expresividad restringida a la propia del corpus. A fin de mejorar la calidad de la salida de la síntesis, la tendencia actual es construir bases de datos de voz cada vez más grandes, siguiendo especialmente la aproximación de síntesis llamada End-to-End basada en técnicas de aprendizaje profundo. Sin embargo, gravar corpus ad-hoc para cada estilo expresivo deseado puede ser extremadamente costoso o incluso inviable si el locutor no es capaz de realizar adecuadamente los estilos requeridos para una aplicación dada (ej: canto en el dominio de la narración de cuentos). Alternativamente, nuevos métodos basados en la física de la producción de voz se han desarrollado en la última década gracias al incremento en la potencia computacional. Por ejemplo, vocales o diptongos pueden ser obtenidos utilizando el método de elementos finitos (FEM) para simular la propagación de ondas acústicas a través de una geometría 3D realista del tracto vocal obtenida a partir de resonancias magnéticas (MRI). Sin embargo, dado que los principales esfuerzos en estos métodos de producción numérica de voz se han focalizado en la mejora del modelado del proceso de generación de voz, hasta ahora se ha prestado poca atención a su expresividad. Además, la colección de datos para estas simulaciones es muy costosa, además de requerir un largo postproceso manual como el necesario para extraer geometrías 3D del tracto vocal a partir de MRI. El objetivo de la tesis es añadir expresividad en un sistema que genera voz neutra, sin tener que adquirir datos expresivos del locutor original. Per un lado, se añaden capacidades expresivas a un sistema de conversión de texto a habla basado en selección de unidades (US-TTS) dotado de un corpus de voz neutra, para abordar necesidades específicas y concretas en el ámbito de la narración de cuentos, como son la voz cantada o situaciones de suspense. Para ello, la voz se parametriza utilizando un modelo harmónico y se transforma al estilo expresivo deseado de acuerdo con un sistema experto. Se presenta una primera aproximación, centrada en la síntesis de suspense creciente para la narración de cuentos, y se demuestra su viabilidad en cuanto a naturalidad y calidad de narración de cuentos. También se añaden capacidades de canto al sistema US-TTS mediante la integración de módulos de transformación de habla a voz cantada en el pipeline del TTS, y la incorporación de un módulo de generación de prosodia expresiva que permite al módulo de US seleccionar unidades más cercanas a la prosodia cantada obtenida a partir de la partitura de entrada. Esto resulta en un framework de síntesis de conversión de texto a habla y voz cantada basado en selección de unidades (US-TTS&S) que puede generar voz hablada y cantada a partir del mismo pequeño corpus de voz neutra (~2.6h). De acuerdo con los resultados objetivos, la estrategia de US guiada por la partitura permite reducir los factores de modificación de pitch requeridos para producir voz cantada a partir de las unidades de voz hablada seleccionadas, pero en cambio tiene una efectividad limitada con los factores de modificación de duraciones debido a la corta duración de las vocales habladas neutras. Los resultados de las pruebas perceptivas muestran que, a pesar de obtener una naturalidad obviamente inferior a la ofrecida por un sintetizador profesional de voz cantada, el framework puede abordar necesidades puntuales de voz cantada para la síntesis de narración de cuentos con una calidad razonable. La incorporación de expresividad se investiga también en la simulación numérica 3D de vocales basada en FEM mediante modificaciones en las señales de excitación glotal utilizando una aproximación fuente-filtro de producción de voz. Estas señales se generan utilizando un modelo Liljencrants-Fant (LF) controlado con el parámetro de forma del pulso Rd, que permite explorar el continuo de fonación laxo-tenso además del rango de frecuencias fundamentales, F0, de la voz hablada. Se analiza la contribución de la fuente glotal a los modos de alto orden en la síntesis FEM de las vocales cardinales [a], [i] y [u] mediante la comparación de los valores de energía de alta frecuencia (HFE) obtenidos con geometrías realistas y simplificadas del tracto vocal. Las simulaciones indican que los modos de alto orden se prevén perceptivamente relevantes de acuerdo con valores de referencia de la literatura, particularmente para fonaciones tensas y/o F0s altas. En cambio, para vocales con una fonación laxa y/o F0s bajas los niveles de HFE pueden resultar inaudibles, especialmente si no hay ruido de aspiración en la fuente glotal. Después de este estudio preliminar, se han analizado las características de excitación de vocales alegres y agresivas de un corpus paralelo de voz en castellano con el objetivo de incorporar estos estilos expresivos de voz tensa en la simulación numérica de voz. Para ello, se ha usado el vocoder GlottDNN para analizar variaciones de F0 y pendiente espectral relacionadas con la excitación glotal en vocales [a]. Estas variaciones se mapean mediante la comparación con vocales sintéticas en valores de F0 y Rd para simular vocales que se asemejen a los estilos alegre y agresivo. Los resultados muestran que es necesario incrementar la F0 y disminuir la Rd respecto la voz neutra, con variaciones mayores para alegre que para agresivo, especialmente para vocales acentuadas. Los resultados conseguidos en las investigaciones realizadas validan la posibilidad de añadir expresividad a la síntesis basada en corpus US-TTS y a la simulación numérica de voz basada en FEM. Sin embargo, hay margen de mejora. Por ejemplo, la estrategia aplicada a la producción numérica de voz se podría mejorar estudiando y desarrollando métodos de filtrado inverso, así como incorporando modificaciones del tracto vocal, mientras que el framework US-TTS&S desarrollado se podría beneficiar de los avances en técnicas de transformación de voz incluyendo transformaciones de la calidad de la voz, aprovechando la experiencia adquirida en la simulación numérica de vocales expresivas.
Speech is one of the most natural and direct forms of communication between human beings, as it codifies both a message and paralinguistic cues about the emotional state of the speaker, its mood, or its intention, thus becoming instrumental in pursuing a more natural Human Computer Interaction (HCI). In this context, the generation of expressive speech for the HCI output channel is a key element in the development of assistive technologies or personal assistants among other applications. Synthetic speech can be generated from recorded speech using corpus-based methods such as Unit-Selection (US), which can achieve high quality results but whose expressiveness is restricted to that available in the speech corpus. In order to improve the quality of the synthesis output, the current trend is to build ever larger speech databases, especially following the so-called End-to-End synthesis approach based on deep learning techniques. However, recording ad-hoc corpora for each and every desired expressive style can be extremely costly, or even unfeasible if the speaker is unable to properly perform the styles required for a given application (e.g., singing in the storytelling domain). Alternatively, new methods based on the physics of voice production have been developed in the last decade thanks to the increase in computing power. For instance, vowels or diphthongs can be obtained using the Finite Element Method (FEM) to simulate the propagation of acoustic waves through a 3D realistic vocal tract geometry obtained from Magnetic Resonance Imaging (MRI). However, since the main efforts in these numerical voice production methods have been focused on improving the modelling of the voice generation process, little attention has been paid to its expressiveness up to now. Furthermore, the collection of data for such simulations is very costly, besides requiring manual time-consuming postprocessing like that needed to extract 3D vocal tract geometries from MRI. The aim of the thesis is to add expressiveness into a system that generates neutral voice, without having to acquire expressive data from the original speaker. One the one hand, expressive capabilities are added to a Unit-Selection Text-to-Speech (US-TTS) system fed with a neutral speech corpus, to address specific and timely needs in the storytelling domain, such as for singing or in suspenseful situations. To this end, speech is parameterised using a harmonic-based model and subsequently transformed to the target expressive style according to an expert system. A first approach dealing with the synthesis of storytelling increasing suspense shows the viability of the proposal in terms of naturalness and storytelling quality. Singing capabilities are also added to the US-TTS system through the integration of Speech-to-Singing (STS) transformation modules into the TTS pipeline, and by incorporating an expressive prosody generation module that allows the US to select units closer to the target singing prosody obtained from the input score. This results in a Unit Selection based Text-to-Speech-and-Singing (US-TTS&S) synthesis framework that can generate both speech and singing from the same neutral speech small corpus (~2.6 h). According to the objective results, the score-driven US strategy can reduce the pitch scaling factors required to produce singing from the selected spoken units, but its effectiveness is limited regarding the time-scale requirements due to the short duration of the spoken vowels. Results from the perceptual tests show that although the obtained naturalness is obviously far from that given by a professional singing synthesiser, the framework can address eventual singing needs for synthetic storytelling with a reasonable quality. The incorporation of expressiveness is also investigated in the 3D FEM-based numerical simulation of vowels through modifications of the glottal flow signals following a source-filter approach of voice production. These signals are generated using a Liljencrants-Fant (LF) model controlled with the glottal shape parameter Rd, which allows exploring the tense-lax continuum of phonation besides the spoken vocal range of fundamental frequency values, F0. The contribution of the glottal source to higher order modes in the FEM synthesis of cardinal vowels [a], [i] and [u] is analysed through the comparison of the High Frequency Energy (HFE) values obtained with realistic and simplified 3D geometries of the vocal tract. The simulations indicate that higher order modes are expected to be perceptually relevant according to reference values stated in the literature, particularly for tense phonations and/or high F0s. Conversely, vowels with a lax phonation and/or low F0s can result in inaudible HFE levels, especially if aspiration noise is not present in the glottal source. After this preliminary study, the excitation characteristics of happy and aggressive vowels from a Spanish parallel speech corpus are analysed with the aim of incorporating this tense voice expressive styles into the numerical production of voice. To that effect, the GlottDNN vocoder is used to analyse F0 and spectral tilt variations associated with the glottal excitation on vowels [a]. These variations are mapped through the comparison with synthetic vowels into F0 and Rd values to simulate vowels resembling happy and aggressive styles. Results show that it is necessary to increase F0 and decrease Rd with respect to neutral speech, with larger variations for happy than aggressive style, especially for the stressed [a] vowels. The results achieved in the conducted investigations validate the possibility of adding expressiveness to both corpus-based US-TTS synthesis and FEM-based numerical simulation of voice. Nevertheless, there is still room for improvement. For instance, the strategy applied to the numerical voice production could be improved by studying and developing inverse filtering approaches as well as incorporating modifications of the vocal tract, whereas the developed US-TTS&S framework could benefit from advances in voice transformation techniques including voice quality modifications, taking advantage of the experience gained in the numerical simulation of expressive vowels.

This work is concerned with the numerical simulation of percussion instruments based on physical principles. Three novel modular environments for sound synthesis are presented: a system composed of various plates vibrating under nonlinear conditions, a model for a nonlinear double membrane drum and a snare drum. All are embedded in a 3D acoustic environment. The approach adopted is based on the finite difference method, and extends recent results in the field. Starting from simple models, the modular instruments can be created by combining different components in order to obtain virtual environments with increasing complexity. The resulting numerical codes can be used by composers and musicians to create music by specifying the parameters and a score for the systems. Stability is a major concern in numerical simulation. In this work, energy techniques are employed in order to guarantee the stability of the numerical schemes for the virtual instruments, by imposing suitable coupling conditions between the various components of the system. Before presenting the virtual instruments, the various components are individually analysed. Plates are the main elements of the multiple plate system, and they represent the first approximation to the simulation of gongs and cymbals. Similarly to plates, membranes are important in the simulation of drums. Linear and nonlinear plate/membrane vibration is thus the starting point of this work. An important aspect of percussion instruments is the modelling of collisions. A novel approach based on penalty methods is adopted here to describe lumped collisions with a mallet and distributed collisions with a string in the case of a membrane. Another point discussed in the present work is the coupling between 2D structures like plates and membranes with the 3D acoustic field, in order to obtain an integrated system. It is demonstrated how the air coupling can be implemented when nonlinearities and collisions are present. Finally, some attention is devoted to the experimental validation of the numerical simulation in the case of tom tom drums. Preliminary results comparing different types of nonlinear models for membrane vibration are presented.

In 1976, Hunt recovered screw theory by through geometric considerations and applied it to the analysis and synthesis of mechanisms. He has also discussed the special cases of various screw systems and proposed for them a classification based on a canonical bases of motion formed by principal screws. In addition to his classification, one of the most important result from Hunt's work, related to this thesis, is that some of the classified systems guarantee "full-cycle mobility" of mechanisms. They are known as Invariant screw systems (ISSs) and they are subalgebras of the Lie algebra se(3), which is the tangent space at the identity of the Lie group SE(3). This last one, constitutes a group of isometries of R^3, known as Special Euclidean Group. Recently a more general concept was presented: Persistent screw systems (PSSs) still exhibit relevant properties for "full-cycle motions". They represent the main topic of this thesis. Hence, a numerical method that allows us to find out what types of screw system that have dimension three are PSS, is proposed. Chapter 1 focuses on the main event regarding screw theory, tracing an historical line in order to introduce the state of art related to this work. Chapter 2 deals with some basic concepts related to screw theory. Chapter 3 introduces ISS ad PSS, with particular emphasis on their properties, which are important for guaranteeing "full-cycle motions" of mechanisms. It introduces also some basic procedures that allow the synthesis of many PSS generators. Chapter 4 formulates the problem on how find out PSSs of dimension three by presenting the characteristic equations associated to persistent systems and explains how validate them numerically with the aim to solve the equations properly. Further, the mathematical parametrizations are developed in order to establish what types of screw systems, according to Hunt's classification, are PSS. Chapter 5 summarizes the obtained results and discusses further developments.

University of Central Florida College of Engineering Thesis
Real-time digital simulation is a powerful means for engineers and scientists in government, industry, and academia to perform research and training as well as serving as a basis for many commercial applications. Due to the special constraints imposed by digitally simulating continuous systems in real time, however, many of these systems either require costly high-speed components or are unable to provide suitable performance characteristics using affordable computers. This dissertation describes a new technique for the synthesis of numerical integrators specifically designed for the real-time digital simulation of continuous systems. This methodology is based upon the fact that the state derivatives in a simulation model typically have a significantly limited bandwidth. This information is exploited to improve the efficiency of numerical integrators by selecting the coefficients of a general-form integrator such that it approximates an ideal integrator over the limited frequency spectrum of the state derivative.
Ph.D.
Doctorate;
Department of Electrical and Computer Engineering
Engineering
Electrical and Computer Engineering
135 p.
xix, 135 leaves, bound : ill. ; 28 cm.

Approved for public release; distribution is unlimited
Structural synthesis is the analysis of the dynamic response of a system when either subsystems are combined (substructure coupling) or modifications are made to substructures (structural modification). The integral equation formulation for structural synthesis is a method that requires only the baseline transient response, the baseline modal parameters, and the impedance of the structural modification. The integral formulation results in a Volterra integral equation of the second-kind. An adaptive time-marching scheme is utilized to solve the integral equation formulation for structural synthesis. When structural modifications of large magnitude are made, the solution to the integral equation can become unstable. To overcome this conditional stability, the derivative of the synthesis equation is examined and demonstrated to be stable regardless of the magnitude of the structural modification.

Thesis (MScEng)--University of Stellenbosch, 2002.
ENGLISH ABSTRACT: A computational tool for numerical synthesis via optimization is developed. Only two port waveguide devices are considered. The Finite Element Method (FEM) is used for the electromagnetic analysis. Specifically, the frequency domain electric field FEM is used with vector curl-conforming constant tangential/linear normal brick-shaped elements. Special boundary conditions are used at the ports. These boundary conditions only consider dominant mode propagation. The issues surrounding the implementation of this formulation are discussed. The results generated using this code compare favorably to examples from independent sources. A parametric mesher that is used in conjunction with the FEM is developed. This is done to eliminate the need for human intervention during each iteration of the synthesis procedure. Fast Frequency (FF) techniques are presented to reduce the computational requirements of the synthesis. FF techniques reduce the cost of calculating many frequency samples in a specified band and do not reduce the computational requirements of computing a FEM solution at a single frequency. The FF techniques presented are: Asymptotic Waveform Evaluation (AWE), Model Based Asymptotic Waveform Evaluation (MB-AWE) and Model Based Parameter Estimation (MBPE) . The results obtained using these techniques are compared and the most suitable technique for the synthesizer is selected. MBPE is selected as the most suitable technique for this application. An adaptive sampling algorithm for Model Based Parameter Estimation is presented. The algorithm relies on the difference between multiple models generated from the same samples to determine the sample locations. The use of this algorithm enables a model of a narrow band filter at X-band to be determined using only fourteen FEM solutions. The difference between the model- and the FEM solutions is less then -lOOdBacross the band. A sample synthesis using generalized simulated annealing is presented. A single pole filter in X-band waveguide is successfully synthesized to illustrate the usefulness of the code. The use of FF techniques results in a computational cost saving of a factor of forty times.
AFRIKAANSE OPSOMMING: 'n Rekenaar werktuig vir numeriese sintese deur middel van optimering word ontwikkel. Slegs twee-poort golfleierkomponente word beskou. Die Eindige Element-metode (EEM) word vir die elektromagnetiese analise gebruik. Meer spesifiek, die frekwensiegebied, elektriese-veld EE-formuleering word gebruik, met eurl-ondersteunende, konstant-tagensiaaljlineêr-normaal, baksteenvormige vektorelemente. Spesiale grensvoorwaardes word by die poorte gebruik. Hierdie grensvoorwaardes neem slegs voortplanting van die dominante modus in ag. Die kwessies rondom die implementering van hierdie EEM word bespreek. Resultate wat met hierdie kode verkry word, vergelyk goed met dié vanuit onafhanklike bronne. 'n Parametriese diskretisasie prosedure in ontwikkel, vir gebruik saam met die genoemde EEM, met die doelom menslike interaksie uit die weg te ruim, tydens die sintese proses. Vinnige Frekwensie (VF) tegnieke word beskryf, met die doelom die berekeningskoste van die sintese te verminder. VF tegnieke verminder die berekeningskoste verbonde aan 'n reeks EEM oplosings binne 'n gegewe frekwensieband, maar verminder nie die koste verbonde aan 'n enkel-frekwensie EEM oplossing nie. Die VF tegnieke wat beskryf word, is die volgende: Asimptotiese Golfvorm Evaluasie (AGE), Model Gebaseerder Asimptotiese Golfvormevaluasie (MGAGE) en Model- Gebaseerde Parameterekstraksie (MGPE). Die resultate wat met hierdie metodes verkry word, word vergelyk om sodoende die mees toepaslike VF tegniek te kies. MGPE word gekies as die mees toepaslike tegniek. 'n Aanpasbase monsteringsalgoritme vir MGPE word beskryf. Die algoritme berus op die verskil tussen twee modelle wat vanaf dieselfde stel punte geskep word, om monsterfrekwensiewaardes te bepaal. Die gebruik van hierdie algoritme lei tot 'n model van 'n nou-, X-band filter, vanuit slegs veertien EEM oplossings. Die verskil tussen hierdie model en enige EEM oplossings binne die band, is kleiner as -lOOdB. 'n Voorbeeld sintese, wat gebruik maak van veralgemeende, gesimuleerde versmelting, word beskryf. 'n Enkel-pool filter by X-band word suksesvol gesintetiseer om die bruikbaarheid van die kode te illustreer. 'n Faktor veertig vermindering III berekeningskostes word behaal deur gebruik te maak van VF tegnieke.

Questa tesi affronta una varietà di temi di ricerca, spaziando dalla interazione uomo-macchina alla modellizzazione fisica. Ciò che unisce queste ampie aree di interesse è l'idea di utilizzare simulazioni numeriche di fenomeni acustici basate sulla fisica, al fine di implementare interfacce uomo-macchina che offrano feedback sonoro coerente con l'interazione dell'utente. A questo proposito, negli ultimi anni sono nate numerose nuove discipline che vanno sotto il nome di -- per citarne alcune -- auditory display, sonificazione e sonic interaction design. In questa tesi vengono trattate la progettazione e la realizzazione di algoritmi audio efficienti per la sonificazione interattiva. A tale scopo si fa uso di tecniche di modellazione fisica di suoni ecologici (everyday sounds), ovvero suoni che non rientrano nelle famiglie del parlato e dei suoni musicali.
The work presented in this thesis ranges over a variety of research topics, spacing from human-computer interaction to physical-modeling. What combines such broad areas of interest is the idea of using physically-based computer simulations of acoustic phenomena in order to provide human-computer interfaces with sound feedback which is consistent with the user interaction. In this regard, recent years have seen the emergence of several new disciplines that go under the name of -- to cite a few -- auditory display, sonification and sonic interaction design. This thesis deals with the design and implementation of efficient sound algorithms for interactive sonification. To this end, the physical modeling of everyday sounds is taken into account, that is sounds not belonging to the families of speech and musical sounds.

PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO
Transformadores de guia de onda são amplamente empregados no projeto de componentes em onda guiada e são encontrados em praticamente todas as cadeias alimentadoras de antenas e demais estruturas de onda guiada na faixa de microondas. Embora a teoria de transformadores seja conhecida, os requisitos de ordem sistêmica têm levado os projetos de transformadores de guia de onda ao seu limite. Para tal nível de exigência, e considerando o número de variáveis no projeto de transformadores, técnicas numéricas de análise (tais como FDTD e expansão modal dentre outros), e otimização têm sido obrigatoriamente empregadas. Por outro lado, o número de variáveis de um transformador, acaba sendo um processo de alto consumo de tempo computacional, incoerente com o porte e objetivo de custo desses transformadores. Este trabalho propõe uma possibilidade alternativa para a análise mais rápida para essas estruturas, através do emprego de formulações fechadas derivadas de métodos varacionais. Um modelo heurístico é proposto para o caso de descontinuidades em dois planos, sejam para o caso de descontinuidades homogêneas ou para não-homogêneas.
Waveguide transformers are widely used on antenna’s feeder chains and other microwave devices. Although the theory of quarter wavelength transformers is well known, the current electrical performance of such microwave devices has been pushing the waveguide transformers design to its limit. For attending such level of requirements, and considering the number of existing variables on a waveguide transformer design, very accurate numerical techniques has been applied on its analyses, (such as FDTD, mode matching, etc), and optimization techniques as well. On the other hand, such numerical techniques are very memory and/or CPU/time consuming, which do not match with the cost objective of those simple concept transformers. This work proposes an alternative technique, based on close-form models derived from varational theory. A heuristic model is also proposed for attending the two plane transformer case, which can be easily applied for both homogeneous and inhomogeneous structures. Keywords Waveguide;

La simulation informatique par modele physique permet de modeliser la chaine causale qui va de l'action humaine (le geste) a l'emission du son selon une serie de composants structurels (systemes excitateurs, structures vibrantes, resonateurs). Le theme central de ce travail de these est l'etude de la structure vibrante, objet producteur du phenomene sonore. Sur ce theme s'articulent plusieurs niveaux theoriques et experimentaux axes sur la mise au point d'un systeme de modelisation et simulation complet pour la creation musicale

Les vibrations de plaques minces présentent des dynamiques très riches et variées, allant de comportements linéaire à fortement non linéaire en fonction de leur amplitude par rapport à l'épaisseur. Cette thèse présente le développement d'un code numérique capable de simuler sans restriction cette dynamique complexe, décrite par les équations de Von Karman, dans le cas de plaques homogènes et présentant une géométrie rectangulaire. L'application principale de ce code est de produire des sons de cymbales et de gongs: cette partie du travail s'inscrit donc dans le contexte de la synthèse sonore par modélisation physique. Pour cela, une approche modale est utilisée, afin de réduire les équations aux dérivées partielles à un ensemble d'équations différentielles ordinaires couplées. Un schéma d'intégration temporelle est proposé, pour lequel la conservation de l'énergie produit une condition de stabilité. Les caractéristiques les plus intéressantes du schéma modal sont sa précision et la possibilité de mettre en place des lois d'amortissements complexes à moindre coût. Le son produit par le code numérique est systématiquement comparée à celui calculé par une autre méthode fondée sur les techniques de différences finies. Les aspects fondamentaux de la physique des vibrations non linéaires sont également pris en compte au cours de ce travail. Lorsqu'une plaque vibre dans un régime faiblement non linéaire, les couplages modaux produisent des vibrations qui dépendent de l'amplitude, des résonances internes, des instabilités, des sauts et des bifurcations. Le schéma modal est utilisée pour construire et analyser la réponse non linéaire de la plaque au voisinage de ses premières fréquences propres, dans un cas conservatif, puis en prenant en compte les effets de l'amortissement et du forçage, montrant ainsi leurs effets sur les modes normaux non linéaires du système hamiltonien. Lorsque les plaques vibrent dans un régime fortement non linéaire, la description la plus appropriée de la dynamique est donnée en termes des propriétés statistiques du système, en raison de la multitude de degrés de liberté activés. Théoriquement, ce cadre est offert par la théorie de turbulence d'ondes. À cause de la grande quantité de modes activés dans de telles vibrations, le code en différence finie conservatif est préféré au schéma modal. Lorsque la plaque est excitée avec un forçage sinusoïdal autour d'un de ses modes propres de basse fréquence, une cascade d'énergie se produit, activant des milliers de modes à plus hautes fréquences. Une interprétation statistique des résultats des simulations est proposée, ainsi qu'une comparaison avec des données expérimentales et des autres résultats numériques trouvés dans la littérature. En particulier, les effets du forçage ponctuel ainsi que des imperfections géométriques des plaques sont analysées
Thin plate vibrations display a rich and complex dynamics that ranges from linear to strongly nonlinear regimes when increasing the vibration amplitude with respect to the thickness. This thesis is concerned with the development of a numerical code able to simulate without restrictions this large spectrum of dynamical features, described by the von Kármán equations, in the case of flat, homogeneous plates presenting a rectangular geometry. The main application of such a code is to produce gong-like sounds, in the context of sound synthesis by physical modelling. For that, a modal approach is used, in order to reduce the original Partial Differential Equations to a set of couped Ordinary Differential Equations. An energy-conserving, second-order accurate time integration scheme is developed in order to yield a stability condition. The most appealing features of the modal scheme are its accuracy and the possibility of implementing a rich loss mechanism by selecting an appropriate damping factor for each one of the modes. The sound produced by the numerical code is systematically compared to another numerical technique based on Finite Difference techniques. Fundamental aspects of the physics of nonlinear vibrations are also considered in the course of this work. When a plate vibrates in a weakly nonlinear regime, modal couplings produce amplitude-dependent vibrations, internal resonances, instabilities, jumps and bifurcations. The modal scheme is used to construct and analyse the nonlinear response of the plate in the vicinity of its first eigenfrequencies, both in free and forced-damped vibrations, showing as a result the effect of damping and forcing on the nonlinear normal modes of the underlying Hamiltonian system. When plates vibrate in a strongly nonlinear regime, the most appropriate description of the dynamics is given in terms of the statistical properties of the system, because of the vast number of interacting degrees-of-freedom. Theoretically, this framework is offered by the Wave Turbulence theory. Given the large amount of modes activated in such vibrations, a Finite Difference, energy-conserving code is preferred over the modal scheme. Such a scheme allows to produce a cascade of energy including thousands of modes when the plate is forced sinusoidally around one of its lowest eigenfrequencies. A statistical interpretation of the outcome of the simulation is offered, along with a comparison with experimental data and other numerical results found in the literature. In particular, the effect of the pointwise forcing as well as geometrical imperfections of the plates are analysed

Pour exécuter un algorithme abstrait sur un ordinateur quantique il faut compiler l'algorithme en une séquence d'instructions bas niveau exécutables par le processeur. L'étape de compilation est cruciale car elle détermine la quantité de ressources nécessaire pour l'exécution d'un algorithme ; par conséquent elle se doit d'être optimisée. Dans cette thèse nous nous intéressons à une brique de la compilation~: la synthèse de circuits quantiques à partir d'une spécification abstraite d'un opérateur. Dans un premier temps nous étudions le cas où la matrice unitaire d'un opérateur quantique nous est donnée et nous explorons la minimisation des ressources quantiques et la minimisation des ressources classiques. Même si l'optimisation simultanée de ces deux types de ressources semble difficile, nous proposons de meilleurs compromis améliorant la littérature.Dans un second temps nous nous intéressons à la classe des opérateurs dits linéaires réversibles. Nous nous intéressons cette fois-ci exclusivement à l'optimisation des ressources quantiques et nous améliorons l'état de l'art dans diverses cas de métriques (taille et profondeur du circuit) et de processeurs quantiques (processeurs NISQ, ou à connectivité complète)
To run an abstract algorithm on a quantum computer, the algorithm must be compiled into a sequence of low-level instructions that can be executed by the processor. The compilation step is crucial because it determines the quantity of resources necessary for the execution of an algorithm. Therefore, the compilation stage must be optimized. In this thesis, we are interested in a brick of compilation: the synthesis of quantum circuits from an abstract specification of an operator.First, we study the case where the unitary matrix of a quantum operator is given to us and we explore the minimization of both quantum resources and classical resources. Even if the simultaneous optimization of these two types of resources seems difficult, we propose better compromises improving the literature.Secondly, we are interested in the class of so-called reversible linear operators. This time we are exclusively interested in the optimization of quantum resources and we improve the state of the art in various cases of quantum metrics (circuit size, circuit depth) and processors (NISQ, fully-connected processors)

À cause de la nature relativement jeune des outils de synthèse de haut-niveau (HLS), de nombreuses optimisations arithmétiques n'y sont pas encore implémentées. Cette thèse propose des optimisations arithmétiques se servant du contexte spécifique dans lequel les opérateurs sont instanciés. Certaines optimisations sont de simples spécialisations d'opérateurs, respectant la sémantique du C. D'autres nécessitent de s'éloigner de cette sémantique pour améliorer le compromis précision/coût/performance. Cette proposition est démontrée sur des sommes de produits de nombres flottants. La somme est réalisée dans un format en virgule-fixe défini par son contexte. Quand trop peu d’informations sont disponibles pour définir ce format en virgule-fixe, une stratégie est de générer un accumulateur couvrant l'intégralité du format flottant. Cette thèse explore plusieurs implémentations d'un tel accumulateur. L'utilisation d'une représentation en complément à deux permet de réduire le chemin critique de la boucle d'accumulation, ainsi que la quantité de ressources utilisées. Un format alternatif aux nombres flottants, appelé posit, propose d'utiliser un encodage à précision variable. De plus, ce format est augmenté par un accumulateur exact. Pour évaluer précisément le coût matériel de ce format, cette thèse présente des architectures d'opérateurs posits, implémentés avec le même degré d'optimisation que celui de l'état de l'art des opérateurs flottants. Une analyse détaillée montre que le coût des opérateurs posits est malgré tout bien plus élevé que celui de leurs équivalents flottants. Enfin, cette thèse présente une couche de compatibilité entre outils de HLS, permettant de viser plusieurs outils avec un seul code. Cette bibliothèque implémente un type d'entiers de taille variable, avec de plus une sémantique strictement typée, ainsi qu'un ensemble d'opérateurs ad-hoc optimisés
High-level synthesis (HLS) tools offer increased productivity regarding FPGA programming. However, due to their relatively young nature, they still lack many arithmetic optimizations. This thesis proposes safe arithmetic optimizations that should always be applied. These optimizations are simple operator specializations, following the C semantic. Other require to a lift the semantic embedded in high-level input program languages, which are inherited from software programming, for an improved accuracy/cost/performance ratio. To demonstrate this claim, the sum-of-product of floating-point numbers is used as a case study. The sum is performed on a fixed-point format, which is tailored to the application, according to the context in which the operator is instantiated. In some cases, there is not enough information about the input data to tailor the fixed-point accumulator. The fall-back strategy used in this thesis is to generate an accumulator covering the entire floating-point range. This thesis explores different strategies for implementing such a large accumulator, including new ones. The use of a 2's complement representation instead of a sign+magnitude is demonstrated to save resources and to reduce the accumulation loop delay. Based on a tapered precision scheme and an exact accumulator, the posit number systems claims to be a candidate to replace the IEEE floating-point format. A throughout analysis of posit operators is performed, using the same level of hardware optimization as state-of-the-art floating-point operators. Their cost remains much higher that their floating-point counterparts in terms of resource usage and performance. Finally, this thesis presents a compatibility layer for HLS tools that allows one code to be deployed on multiple tools. This library implements a strongly typed custom size integer type along side a set of optimized custom operators

Pour réduire les coûts des systèmes embarqués, ces derniers sont livrés avec des micro-processeurs peu puissants. Ces processeurs sont dédiés à l'exécution de tâches calculatoires dont certaines, comme la transformée de Fourier rapide, peuvent s'avérer exigeantes en termes de ressources de calcul. Afin que les implémentations de ces algorithmes soient efficaces, les programmeurs utilisent l'arithmétique à virgule fixe qui est plus adaptée aux processeurs dépourvus d'unité flottante. Cependant, ils se retrouvent confrontés à deux difficultés: D'abord, coder en virgule fixe est fastidieux et exige que le programmeur gère tous les détails arithmétiques. Ensuite, et en raison de la faible dynamique des nombres à virgule fixe par rapport aux nombres flottants, les calculs en fixe sont souvent perçus comme intrinsèquement peu précis. La première partie de cette thèse propose une méthodologie pour dépasser ces deux limitations. Elle montre comment concevoir et mettre en œuvre des outils pour générer automatiquement des programmes en virgule fixe. Ensuite, afin de rassurer l'utilisateur quant à la qualité numérique des codes synthétisés, des certificats sont générés qui fournissent des bornes sur les erreurs d'arrondi. La deuxième partie de cette thèse est dédiée à l'étude des compromis lors de la génération de programmes en virgule fixe pour les briques d'algèbre linéaire. Des données expérimentales y sont fournies sur la synthèse de code pour la multiplication et l'inversion matricielles
To be cost effective, embedded systems are shipped with low-end micro-processors. These processors are dedicated to one or few tasks that are highly demanding on computational resources. Examples of widely deployed tasks include the fast Fourier transform, convolutions, and digital filters. For these tasks to run efficiently, embedded systems programmers favor fixed-point arithmetic over the standardized and costly floating-point arithmetic. However, they are faced with two difficulties: First, writing fixed-point codes is tedious and requires that the programmer must be in charge of every arithmetical detail. Second, because of the low dynamic range of fixed-point numbers compared to floating-point numbers, there is a persistent belief that fixed-point computations are inherently inaccurate. The first part of this thesis addresses these two limitations as follows: It shows how to design and implement tools to automatically synthesize fixed-point programs. Next, to strengthen the user's confidence in the synthesized codes, analytic methods are suggested to generate certificates. These certificates can be checked using a formal verification tool, and assert that the rounding errors of the generated codes are indeed below a given threshold. The second part of the thesis is a study of the trade-offs involved when generating fixed-point code for linear algebra basic blocks. It gives experimental data on fixed-point synthesis for matrix multiplication and matrix inversion through Cholesky decomposition

Ce travail présente les dimensions physiologiques et pathologiques de la circulation sanguine artérielle et détaille différentes modalités de réparation vasculaire. Il s'intéresse particulièrement aux technologies innovantes de suture vasculaire permettant de réparer le système circulatoire. Différentes stratégies de restauration du flux sanguin ont été extraites de la pratique clinique et étudiées sur un modèle numérique original du réseau vasculaire simplifié en 55 artères, à la fois en en 0D et en 1D. Nous avons ainsi exploré les différentes techniques de restauration du flux sanguin au membre inférieur au cours d'une oblitération d'une artère iliaque par plusieurs types de pontages anatomiques et extra-anatomiques mais aussi par l'interposition d'un stent sur le réseau natif. Nous avons ainsi montré à chaque fois la présence d'un flux restitué en aval du pontage et conforme aux constatations cliniques, validant notre réseau numérique. Nous avons également appliqué les outils OD de ce réseau numérique à une fistule artérioveineuse. Nous avons modulé différents paramètres afin d'anticiper les conséquences d'une intervention sur une sténose ou un hyperdébit avec comme ambition d'apporter une aide à la réflexion du chirurgien vasculaire
This study presents the physiological and pathological aspects of the arterial blood flow and draws up various methods of vascular repair. It focuses on innovative suture solutions for circulatory system repair. Various blood flow restoration strategies, retrieved from the surgical practice, were examined on the basis of a new digital model of the vascular network simplified into 55 arteries, in both 0D and 1D. We thus studied several techniques of blood flow restoration to the lower limb during an iliac artery obliteration, those based on different types of anatomical and extra-anatomical bypasses, but also one based on a stent being inserted in the original network. At each attempt, we found the flow to be restored downstream and congruent to the clinical observations, thus confirming our digital network. We have also applied its 0D tools to an arteriovenous fistula. With the aim of providing our model as a tool to assist the surgeon’s decision making, we then have adjusted various parameters in order to anticipate the repercussions of surgical procedures to treat both stenosis and hypertension

Les principales techniques d'exploitation des donnees numeriques sur ordinateur sont introduites. Une methodologie d'analyse par synthese d'image et ses differentes mises en oeuvre algorithmiques sont decrites. Dans une deuxieme partie, il est presente l'etude d'un codage particulier des donnees : le codage octree. Son adaptation a la manipulation de volumes numeriques est discutee

This thesis describes the development and validation of a new method for the generation of synthetic inlet conditions, referred to as the Synthetic Eddy Method (SEM), for Large-Eddy Simulation (LES). The motivation for this work is the growing interest of the engineering community in hybrid methods coupling Reynolds-averaged Navier-Stokes (RANS) approaches in regions of the flow that are at equilibrium (where RANS can be trusted), with LES approaches elsewhere. The focus of this thesis is on the RANS-to-LES interface inside attached turbulent boundary layers, where an unsteady LES content has to be explicitly generated from a steady RANS solution. The SEM is a stochastic algorithm that generates instantaneous velocity fluctuations from input statistical quantities that are typically available from a RANS solution. The method is based on the classical view of turbulence as a superposition of eddies. The signal is expressed as a sum of synthetic eddies with random position and intensity, and which are subsequently convected through the LES domain inlet. The method generates stochastic signals with prescribed mean velocity, Reynolds stresses, and length and time scale distributions. The SEM is implemented into the unstructured finite volume code, Code Saturne, and used to generate inflow data for the LES of plane channel flow. It is shown that the robustness of the SEM depends strongly on the correct specification of its input parameters (i.e. mean velocity, turbulent kinetic energy, and integral length and time scales). Equations to compute all the input parameters of the SEM from simple RANS statistics are then derived, and the SEM is used to couple an upstream RANS simulation with a LES in the case of simple wall-bounded flows (i.e. channel, boundary layer and duct flows). Generally with synthetic turbulence, some distance is required downstream of the inlet for realistic fluctuations to develop. With the SEM, this development length is found to be approximately 3,000 wall units for all the cases simulated - much shorter than other comparable methods of generation of synthetic turbulence. Hybrid simulations of more complicated turbulent flows involving separation and reattachment (i.e. the flow over a backward facing step and over an airfoil trailing edge) are then performed. The SEM is compared to (and found to perform better than) other existing methods of generation of synthetic turbulence. It is shown that when the SEM is used, the RANS-to-LES interface can be placed only 1−2 boundary layer thicknesses upstream of the region of interest (where the flow separates) without significantly alterating the results.

The fundamental problem of orthometric heights is that the mean gravity value cannot be determined due to the lack of precise topographical mass information. This thesis employs a global synthetic Earth gravity model, based on known and simulated global masses, in order to circumvent this problem. Applying forward gravity modelling techniques, the behaviour of gravity inside the topography as well as orthometric heights are studied in detail.

Dans le domaine des vibrations de structures, les performances croissantes des calculateurs permettent de traiter des modèles de plus en plus complexes, conduisant immanquablement à la prise en compte de phénomènes non linéaires. Le contexte industriel mène par ailleurs à vouloir considérer des systèmes toujours plus gros. Ces travaux de thèse sont axés autour du développement de procédés algorithmiques permettant de résoudre efficacement, des problèmes de taille élevée en dynamique non linéaire. Le parti pris est pour cela de calculer les Modes Non Linéaires (MNLs) des structures, objets représentatifs non seulement de l'état vibratoire du système mais aussi de ses non linéarités. Après avoir proposé une méthode de calcul des MNLs compacte et économe, ce manuscrit propose dans un second temps d'exploiter l'information contenue dans ces objets pour tracer rapidement et à l'aide de peu de calculs la réponse de systèmes soumis à des efforts extérieurs
In the field of structural vibrations, the increasing performance of computers allows to handle more and more complex and realistic systems. This inevitably leads to the consideration of nonlinear phenomena. The industrial context is also characterized by the need to solve ever larger systems. The work presented in this PhD thesis focuses on the development of algorithmic processes to effectively solve large scale problems in nonlinear dynamics. To do this, the choice is made to calculate the Nonlinear Normal Modes (NNMs) of the structures. These objects are not only representative of the vibratory state of the system but also of its nonlinearities.After having proposed a compact and economical method for calculating NNMs, this manuscript then proposes to exploit the data contained in these objects to quickly plot the response of systems subjected to external forces. The implemented methods perform only a few calculations to achieve this

This thesis investigates the impact of upstream duct convolution on the plume development for high speed jets. In particular, investigations are carried out into an unconventional aero-engine exhaust systems comprised of a modified convergent-divergent rectangular nozzle where the converging section of the nozzle includes an S-bend in the duct. The motivation for this work comes from both the military and civilian sectors of the aerospace industry. The growing interest into highly efficient engines in the civilian sector and increasing complexities involved in stealth technologies for military applications has led to new design constraints on aero-engine exhaust systems that require further research into flows through more complex duct geometries. Due to a lack of experimental data into this area in the open literature validation studies are undertaken into flows through an S-bend duct and exhaust plume development from a rectangular convergent-divergent nozzle. The validation work is simulated using RANS CFD with common industrial turbulence models as well as LES with artificial inlet conditions. Subsequently, a CFD investigation into three unconventional aero-engine exhaust systems, with over-expanded conditions, with differing angles of curvature across the converging S-bend is undertaken using both RANS and LES methodologies governed by the validation work. As the curvature of the S-bend was increased it was found that the thrust and effective NPR both decrease. Whilst these changes were within acceptable levels (with some optimisation) for a circumferential extent of up to 53.1 the losses became prohibitive large at extents. For the ducts with a greater circumferential extents separation was seen to occur at the throat of the nozzle; this changes the design parameters of the nozzle leading to a higher Mach number and could potentially be harnessed to improve performance of the engine creating a `variable throat' nozzle. The impact of using different numerical solvers to simulate the flow through an unconventional aero-engine exhaust system has also been considered. The use of LES has shown that the octagonal, hexahedral and trapezoidal shapes initially observed in the development of the plumes of the RANS cases are likely to be an artifact caused by the RANS solver, as would the transverse total pressure gradients observed in the RANS cases at the nozzle exit as they are both absent from all of the LES results. Likewise the implementation of realistic inlet conditions has a significant impact on the development of the plume, particularly in the length of the potential core and the number of shock cells.

The interactions between laminar premixed flames and counter-rotating vortex pairs in natural and synthetic gas mixtures have been computationally investigated through the use of Direct Numerical Simulations and parallel processing. Using a computational model for premixed combustion, laminar flames are simulated for single- and two-component fuel mixtures of methane, carbon monoxide, and hydrogen. These laminar flames are forced to interact with superimposed laminar vortex pairs, which mimic the effects of a pulsed, two-dimensional slot-injection. The premixed flames are parameterized by their unstretched laminar flame speed, heat release, and flame thickness. The simulated vortices are of a fixed size (relative to the flame thickness) and are parameterized, solely, by their rotational velocity (relative to the flame speed). Strain rate and surface curvature measurements are made along the stretched flame surfaces to study the effects of additive syngas species (CO and H2) on lean methane-air flames. For flames that share the same unstretched laminar flame speed, heat release, and flame thickness, it is observed that the effects of carbon monoxide on methane-air mixtures are essentially negigible while the effects of hydrogen are quite substantial. The dynamics of stretched CH4/Air and CH4/CO/Air flames are nearly identical to one another for interactions with both strong and weak vortices. However, the CH4/H2/Air flames demonstrate a remarkable tendency toward surface area growth. Over comparable interaction periods, the flame surface area produced during interactions with CH4/H2/Air flames was found to be more than double that of the pure CH4/Air flames. Despite several obvious differences, all of the interactions revealed the same basic phenomena, including vortex breakdown and flame pinch-off (i.e. pocket formation). In general, the strain rate and surface curvature magnitudes were found to be lower for the CH4/H2/Air flames, and comparable between CH4/Air and CH4/CO/Air flames. Rates of flame stretching are not explicitely determined, but are, instead, addressed through observation of their individual components. Two different models are used to determine local displacement speed values. A discrepancy between practical and theoretical definitions of the displacement speed is evident based on the instantaneous results for CH4/Air and CH4/H2/Air flames interacting with weak and strong vortices.

Flow control is a key factor in optimizing the performance of any vehicle moving through fluids. Particularly, in aerodynamics there are many potential benefits for implementing synthetic jets to achieve aircraft designs with less moving parts, uper- maneuverability, and separation control for fuel economy. Piezoelectric synthetic jets are of special interest because of their lightweight and low power consumption. Numerous publications on such jets are available. Actuator properties and boundary conditions relevant to this particular application however are often overlooked. The focus of this project is to numerically model synthetic jets in quiescent air to study the influence of cavity geometry and boundary conditions of the piezoelectric diaphragm on jet velocity. Numerical simulation is performed for two synthetic jet cavities of different height and orifice diameter. The numerical modeling utilizes a turbulent RNG κ – ε model and a moving boundary condition with two oscillating deflection profiles, parabolic and logarithmic, applied to the diaphragm. The actuators modeled are typical Bimorph and Thunder piezoelectric actuators. The initial conditions for the actuators are obtained experimentally resulting in 0.396mm and 0.07mm respectively when driven with a sinusoidal wave input at 1524 V/m and 4064 V/m. Although the velocity boundary numerical model gave overall better results than the current moving-boundary numerical model, the moving-boundary model is more accurate since it better approximates the movement of the diaphragm. From an optimizing viewpoint the moving boundary is more suitable to attempt to optimize the design because displacement magnitude of the diaphragm can be measured directly from experiments. For the higher displacement Bimorph actuator, a logarithmic profile matches the experimental results, whereas the parabolic profile provided better results for the relatively small displacement Thunder actuator. It is thus hypothesized that both tested actuators, Bimorph and Thunder, oscillate according to the specified logarithmic and parabolic profile respectively. Cavity height was briefly investigated for the Bimorph actuator. Results show that cavity height did not make a difference in the centerline velocity for the numerical model. The model fails to consider the important effect of the dynamic coupling of the actuator displacement and the pressure that develops inside the cavity. The pressure values obtained are comparable to the theoretical blocking pressure for the Bimorph in the cavity. The results of this study show that jet formation and development has unique characteristics for each actuator and cavity configuration. The smaller orifice cavity configuration produced a faster, longer, thinner jet with larger vortices than the bigger orifice. During max expulsion, t = 0.25T, and max ingestion, t = 0.75T, a low-pressure area localized at the corners of the orifice, inlet and exit respectively, were observed. All cavity configurations passed all three known jet formation criterions that include, Lo/Do>1, Re > 50, and Re/S2 > 0.16.

A numerical study of axisymmetric synthetic jet flow was conducted. The synthetic jet cavity was modeled as a rigid chamber with a piston-like moving diaphragm at its bottom. The Shear-Stress-Transportation (SST) k-omega and #61559; turbulence model was employed to simulate turbulence. Based on time-mean analysis, three flow regimes were identified for typical synthetic jet flows. Typical vortex dynamics and flow patterns were analyzed. The effects of changes of working frequency, cavity geometry (aspect ratio), and nozzle geometry were investigated. A control-volume model of synthetic jet cavity was proposed based on the numerical study, which consists of two first-order ODEs. With appropriately selected parameters, the model was able to predict the cavity pressure and average velocity through the nozzle within 10% errors compared with full simulations. The cavity model can be used to generate the boundary conditions for synthetic jet simulations and the agreement to the full simulation results was good. The saving of computational cost is significant. It was found that synthetic jet impingement heat transfer outperforms conventional jet impingement heat transfer with equivalent average jet velocity. Normal jet impingement heat transfer using synthetic jet was investigated numerically too. The effects of changes of design and working parameters on local heat transfer on the impingement plate were investigated. Key flow structures and heat transfer characteristics were identified. At last, a parametric study of an active heat sink employing synthetic jet technology was conducted using Large Eddy Simulation (LES). Optimal design parameters were recommended base on the parametric study.

This numerical study focuses on the implementation of active flow control using synthetic jets on vertical-axis wind turbine (VAWT) blades. This study demonstrates that synthetic-jet based flow control improves the efficiency of the turbine and reduces the risk of structural fatigue.

In VAWTs, the blades experience a significant variation in the angle of attack over each rotation cycle and associated with it are sudden changes in the flow-induced loading on the blades. For example, a sudden variation in blade loading is experienced due to the detachment of the leading edge vortex at high angles of attack. This is in-turn reduces the axial force and hence the overall power output of the turbine. Additionally, such force variations lead to structural fatigue and possibly failure. Current simulations consider a cross-section of a three-blade VAWT model (with straight blades). VAWT models with two different airfoils, NACA 0018 and DU 06-W-200, are considered at tip-speed-ratios of 2 and 3. In these simulations, unsteady, Reynolds-averaged Navier-Stokes equations along with the Spalart-Allmaras turbulence model are employed, where stabilized finite element method is utilized along with an implicit time-integration scheme.

The idea of using synthetic jets is to control the variation in flow-induced loading during each rotation cycle. At first the dominant location of the flow separation is determined for both airfoils. The jets are then placed at this location. Jet parameters of blowing ratio and reduced frequency are specified within a range (i.e., O(0.5-1.5) and O(1-10), respectively) and their effects on jet performance are studied. The jets are activated only in a selected portion of the rotation cycle. This is referred to as the partial cycle control in contrast to the full cycle (the latter is found to be detrimental). For given jet parameters, simulations results are used to determine whether the jets improve axial force, flow separation and blade-vortex interaction. At blowing ratio of 1.5 and reduced frequency of 5, we observe above 12% increase in the average axial force over the rotation cycle for both airfoils.

La thèse porte sur l'interprétation des données de réflectométrie pour extraire les caractéristiques de la turbulence construites à partir de simulations numériques bidimensionnelles. Il a été démontré que la résonance due au piégeage de l'onde peut apparaître dans le plasma fluctuant et produire des sauts de phase. Cette interprétation à faible niveau de turbulence est directe. Cependant, le niveau de turbulence du bord du plasma est généralement élevé menant ainsi le réflectomètre à un comportement non linéaire. En conséquence, il y a une perte de cohérence de l'onde de sondage et un élargissement du faisceau-sonde après la traversée de la couche de turbulence. Cette étude a montré qu'une petite longueur de corrélation de la turbulence conduit à un faible élargissement et à de fortes variations de la phase du faisceau-sonde. Pour étudier comment une forte turbulence de bord affecte le signal de réflectométrie à balayage ultra rapide en fréquence (USFR) obtenu lors d'un sondage. Pour étudier cela des séries de simulations 2D ont été réalisées. Simultanément les spectres de variations de phase et de variations d'amplitude du réflectomètre ont été analysés. Il a été constaté que des pics spectraux correspondant à une diffusion accrue dans la région de turbulence de bord peuvent être observés dans les spectres de variations d'amplitude du signal. Un USFR utilisant une configuration de réflectométrie poloïdale a été proposé pour accéder à plus d'informations sur la turbulence de bord où le déplacement poloïdal des antennes réceptrices entraîne un glissement du pic de diffusion. En perspective, ces mesures peuvent fournir des informations supplémentaires sur, la déformation du faisceau-sonde, les propriétés de la turbulence et faciliter la mesure du signal cohérent porteur de l'information sur la turbulence de cœur du plasma. En plus, le code 2D "full-wave" a été appliqué en tant que diagnostic synthétique aux données de simulation gyro-cinétique du code de turbulence Gysela pour une décharge du tokamak de Tore-Supra. Les signaux de réflectométrie à fréquence fixe ont montré un bon accord entre la longueur de corrélation d'amplitude du signal avec celle de la turbulence utilisée comme donnée d'entrée. Il en a été de même pour analyser la longueur de corrélation et les spectres de nombre d'onde obtenus par un USFR pour le tokamak ASDEX-Upgarde
Plasma turbulence studies are essential for successful operation of magnetic confinement fusion devices. Ultra-Fast Swept Reflectometry (USFR), a diagnostic widely used for the measurement of turbulence radial wave-number spectra. While the interpretation of reflectometry data is quite straightforward for small levels of turbulence, it becomes much trickier for larger levels as the reflectometer answer is no longer linear with the turbulence level. It has been shown for instance that resonances due to probing field trapping can appear in turbulent plasma and produce jumps of the signal phase. In the plasma edge region the turbulence level is usually high and can lead to a non-linear regime of the reflecetometer response. The loss of probing beam coherency and beam widening when the probing beam crosses the edge turbulence layer can affect USFR core measurements. Edge turbulence with a long correlation length leads to small beam widening and strong distortion of the probing wave phase. However backscattering effects from turbulence with short correlation lengths are also able to cause reflectometer signal change. To study turbulence wave-number spectra together with reflectometer signal phase variations, signal amplitude variations can be analyzed. Unlike signal phase variation, amplitude does not suffer from resonant jumps, and can give more clear qualitative evaluation of turbulence structure. In the case when the turbulence amplitude peaked in the edge region, it can be detected as spectral peak near local Bragg resonance wave-number. USFR with a set of receiving antennas arranged poloidally was proposed to obtain more information on the edge turbulence properties. A displacement of the spectral peak appears when the receiving antenna is misaligned with the emitting one. In perspective peak displacement measurements can provide additional information on probing beam shaping and turbulence properties and help in coherent mode observation. A 2D full wave code was applied as a synthetic diagnostic to Gysela gyro-kinetic for study of Tore-Supra tokamak core turbulence. Radial correlation lengths computed from the amplitude of multi-channel fixed frequency reflectometry signals have shown good agreement with the turbulence correlation length. The synthetic diagnostic was then applied to analyze the correlation length and wave-number spectra obtained by USFR in the ASDEX-Upgrade tokamak. A comparison between 1D and 2D results have shown different behavior. However correlation lengths measured with UFSR signals are in the same order with turbulence ones

Synthetic jets are produced by the oscillatory movement of a membrane inside a cavity, causing fluid to enter and leave through a small orifice. This results in a net jet that is able to transfer kinetic energy and momentum to a fluid medium without the need of an external fluid source. This is why synthetic jets are interesting and will have key roles in a wide range of relevant applications such as active flow control, thermal cooling or fuel mixing. From the phenomenological point of view, synthetic jets are formed by elaborate flow patterns given their non-linear nature and, under certain conditions, unstable complex flows can be observed. The present dissertation is focused on the investigation of the fluid flow and thermal performance of synthetic jets. Two different synthetic jet actuator geometries (i.e., slotted and circular) are studied. The jets in both configurations are confined by two parallel isothermal plates with an imposed temperature difference, and impinge into a heated plate located at a certain distance from the actuator orifice. The unsteady three-dimensional Navier-Stokes equations are solved for a range of Reynolds numbers using time-accurate numerical simulations. Moreover, a detailed model of the actuator that uses Arbitrary Lagrangian-Eulerian (ALE) formulation to account for the movement of the actuator membrane is developed. This model, based on the governing numbers of the flow, is used to conduct the numerical analyses. The flows obtained in both configurations are noticeably different and three-dimensional for almost all the Reynolds numbers considered. The jet in the slotted configuration is formed by a pair of vortices that undergo turbulent transition and eventually coalesce into the jet. The external flow is dominated by two major recirculation structures that find their counterparts inside the actuator cavity. A new vortical structure, observed in confined slotted jets, appears as an interaction of the synthetic jet flow with the bottom wall and results in a change on the jet’s heat transfer mechanisms. On the other hand, the jet in the circular configuration presents three different flow regions that have been identified according to the literature: the main vortex ring, the trailing jet and the potential core. In this case, the external flow is dominated by the main vortex ring and the trailing jet, thus presenting a different morphology and heat transfer behavior than the slotted configuration. A detailed analysis of the vortex trajectories has shown that the advected vortices on the circular configuration reach the impingement before their slotted counterparts. Distributions of turbulent kinetic energy at the expulsion and vortex swirl and shear strength have revealed that the flow on the circular jet is mostly concentrated near the jet centerline, while it is more spread for the slotted configuration. For these reasons, at the same jet ejection velocity and actuator geometry, synthetic jet formation on the circular configuration can occur at higher frequencies than on the slotted configuration. The analysis of the synthetic jet outlet temperature has shown that assuming a uniform profile is reasonable if the Reynolds number is high enough. Moreover, the outlet jet temperature is significantly higher than the cold plate temperature. The two configurations present different impinging behaviors due to the differences on the flow. Heat transfer analysis on the hot wall has revealed that the circular configuration reaches a higher heat transfer peak than the slotted configuration, however, heat transfer decays faster in the circular configuration when moving away from the jet centerline. Eventually, correlations for the heat transfer at the hot wall and the outlet temperature with the Reynolds number are proposed. They can be useful to include the cavity effects when using simplified models that do not account for actuator cavity.
Els jets sintètics (SJ) són produïts pel moviment oscil·latori d'una membrana a l'interior d'una cavitat, cosa que fa que el líquid entri i surti per un petit orifici. Això es tradueix en un jet que és capaç de transferir energia cinètica i impuls a un medi fluid sense la necessitat d'una font externa. És per això que els SJ són interessants i tindran un paper clau en una àmplia gamma d'aplicacions rellevants, com ara el control actiu de flux, el refredament tèrmic o la barreja de combustible. Des del punt de vista fenomenològic, els SJ estan formats per patrons de flux elaborats per la seva naturalesa no lineal i, sota certes condicions, es poden observar fluxos complexos i inestables. Aquesta tesis està centrada en la investigació del flux de fluids i el rendiment tèrmic dels jets sintètics. S'estudien dues geometries diferents d’actuadors de SJ (és a dir, ranurats i circulars). Els jets en ambdues configuracions estan confinats per dues plaques isotèrmiques paral·leles amb una diferència de temperatura imposada i afecten a una placa escalfada situada a una certa distància de l'orifici de l'actuador. Les equacions tridimensionals inestables de Navier-Stokes es resolen per un nombre de Reynolds utilitzant simulacions numèriques precises en el temps. A més, es desenvolupa un model detallat de l'actuador que utilitza la formulació arbitrària lagrangiana-euleriana (ALE) per explicar el moviment de la membrana de l'actuador. Aquest model, basat en els números de govern del flux, s'utilitza per realitzar els anàlisis numèrics. Els fluxos obtinguts en ambdues configuracions són notablement diferents i tridimensionals per a gairebé tots els números de Reynolds considerats. El jet en la configuració ranurada està format per un parell de vòrtexs que experimenten una transició turbulenta que finalment formen el jet. El flux extern està dominat per dues recirculacions principals amb els seus homòlegs dins de la cavitat de l'actuador. Una nova estructura, observada en els jets ranurats confinats, apareix com una interacció del flux amb la paret inferior i provoca un canvi en els mecanismes de transferència de calor del jet. D'altra banda, el jet en la configuració circular presenta tres regions de flux diferents que s'han identificat segons la literatura: l'anell de vòrtex principal, el jet final i el nucli potencial. En aquest cas, el flux extern està dominat per l'anell de vòrtex principal i el jet de sortida, presentant així un comportament diferent de morfologia i transferència de calor que la configuració ranurada. Un anàlisi detallat de les trajectòries de vòrtex ha demostrat que els vòrtexs de la configuració circular arriben a la paret superior abans que els seus homòlegs ranurats. Les distribucions d'energia cinètica turbulenta a l'expulsió, entre altres, han revelat que el flux del jet circular es concentra majoritàriament a prop de la línia central del jet, mentre que és més estès per a la configuració ranurada. Per aquestes raons, a la mateixa velocitat d'ejecció del jet i geometria de l'actuador, la formació de SJ en la configuració circular pot produir-se a freqüències més altes que a la configuració ranurada. L'anàlisi de la temperatura de sortida dels SJ ha demostrat que assumir un perfil uniforme és raonable si el nombre de Reynolds és prou elevat. A més, la temperatura del jet de sortida és significativament superior a la temperatura de la placa freda. Les dues configuracions presenten diferents comportaments a causa de les diferències en el flux. L’anàlisi de la transferència de calor a la paret calenta ha revelat que la configuració circular arriba a un màxim de transferència de calor més gran que la configuració ranurada, però, la transferència de calor es desaccelera més ràpidament en la configuració circular quan s’allunya de la línia central. Finalment, es proposen correlacions per a la transferència de calor a la paret calenta i la temperatura de sortida amb el nombre de Reynolds. Poden ser útils per incloure els efectes de la cavitat quan s’utilitzen models simplificats que no tenen en compte la cavitat de l’actuador.

Dans le cadre de la conception des planches de bord en phase d'études préliminaires, nous proposons une stratégie d'optimisation permettant de réaliser des gains en masse rapidement à partir d'un cahier des charges. Ce cahier des charges comprend en particulier des critères vibratoires. En fonction des besoins d'études ainsi que des caractéristiques d'une planche de bord, la stratégie développée fait appel à une utilisation conjointe des techniques de sous-structuration et d'optimisation. Elle consiste à optimiser séparément les éléments (ou sous-structures) modifiables. Pour cela, nous étudions les possibilités offertes par les techniques de synthèse modale, puis nous examinons les principaux concepts nécessaires à la mise en forme d'un problème d'optimisation. À partir de cette dernière, nous proposons un développement particulier du calcul des sensibilités paramétriques basé sur la dérivation d'une équation de synthèse modale. Nous confrontons cette nouvelle approche à des techniques usuelles a partir d'un cas test élémentaire. Nous définissons ensuite les hypothèses de passage d'une optimisation de l'ensemble de la planche de bord, vers une optimisation séparée des éléments modifiables. Nous spécifions alors une modélisation des restrictions locales relatives aux problèmes d'optimisation des éléments modifiables. Nous abordons ensuite la validation expérimentale de la stratégie d'optimisation proposée, sur la base d'une structure minimale représentative du comportement vibratoire d'une planche de bord réelle. En conclusion, nous présentons l'optimisation de la planche de bord du véhicule zx, qui constitue l'aboutissement de la stratégie d'optimisation sur des planches de bord réelles.

In this work, an active flow control method is studied numerically by using a synthetic jet over a NACA 0015 airfoil. Unsteady, turbulent flows over the NACA 0015 airfoil are computed using a Navier-Stokes solver. The Spalart-Allmaras turbulence model is employed in all computations. Unsteady flow solutions are computed in parallel using Parallel Virtual Machine library routines in a computer cluster. The synthetic jet is implemented to the flow solver as a boundary condition. Response Surface Methodology is employed for the optimization of synthetic jet parameters at various angles of attack. The synthetic jet parameters
the jet velocity, the jet location, the jet angle and the jet frequency are optimized to maximize the lift to drag ratio. The optimization study is performed for a constant value of jet power coefficient. The jet slot size is used as a dependent parameter in the optimization studies. The optimization study has shown that the jet velocity and the jet location are the dominant synthetic jet parameters. The optimum synthetic jet angle is observed to be increasing as the angle of attack increases. The optimum jet location is observed to be moving through the leading edge as angle of attack increases for the separated flows. It is observed that the application of the synthetic jet delays the flow separation on the suction side of the airfoil and increases the lift to drag ratio significantly especially at post stall angles of attack. The application of the synthetic jet is observed to be less effective for attached flows.

The stringing regulation on greenhouse gases emissions coupled with the rising fuel price and the growth in aviation transportation have imposed increasing demands on the aircraft industry to develop revolutionary technologies to meet such challenges. Methods of delaying flow separation on aircraft high lift systems have been sought which can lead to an increase in the aircraft performance and ultimately a reduction in aircraft operational costs and its impact on the environment. Synthetic jet actuators are a promising method of delivering flow control for aircraft applications due to their ability to inject momentum to an external flow without net mass flux and their potential in being integrated in MEMS through micro-fabrication with relative ease. It has been demonstrated in many laboratory experiments that synthetic jets are capable of delaying flow separation on aerodynamic bodies of various shapes. However, currently the operating conditions of synthetic jets are mostly chosen by trial-and-error, and thus the flow control effectiveness varies from one experiment to another. In order to deliver an effective flow separation control which achieves a desired control effect at minimum energy expenditure, a better understanding of the fluid mechanics of the behaviour of synthetic jets and the interaction between synthetic jets and a boundary layer are required. The aims of the present research were to achieve such a goal through a series of purposely designed numerical simulations. Firstly, synthetic jets issued from a circular orifice into quiescent air were studied to understand the effect of dimensionless parameters on the formation and the extent of roll-up of vortex rings. The computational results confirmed that the Stokes number determines the strength of vortex roll-up of a synthetic jet. Based on the computational results, a parameter map was produced in which three different operational regimes of synthetic jets were indentified and a criterion for vortex roll-up was also established. A circular synthetic jet issued into a zero-pressure-gradient laminar boundary layer was then investigated. The capability of FLUENT in modelling the key characteristics of synthetic jets was validated using experimental data. The formation and evolution of coherent structures produced by the interaction between synthetic jets and a boundary layer, as well as their near-wall effect in terms of the wall shear stress, were examined. A parameter map illustrating how the appearance of the vortical structures and their corresponding shear stress patterns vary as the synthetic jet operating condition changes was established. In addition, the increase in the wall shear stress relative to the jet-off case was calculated to evaluate their potential separation control effect.Finally, the study moved one step forward to investigate the flow separation control effect of an array of three circular synthetic jets issued into a laminar boundary layer which separates downstream on an inclined plate. The impact of synthetic jets on the boundary layer prior to separation and the extent of flow separation delay on the flap, at a range of synthetic jet operating conditions, were examined and the correlation between them was investigated. Furthermore, the optimal operating conditions for this synthetic jet array in the current study were identified by considering both the flow control effect and the actuator power consumption. The characteristics of the corresponding vortical structures were also examined.The findings from this work have produced some further insights of the behaviour and the interaction between synthetic jets and a boundary layer, which will be useful for ensuring an effective application of synthetic jets in practical settings.

In 2009, based on its commitment to take action on the climate change, the aviation industry accorded a group of objectives to reduce carbon dioxide emissions. Although only 2% of all human-induced carbon dioxide (CO2) emissions are produced by the global aviation industry, the aviation industry is set to grow in the next 30 years. In order to maintain this growth without increasing its negative environmental impact, the future aircraft have to be cleaner and greener. In order to reduce carbon emissions and increase the operative efficiency, novel technologies have been developed and applied on aircraft. One of the recently introduced technologies is the flow control over the wing by employing active flow control methods. Amongst the active flow control methods, synthetic jets have emerged as a developing and promising technology. The latter have been extensively investigated since 1990 in laboratory based investigations. In spite of the fact that many experimental studies have been performed to design synthetic jet actuators for optimal flow control, due to the the vast number of operating parameters involved, and the lack of current measurement technologies, they can be impractical and highly expensive. Hence, there is a need for a systematic analysis to establish the optimal operating conditions with the highest effectiveness at the cost of minimum energy input, and the most suitable orientation of synthetic jet orifices. This would require enhanced comprehension of the inherent features of synthetic jets and their corresponding near wall effects. By using numerical simulations with a commercial CFD software (Star-CCM+), this thesis investigates some features associated with synthetic jet performance that are not fully understood, such as: • The optimal working configuration of a synthetic jet array embedded into a laminar detached boundary layer for flow separation control. • The effect of orifice orientation (inclined and skewed synthetic jets) over normal synthetic jets and their optimal working configuration in an attached laminar boundary layer.

Galactic winds are multi-phase outflows that probe how feedback regulates the mass and metallicity of galaxies. Their cold phase, mainly observable with absorption lines, is often detected hundreds to thousands of pc away from the galactic plane and with velocities of hundreds of km $\rm s^{-1}$. To understand observations, it is important to theoretically study how such lines are produced via numerical simulations of cloud systems exposed to winds and starburst UV backgrounds. In this thesis we study the thermodynamics, ion populations, and ion absorption lines of cold and warm radiative clouds evolving from magnetised wind-cloud systems and an unmagnetised shock-multicloud model. We account for radiative cooling with two different cooling floors and magnetic fields with two different orientations. In our wind-cloud simulations, cold clouds survive the interaction with the wind for longer, since they are less exposed to instabilities, than warmer clouds. Magnetic fields have a larger influence on warm clouds than in cold clouds. If transverse to the wind direction, the field creates a shield that confines the expansion of the cloud, delaying its evaporation. In our shock-multicloud simulation, cold gas at large distances is not accelerated by ram-pressure, but, instead, precipitates from mixed gas out of thermal equilibrium. To study ion populations and create synthetic spectra, we developed a flexible python interface to link our PLUTO simulations to TRIDENT via the YT-package infrastructure and CLOUDY. Our ion population analysis reveals that setting different cooling floors and magnetic fields affect the column densities of several ions. H\,{\sc i}, O\,{\sc vi}, Mg\,{\sc ii}, C\,{\sc iii}, and Si\,{\sc iv} are more sensitive to the cooling floors, and H\,{\sc i}, Mg\,{\sc ii}, C\, {\sc iii}, and Si\, {\sc iv} can also trace the initial magnetic field direction, making them good candidates for comparisons with observations.

Coal derived synthetic gas (syngas) fuel is a promising solution for today s increasing demand for clean and reliable power. Syngas fuels are primarily mixtures of H2 and CO, often with large amounts of diluents such as N2, CO2, and H2O. The specific composition depends upon the fuel source and gasification technique. This requires gas turbine designers to develop fuel flexible combustors capable of operating with high conversion efficiency while maintaining low emissions for a wide range of syngas fuel mixtures. Design tools often used in combustor development require data on various fundamental gas combustion properties. For example, laminar flame speed is often an input as it has a significant impact upon the size and static stability of the combustor. Moreover it serves as a good validation parameter for leading kinetic models used for detailed combustion simulations. Thus the primary objective of this thesis is measurement of laminar flame speeds of syngas fuel mixtures at conditions relevant to ground-power gas turbines. To accomplish this goal, two flame speed measurement approaches were developed: a Bunsen flame approach modified to use the reaction zone area in order to reduce the influence of flame curvature on the measured flame speed and a stagnation flame approach employing a rounded bluff body. The modified Bunsen flame approach was validated against stretch-corrected approaches over a range of fuels and test conditions; the agreement is very good (less than 10% difference). Using the two measurement approaches, extensive flame speed information were obtained for lean syngas mixtures at a range of conditions: 1) 5 to 100% H2 in the H2/CO fuel mixture; 2) 300-700 K preheat temperature; 3) 1 to 15 atm pressure, and 4) 0-70% dilution with CO2 or N2. The second objective of this thesis is to use the flame speed data to validate leading kinetic mechanisms for syngas combustion. Comparisons of the experimental flame speeds to those predicted using detailed numerical simulations of strained and unstrained laminar flames indicate that all the current kinetic mechanisms tend to over predict the increase in flame speed with preheat temperature for medium and high H2 content fuel mixtures. A sensitivity analysis that includes reported uncertainties in rate constants reveals that the errors in the rate constants of the reactions involving HO2 seem to be the most likely cause for the observed higher preheat temperature dependence of the flame speeds. To enhance the accuracy of the current models, a more detailed sensitivity analysis based on temperature dependent reaction rate parameters should be considered as the problem seems to be in the intermediate temperature range (~800-1200 K).

Orientador: Maurílio Boaventura
Banca: Evanildo Castro Silva Júnior
Banca: Alagacone Sri Ranga
Resumo: Neste trabalho propomos quatro novas abordagens para tratar o problema de restauração de imagens reais contendo texturas sob a perspectiva dos temas: reconstrução de regiões danificadas, remoção de objetos, e eliminação de ruídos. As duas primeiras abor dagens são designadas para recompor partes perdias ou remover objetos de uma imagem real a partir de formulações envolvendo decomposiçãode imagens e inpainting por exem- plar, enquanto que as duas últimas são empregadas para remover ruído, cujas formulações são baseadas em decomposição de três termos e equações diferenciais parciais não lineares. Resultados experimentais atestam a boa performace dos protótipos apresentados quando comparados à modelagens correlatas da literatura.
Abstract: In this paper we propose four new approaches to address the problem of restoration of real images containing textures from the perspective of reconstruction of damaged areas, object removal, and denoising topics. The first two approaches are designed to reconstruct missing parts or to remove objects of a real image using formulations based on image de composition and exemplar based inpainting, while the last two other approaches are used to remove noise, whose formulations are based on decomposition of three terms and non- linear partial di®erential equations. Experimental results attest to the good performance of the presented prototypes when compared to modeling related in literature.
Mestre

In this thesis we study methods for solving the neutron transport equation (or linear Boltzmann equation). This is an integro-differential equation that describes the behaviour of neutrons during a nuclear fission reaction. Applications of this equation include modelling behaviour within nuclear reactors and the design of shielding around x-ray facilities in hospitals. Improvements in existing modelling techniques are an important way to address environmental and safety concerns of nuclear reactors, and also the safety of people working with or near radiation. The neutron transport equation typically has seven independent variables, however to facilitate rigorous mathematical analysis we consider the monoenergetic, steady-state equation without fission, and with isotropic interactions and isotropic source. Due to its high dimension, the equation is usually solved iteratively and we begin by considering a fundamental iterative method known as source iteration. We prove that the method converges assuming piecewise smooth material data, a result that is not present in the literature. We also improve upon known bounds on the rate of convergence assuming constant material data. We conclude by numerically verifying this new theory. We move on to consider the use of a specific, well-known diffusion equation to approximate the solution to the neutron transport equation. We provide a thorough presentation of its derivation (along with suitable boundary conditions) using an asymptotic expansion and matching procedure, a method originally presented by Habetler and Matkowsky in 1975. Next we state the method of diffusion synthetic acceleration (DSA) for which the diffusion approximation is instrumental. From there we move on to explore a new method of seeing the link between the diffusion and transport equations through the use of a block operator argument. Finally we consider domain decomposition algorithms for solving the neutron transport equation. Such methods have great potential for parallelisation and for the local application of different solution methods. A motivation for this work was to build an algorithm applying DSA only to regions of the domain where it is required. We give two very different domain decomposed source iteration algorithms, and we prove the convergence of both of these algorithms. This work provides a rigorous mathematical foundation for further development and exploration in this area. We conclude with numerical results to illustrate the new convergence theory, but also solve a physically-motivated problem using hybrid source iteration/ DSA algorithms and see significant reductions in the required computation time.

It is the purpose of this thesis to investigate different regional geoid determination methods with respect to their feasibility for use with a future GOCE satellite-only Earth Gravity Model (EGM). This includes investigations of various techniques, which involve different approximations, as well as the expected accuracy. Many, but not all, of these tasks are tested by means of Synthetic Earth Gravity Models (SEGMs). The study is limited to remove-compute-restore methods using Helmert condensation and to Sjöberg's combined approach (method with additive corrections).

First, a number of modifications of Stokes' formula are tested with respect to their compatibility with a GOCE EGM having negligible commission error. It is concluded that the least squares modification method should be preferred.

Next, two new point-mass SEGMs are constructed in such a way that the resulting models have degree variances representative for the full and topographically reduced gravity fields, respectively. These SEGMs are then used to test different methods for modified Stokes' integration and downward continuation. It is concluded that the combined method requires dense observations, obtained from the given surface anomalies by interpolation using a reduction for all known density anomalies, most notably the topography. Examples of other conclusions are that the downward continuation method of Sjöberg (2003a) performs well numerically.

To be able to test topographic corrections, another SEGM is constructed starting from the reduced point-mass model, to which the topography, bathymetry and isostatic compensation are added. This model, which is called the Nordic SEGM, is then applied to test one strict and one more approximate approach to Helmert's condensation. One conclusion here is that Helmert's 1st method with the condensation layer 21 km below sea level should be preferred to Helmert's 2nd condensation strategy.

The thesis ends with a number of investigations of Sjöberg's combined approach to geoid determination, which include tests using the Nordic SEGM. It is concluded that the method works well in practice for a region like Scandinavia. It is finally shown how the combined strategy may preferably be used to estimate height anomalies directly.