Dissertations / Theses on the topic 'Low-order method'

Dissertation (Ph.D.)--Worcester Polytechnic Institute.
Keywords: patch antennas; volume integral equation (VIE); method of moments (MoM); low order basis functions; convergence. Includes bibliographical references (leaves 169-186 ).

The aerospace community is challenged as of today for being able to manage accurate overnight computational fluid dynamics (CFD) simulations of compressible flow problems. Well-established CFD solvers based on second-order finite volume (FV) methods provide accurate approximations of steady-state turbulent flows but are incapable to produce reliable predictions of the full flight envelope. Alternatively, promising high-order discretisations, claimed to permit feasible highfidelity simulations of unsteady turbulent flows, are still subject to strong limitations in robustness and efficiency, placing their level of maturity far away from industrial requirements. In consequence, the CFD paradigm is immersed at this point into the crossroads outlined by the inherent limitations of low-order methods and the yet immature state of high-order discretisations. Accordingly, this thesis develops a twofold strategy for the high-fidelity simulation of compressible flows introducing two methodologies, at the low and high-order levels, respectively, based on hybridised formulations. First, a new finite volume paradigm, the face-centred finite volume (FCFV) method, is proposed for the formulation of steady-state compressible flows. The present methodology describes a hybrid mixed FV formulation that, following a hybridisation process, defines the unknowns of the problem at the face barycentres. The problem variables, i.e. the conservative quantities and the stress tensor and heat flux in the viscous case, are retrieved with optimal first-order accuracy inside each cell by means of an inexpensive postprocessing step without need of reconstruction of the gradients. Hence, the FCFV solver preserves the accuracy of the approximation even in presence of highly stretched or distorted cells, providing a solver insensitive to mesh quality. In addition, the FCFV method is a monotonicity-preserving scheme, leading to non-oscillatory approximations of sharp gradients without resorting to shock capturing or limiting techniques. Finally, the method is robust in the incompressible limit and is capable of computing accurate solutions for flows at low Mach number without the need of introducing specific pressure correction strategies. In parallel, the high-order hybridisable discontinuous Galerkin (HDG) method is reviewed in the context of compressible flows, presenting an original unified framework for the derivation of Riemann solvers in hybridised formulations. The framework includes, for the first time in an HDG context, the HLL and HLLEM Riemann solvers as well as the traditional Lax-Friedrichs and Roe solvers. The positivity preserving properties of HLL-type Riemann solvers are displayed, demonstrating their superiority with respect to Roe in supersonic cases. In addition, HLLEM specifically outstands in the approximation of boundary layers because of its shear preservation, which confers it an increased accuracy with respect to HLL and Lax-Friedrichs. An extensive set of numerical benchmarks of practical interest is introduced along this study in order to validate both the low and high-order approaches. Different examples of compressible flows in a great variety of regimes, from inviscid to viscous laminar flows, from subsonic to supersonic speeds, are presented to verify the accuracy properties of each of the proposed methodologies and the performance of the introduced Riemann solvers.
La comunitat aeroespacial té el repte a dia d’avui de poder tractar amb precisió simulacions de mecànica de fluids computacional (CFD) de problemes de flux compressible en càlcul nocturn. Programes convencionals de simulació CFD basats en mètodes de volums finits (VF) de segon ordre ofereixen aproximacions precises de fluxos turbulents estacionaris però són incapaços de produir prediccions fidels de l’entorn de vol complet. Alternativament, les discretitzations prometedores d’alt ordre, de les quals s’espera que permetin simulacions accessibles d’alta fidelitat per a fluxos turbulents transitoris, encara estan subjectes a fortes limitacions en eficiència i robustesa, delimitant-ne el nivell de maduresa encara lluny de requeriments industrials. En conseqüència, el paradigma del CFD es troba immers ara mateix en la cruïlla delimitada per les limitacions inherents dels mètodes de baix ordre i l’estat encara immadur de les discretitzacions d’alt ordre. D’acord amb això, aquesta tesi desenvolupa una estratègia doble per a la simulació d’alta fidelitat de flux compressible introduint dues metodologies, als nivells de baix i alt ordre, respectivament, basades en formulacions híbrides. Primer, es proposa un nou paradigma de VF, el mètode de volums finits centrats en les cares (FCFV), per a la formulació de fluxos compressible estacionaris. Aquesta metodologia descriu una formulació mixta híbrida de VF que, seguint un procés d’hibridització, defineix les incògnites del problema als baricentres de les cares. Les variables del problema -quantitats conservatives i tensor de tensions i flux de calor en el cas viscós- són obtingudes amb precisió òptima de primer ordre dins de cada element mitjançant una etapa de postprocessat de cost reduït sense la necessitat de reconstrucció dels gradients. Amb això, el mètode FCFV preserva la qualitat de l’aproximació fins i tot en presència d’elements amb un alt estretament o distorsió, donant lloc a un mètode insensible a la qualitat de la malla. A més a més, el mètode de FCFV és un esquema preservador de monotonia, donant lloc a aproximacions no oscil·latòries de forts gradients sense necessitat d’utilitzar mètodes de captura de xocs o limitadors. Finalment, el mètode és robust en el límit incompressible i és capaç de calcular amb precisió solucions de fluxos amb nombre de Mach baix sense haver d’introduir estratègies específiques de correcció de pressió. En paral·lel, es presenta una revisió del mètode híbrid de Galerkin discontinu (HDG) d’alt ordre en el context de flux compressible, presentant un marc unificat per a la derivació de fluxos numèrics del problema de Riemann en formulacions híbrides. El marc inclou per primera vegada en un entorn HDG, els fluxos numèrics d’HLL i HLLEM, així com els tradicionals de Lax-Friedrichs i Roe. Es mostren les propietats de preservació de positivitat dels fluxos de tipus HLL, que demostren la seva superioritat respecte els de Roe en casos supersònics. Addicionalment, el mètode d’HLLEM destaca especialment en l’aproximació de capes límit com a resultat de la seva preservació d’esforços tallants, la qual li confereix una precisió afegida respecte les d’HLL i Lax-Friedrichs. Al llarg de l’estudi s’introdueix una llista extensa d’exemples numèrics de referència d’interès pràctic per tal de validar les propostes en baix i alt ordre. Es presenten diferents exemples de flux compressible en una gran varietat de règims, des de flux invíscid fins a flux laminar viscós, des de velocitats subsòniques fins a supersòniques, per tal de verificar la precisió de les metodologies proposades i el rendiment dels fluxos numèrics introduïts

When designing controllers with robust performance and stabilization requirements, H-infinity synthesis is a common tool to use. These controllers are often obtained by solving mathematical optimization problems. The controllers that result from these algorithms are typically of very high order, which complicates implementation. Low order controllers are usually desired, since they are considered more reliable than high order controllers. However, if a constraint on the maximum order of the controller is set that is lower than the order of the so-called augmented system, the optimization problem becomes nonconvex and it is relatively difficult to solve. This is true even when the order of the augmented system is low. In this thesis, optimization methods for solving these problems are considered. In contrast to other methods in the literature, the approach used in this thesis is based on formulating the constraint on the maximum order of the controller as a rational function in an equality constraint. Three methods are then suggested for solving this smooth nonconvex optimization problem. The first two methods use the fact that the rational function is nonnegative. The problem is then reformulated as an optimization problem where the rational function is to be minimized over a convex set defined by linear matrix inequalities (LMIs). This problem is then solved using two different interior point methods. In the third method the problem is solved by using a partially augmented Lagrangian formulation where the equality constraint is relaxed and incorporated into the objective function, but where the LMIs are kept as constraints. Again, the feasible set is convex and the objective function is nonconvex. The proposed methods are evaluated and compared with two well-known methods from the literature. The results indicate that the first two suggested methods perform well especially when the number of states in the augmented system is less than 10 and 20, respectively. The third method has comparable performance with two methods from literature when the number of states in the augmented system is less than 25.

Simulations of incompressible flows are performed on a daily basis to solve problems of practical and industrial interest in several fields of engineering, including automotive, aeronautical, mechanical and biomedical applications. Although finite volume (FV) methods are still the preferred choice by the industry due to their efficiency and robustness, sensitivity to mesh quality and limited accuracy represent two main bottlenecks of these approaches. This is especially critical in the context of transient phenomena, in which FV methods show excessive numerical diffusion. In this context, there has been a growing interest towards high-order discretisation strategies in last decades. In this PhD thesis, a high-order adaptive hybidisable discontinuous Galerkin (HDG) method is proposed for the approximation of steady and unsteady laminar incompressible Navier-Stokes equations. Voigt notation for symmetric second-order tensors is exploited to devise an HDG method for the Cauchy formulation of the momentum equation with optimal convergence properties, even when low-order polynomial degrees of approximation are considered. In addition, a postprocessing strategy accounting for rigid translational and rotational modes is proposed to construct an element-by-element superconvergent velocity field. The discrepancy between the computed and postprocessed velocities is utilised to define a local error indicator to drive degree adaptivity procedures and accurately capture localised features of the flow. The resulting HDG solver is thus extended to the case of transient problems via high-order time integration schemes, namely the explicit singly diagonal implicit Runge-Kutta (ESDIRK) schemes. In this context, the embedded explicit step is exploited to define an inexpensive estimate of the temporal error to devise an efficient timestep control strategy. Finally, in order to efficiently solve the global problem arising from the HDG discretisation, a preconditioned iterative solver is proposed. This is critical in the context of high-order approximations in three-dimensional domains leading to large-scale problems, especially in transient simulations. A block diagonal preconditioner coupled with an inexpensive approximation of the Schur complement of the matrix is proposed to reduce the computational cost of the overall HDG solver. Extensive numerical validation of two and three-dimensional steady and unsteady benchmark tests of viscous laminar incompressible flows is performed to validate the proposed methodology.
Simulaciones de flujo incompresible se emplean a diario para resolver problemas de interés práctico e industrial en varios campos de la ingeniería, p.ej. en aplicaciones automovilísticas, aeronáuticas, mecánicas y biomédicas. Aunque los métodos de volúmenes finitos (FV) siguen siendo la opción preferida por la industria debido a su eficiencia y robustez, la sensibilidad a la calidad de la malla y la baja precisión representan dos limitaciones importantes para estas técnicas. Estas limitaciones son todavía más críticas en el contexto de simulaciones de fenómenos transitorios, donde los FV están penalizados por su excesiva difusión numérica. En este contexto, las estrategias de discretización de alto orden han ganado una popularidad creciente en las últimas décadas para problemas transitorios dónde se necesitan soluciones precisas. Esta tesis propone un método de Galerkin discontinuo híbrido (HDG), de alto orden y adaptativo para la aproximación de las ecuaciones de Navier-Stokes incomprensible laminar, en el caso estacionario y transitorio en el entorno de aplicaciones ingenieriles. Para ello, la notación de Voigt para tensores simétricos de segundo orden (habituales en mecánica de los medios continuos) permite introducir un método HDG para la formulación de Cauchy de la ecuación de momento. La novedad de este resultado reside en la convergencia óptima alcanzada por el método, incluso para aproximaciones de orden polinómico bajo. Además, se desarrolla una estrategia de post-proceso local para construir elemento a elemento un campo de velocidad súper-convergente, tomando en cuenta los modos rígidos de traslación y rotación. La discrepancia entre el campo de velocidad calculado y el súper-convergente, obtenido a través del post-proceso, permite definir un indicador del error local. De esta forma, se desarrolla una estrategia para realizar adecuar elemento a elemento el grado de la aproximación polinómica y así mejorar la precisión adaptándose a las características localizadas del flujo. Seguidamente, se extiende el método HDG propuesto al tratamiento de problemas dependientes del tiempo. Más concretamente, se consideran los esquemas de integración temporal de alto orden explicit singly diagonal implicit Runge-Kutta (ESDIRK). En este contexto, se utiliza el paso explícito embedded para calcular una estimación computacionalmente eficiente del error temporal y definir una estrategia de adaptividad del paso de tiempo. Finalmente, se desarrolla un precondicionador adaptado a la estrategia HDG que acelera la convergencia del método iterativo empleado y, de esta forma, obtener resoluciones eficaces del problema global surgido de la discretización HDG. Es importante resaltar la importancia de una herramienta de resolución eficiente para problemas de gran escala en el contexto de aproximaciones de alto orden y en dominios tridimensionales. Estas herramientas se hacen aún más criticas en simulaciones transitorias. Más concretamente, se proponen un precondicionador diagonal por bloques y una aproximación eficiente del complemento Schur de la matriz para reducir el coste computacional del método HDG. Para validar la metodología propuesta, se realizan varias simulaciones numéricas de flujo incompresible laminar viscoso, para problemas estacionarios y transitorios, en dos y tres dimensiones.

A new, well posed, two-dimensional two-mode incompressible Kelvin{Helmholtz instability test case has been chosen to explore the ability of a compressible algorithm, Godunov-type scheme with the low Mach number correction, which can be used for simulations involving low Mach numbers, to capture the observed vortex pairing process due to the initial Kelvin{Helmholtz instability growth on low resolution grid. The order of accuracy, 2nd and 5th , of the compressible algorithm is also highlighted. The observed vortex pairing results and the corresponding momentum thickness of the mixing layer against time are compared with results obtained using the same compressible algorithm but without the low Mach number correction and three other methods, a Lagrange remap method where the Lagrange phase is 2nd order accurate in space and time while the remap phase is 3rd order accurate in space and 2nd order accurate in time, a 5th order accurate in space and time nite di erence type method based on the wave propagation algorithm and a 5th order spatial and 3rd order temporal accurate Godunov method utilising the SLAU numerical ux with low Mach capture property. The ability of the compressible ow solver of the commercial software, ANSYS Fluent, in solving low Mach ows is also examined for both implicit and explicit methods provided in the compressible ow solver. In the present two dimensional two mode incompressible Kelvin{Helmholtz instability test case, the ow conditions, stream velocities, length-scales and Reynolds numbers, are taken from an experiment conducted on the observation of vortex pairing process. Three di erent values of low Mach numbers, 0:2, 0:02 and 0:002 have been tested on grid resolutions of 24 24, 32 32, 48 48 and 64 64 on all the di erent numerical approaches. The results obtained show the vortex pairing process can be captured on a low grid resolution with the low Mach number correction applied down to 0:002 with 2nd and 5th order Godunovtype methods. Results also demonstrate clearly that a speci cally designed low Mach correction or ux is required for all algorithms except the Lagrange-remap approach, where dissipation is independent of Mach number. ANSYS Fluent's compressible ow solver with the implicit time stepping method also captures the vortex pairing on low resolutions but excessive dissipation prevents the instability growth when explicit time stepping method is applied.

In this thesis, low-order nonlinear models for the prediction of the nonlinear behaviour of thermoacoustic systems are developed. These models are based on thermoacoustic networks, in which linear acoustics is combined with a nonlinear heat release model. The acoustic networks considered in this thesis can take into account mean flow and non-trivial acoustic reflection coefficients, and are cast in state-space form to enable analysis both in the frequency and time domains. Starting from linear analysis, the stability of thermoacoustic networks is investigated, and the use of adjoint methods for understanding the role of the system's parameters on its stability is demonstrated. Then, a nonlinear analysis using various state-of-the-art methods is performed, to highlight the strengths and weaknesses of each method. Two novel frameworks that fill some gaps in the available methods are developed: the first, called Flame Double Input Describing Function (FDIDF), is an extension of the Flame Describing Function (FDF). The FDIDF approximates the flame nonlinear response when it is forced simultaneously with two frequencies, whereas the FDF is limited to one frequency. Although more expensive to obtain, the FDIDF contains more nonlinear information than the FDF, and can predict periodic and quasiperiodic oscillations. It is shown how, in some cases, it corrects the prediction of the FDF about the stability of thermoacoustic oscillations. The second framework developed is a weakly nonlinear formulation of the thermoacoustic equations in the Rijke tube, in which the acoustic response is not limited to a single-Galerkin mode, and is embedded in a state-space model. The weakly nonlinear analysis is strictly valid only close to the expansion point, but is much cheaper than any other available method. The above methods are applied to relatively simple thermoacoustic configurations, in which the nonlinear heat release model is that of a laminar conical flame or an electrical heater. However, in real gas turbines more complex flame shapes are found, for which no reliable low-order models exist. Two models are developed in this thesis for turbulent bluff-body stabilised flames: one for a perfectly premixed flame, in which the modelling is focused on the flame-flow interaction, accounting for the presence of recirculation zones and temperature gradients; the second for imperfectly premixed flames, in which equivalence ratio fluctuations, modelled as a passive scalar field, dominate the heat release response. The second model was shown to agree reasonably well with experimental data, and was applied in an industrial modelling project.

A novel high-order finite volume scheme using flux correction methods in conjunction with structured finite difference schemes is extended to low Mach and incompressible flows on strand grids. Flux correction achieves high-order by explicitly canceling low-order truncation error terms in the finite volume cell. The flux correction method is applied in unstructured layers of the strand grid. The layers are then coupled together using a source term containing the derivatives in the strand direction. Proper source term discretization is verified. Strand-direction derivatives are obtained by using summation-by-parts operators for the first and second derivatives. A preconditioner is used to extend the method to low Mach and incompressible flows. We further extend the method to turbulent flows with the Spalart Allmaras model. We verify high-order accuracy via the method of manufactured solutions, method of exact solutions, and physical problems. Results obtained compare well to analytical solutions, numerical studies, and experimental data. It is foreseen that future application in the Naval field will be possible.

Path integral Monte Carlo (PIMC) is a method suitable for quantum liquid simulations at finite temperature. We present in this thesis a study of PIMC dealing with the theory and algorithms related to it, and then two applications of PIMC to current research problems of quantum fluids in the Bolzmann regime.
The first part encompasses a study of the different ingredients of a PIMC code: action, sampling and physical property estimators. Particular attention has been paid to Li-Broughton's higher order approximation to the action. Regarding sampling, several collective movement methods have been derived, including the bisection algorithm, that has been thoroughly tested. We also include a study of estimators for different physical properties, such as, the energy (through the thermodynamic and virial estimators), the pair distribution function, the structure factor, and the momentum distribution.
In relation to the momentum distribution, we have developed a novel algorithm for its estimation, the trail method. It surmounts some of the problems exposed by previous approaches, such as the open chain method or McMillan's algorithm.
The Richardson extrapolation used within PIMC simulations, is another contribution of this thesis. Up until now, this extrapolation has not been used in this context. We present studies of the energy dependence on the number of "beads", along with the betterment provide by the Richardson extrapolation.
Inasmuch as our goal is to perform research of quantum liquids at finite temperature, we have produced a library of codes, written from scratch, that implement most of the features theoretically developed. The most elaborated parts of these codes are included in some of the appendixes.
The second part shows two different applications of the algorithms coded. We present results of a PIMC calculation of the momentum distribution of Ne and normal 4He at low temperatures. In the range of temperatures analysed, exchanges can be disregarded and both systems are considered Boltzmann quantum liquids. Their quantum character is well reflected in their momentum distributions witch show clear departures from the classical limit. The PIMC momentum distributions which show clear departures from the classical limit. The PIMC momentum distributions are sampled using the trail method. Kinetic energies of both systems, as a function of temperature and at a fixed density, are also reported.
Finally, the solid-liquid neon phase transition along the 35 K isotherm has been characterized.While thermodynamic properties of the solid phase are well known the behaviour of some properties, such as the energy or the dessity, during the trasition presen6 some uncertainties For example, experimental data for the place diagram, which determines solid and liquid boundaries, present sizeable differences. The temperature chosen is high enough so that Bose or Fermi statistics corrections are small, although the system is strongly quantum mechanical. The results obtained show a discontinuity in the kinetic energy during the transition.

Cette thèse a pour but l'étude de la mise en œuvre de commandes par asservissement visuel pour le contrôle actif d'un écoulement de Poiseuille. D'un point de vue général, le contrôle d'écoulements vise à modifier ou à maintenir l'état de l'écoulement, malgré une éventuelle perturbation extérieure. Une des situations d'intérêt concerne par exemple la transition vers la turbulence où l'écoulement peut devenir turbulent avec la croissance de sa densité d'énergie cinétique. La réduction de la traînée est également une application potentielle dans des problèmes d'ingénierie. Un des buts applicatifs de cette thèse cherchera ainsi à minimiser à la fois la densité d'énergie cinétique et la traînée. Des modèles numériques peuvent être utilisés pour générer un modèle d'état des équations aux dérivées partielles d'un écoulement de Poiseuille. Le modèle d'état considéré dans cette thèse s'appuie sur une représentation spectrale afin de transformer les équations aux dérivées partielles originelles en un système d'équations différentielles ordinaires. Le vecteur d'état rassemble dans notre cas la vitesse et la vorticité. Les signaux de commande dépendent eux de conditions aux limites de type Dirichlet non homogènes qui correspondent à des actions de soufflage/aspiration. Le nombre de degrés de liberté commandé du problème correspond à la dimension du signal de commande. La densité d'énergie cinétique et la traînée sont modélisées en fonction du vecteur d'état et du signal de commande. Dans cette thèse nous avons plus particulièrement considéré un asservissement visuel partitionné. Celui-ci est appliqué au modèle d'état de l'écoulement avec deux degrés de liberté afin de minimiser simultanément la densité d'énergie cinétique et la traînée. La traînée, contrairement à l'énergie cinétique, diminue de façon monotone en fonction du temps. Une augmentation du nombre de degrés de liberté permet d'améliorer la décroissance de la densité d'énergie cinétique. Lorsque le nombre de degré de liberté correspond à la dimension du vecteur d'état, et en s'appuyant sur une commande par asservissement visuel, nous montrons que la densité d'énergie cinétique décroit de façon monotone au cours du temps. Le modèle d'état de l'écoulement de Poiseuille vit dans un espace de très grande dimension. Par conséquent, il est nécessaire d'un point de vue pratique de réduire la dimension du contrôleur. Nous démontrons que la loi de commande s'appuyant sur un modèle réduit peut être appliquée au système complet. Dans ce cas la densité d'énergie cinétique décroit presque de façon monotone au cours du temps en utilisant une commande par asservissement visuel à deux degrés de liberté
The visual servoing control approach is formulated for the flow control of the plane Poiseuille flow. Generally, the flow control can lead the flow from its current state to a desired state. In transition to turbulence, the growth of kinetic energy density can lead the flow to turbulence. Moreover, the drag reduction is a potential application in the engineering applications. Therefore, this thesis aims to minimize the kinetic energy density and the skin friction drag. The governing equations of the plane Poiseuille flow are modeled to a standard form in the automatic control. More precisely, the partial differential equations of the plane Poiseuille flow are transformed to a state space representation by using the spectral method. The streamwise and spanwise directions are discretized based on the Fourier series while the wall-normal direction is discretized based on the Chebyshev polynomials. The state vector involves the wall-normal velocity and vorticity. The control signals depend on the inhomogeneous Dirichlet boundary conditions which correspond to blowing/suction boundary control. The number of independent control signals is called the number of the degree of freedom. Moreover, the skin-friction drag and the kinetic energy density are modeled as a function of the state vector. The goal is to minimize both the skin-friction drag and the kinetic energy density by appropriate methods. The partitioned visual servoing control is used to minimize, simultaneously, the skin-friction drag and the kinetic energy density with two degrees of freedom. As a result, the behavior of the skin-friction drag monotonically decreases in time. However, the behavior of the kinetic energy density does not monotonically decrease in time, the similar results from the other methods such as: PID and LQR controls. Therefore, the number of the degree of freedom increases, which leads to the improvement of the kinetic energy density. In addition, when the number of the degree of freedom equals the number of state vector, the kinetic energy density monotonically decreases in time by using the visual servoing control. The dimension of linearized plane Poiseuille flow is large, therefore, we need to reduce the order of controller. We demonstrate that the control law based on a mode reduction can be applied for the full system. Moreover, the kinetic energy density almost will monotonically decreases in time even using two degrees of freedom when the visual servoing control is designed based on the model order reduction

La nécessité d’une meilleure compréhension du mécanisme d’entrainement pour l’instabilité à basse fréquence observée dans un écoulement dans une tuyère sur-détendue a été discutée. Le caractère instable de l’onde de choc/couche limite reste un défi pratique important pour les problèmes des écoulements dans les tuyères. De plus, pour une couche limite turbulente incidente donnée, ce type d’écoulement présente généralement des mouvements de choc à basse fréquence plus élevées qui sont moins couplés aux échelles de temps de la turbulence en amont. Cela peut être bon du point de vue d’un expérimentateur, en raison de difficultés à mesurer des fréquences plus élevées, mais c’est plus difficile d’un point de vue calcul numérique en raison de la nécessité d’obtenir des séries temporelles plus longues pour résoudre les mouvements à basse fréquence. En excellent accord avec les résultats expérimentaux, une série de calcul LES de très longue durée a été réalisée, il a été clairement démontré l’existence de mouvements énergétiques à basse fréquence et à large bande près du point de séparation. Des efforts particuliers ont été faits pour éviter tout forçage à basse fréquence en amont, et il a été explicitement démontré que les oscillations de choc à basse fréquence observées n’étaient pas liées à la génération de turbulence d’entrée, excluant la possibilité d’un artefact numérique. Différentes méthodes d’analyse spectrales, et en décomposition en mode dynamique ont été utilisées pour montrer que les échelles de temps impliquées dans un tel mécanisme sont environ deux ordres de grandeur plus grandes que les échelles de temps impliquées dans la turbulence de la couche limite, ce qui est cohérent avec les mouvements de basse fréquence observés. En outre, ces échelles de temps se sont avérées être fortement modulées par la quantité de flux inversé à l’intérieur de la bulle de séparation. Ce scénario peut, en principe, expliquer à la fois l’instabilité des basses fréquences et sa nature à large bande
The need for a better understanding of the driving mechanism for the observed low-frequency unsteadiness in an over-expanded nozzle flows was discussed. The unsteady character of the shock wave/boundary layer remains an important practical challenge for the nozzle flow problems. Additionally, for a given incoming turbulent boundary layer, this kind of flow usually exhibits higher low-frequency shock motions which are less coupled from the timescales of the incoming turbulence. This may be good from an experimenter’s point of view, because of the difficulties in measuring higher frequencies, but it is more challenging from a computational point of view due to the need to obtain long time series to resolve low-frequency movements. In excellent agreement with the experimental findings, a very-long LES simulation run was carried out to demonstrate the existence of energetic broadband low-frequency motions near the separation point. Particular efforts were done in order to avoid any upstream low-frequency forcing, and it was explicitly demonstrated that the observed low-frequency shock oscillations were not connected with the inflow turbulence generation, ruling out the possibility of a numerical artefact. Different methods of spectral analysis and dynamic mode decomposition have been used to show that the timescales involved in such a mechanism are about two orders of magnitude larger than the time scales involved in the turbulence of the boundary layer, which is consistent with the observed low-frequency motions. Furthermore, those timescales were shown to be strongly modulated by the amount of reversed flow inside the separation bubble. This scenario can, in principle, explain both the low-frequency unsteadiness and its broadband nature

L’objectif de ce travail de thèse est de proposer la Méthodes des éléments finis de Galerkin discontinus (DGFEM) à la discrétisation des équations compressibles de Navier-Stokes. Plusieurs challenges font l’objet de ce travail. Le premier aspect a consisté à montrer l’ordre de convergence optimal de la méthode DGFEM en utilisant les polynômes d’interpolation d’ordre élevé. Le deuxième aspect concerne l’implémentation de méthodes de ‘‘shock-catpuring’’ comme les limiteurs de pentes et les méthodes de viscosité artificielle pour supprimer les oscillations numériques engendrées par l’ordre élevé (lorsque des polynômes d’interpolation de degré p>0 sont utilisés) dans les écoulements transsoniques et supersoniques. Ensuite nous avons implémenté des estimateurs d’erreur a posteriori et des procédures d ’adaptation de maillages qui permettent d’augmenter la précision de la solution et la vitesse de convergence afin d’obtenir un gain de temps considérable. Finalement, nous avons montré la capacité de la méthode DG à donner des résultats corrects à faibles nombres de Mach. Lorsque le nombre de Mach est petit pour les écoulements compressibles à la limite de l’incompressible, la solution souffre généralement de convergence et de précision. Pour pallier ce problème généralement on procède au préconditionnement qui modifie les équations d’Euler. Dans notre cas, les équations ne sont pas modifiées. Dans ce travail, nous montrons la précision et la robustesse de méthode DG proposée avec un schéma en temps implicite de second ordre et des conditions de bords adéquats
The aim of this thesis is to deal with compressible Navier-Stokes flows discretized by Discontinuous Galerkin Finite Elements Methods. Several aspects has been considered. One is to show the optimal convergence of the DGFEM method when using high order polynomial. Second is to design shock-capturing methods such as slope limiters and artificial viscosity to suppress numerical oscillation occurring when p>0 schemes are used. Third aspect is to design an a posteriori error estimator for adaptive mesh refinement in order to optimize the mesh in the computational domain. And finally, we want to show the accuracy and the robustness of the DG method implemented when we reach very low mach numbers. Usually when simulating compressible flows at very low mach numbers at the limit of incompressible flows, there occurs many kind of problems such as accuracy and convergence of the solution. To be able to run low Mach number problems, there exists solution like preconditioning. This method usually modifies the Euler. Here the Euler equations are not modified and with a robust time scheme and good boundary conditions imposed one can have efficient and accurate results

Introducción. El objetivo del presente estudio es determinar si existe correlación entre los conocimientos sobre las consecuencias de la obesidad y el grado de actividad física de las personas. Métodos. Se realizó un estudio transversal analítico durante los años 2013 y 2014. Participaron 215 alumnos de pregrado seleccionados por conveniencia no relacionados a carreras del campo de la salud en una universidad de Lima, Perú. Se evaluó el grado de actividad física utilizando el International Physical Activity Questionnaire (IPAQ) y el nivel de conocimientos sobre consecuencias de la obesidad utilizando la escala Obesity Risk Knowledge-10 (ORK-10). También, se consignó las fuentes de información de donde obtuvieron el conocimiento para responder dicho cuestionario. Resultados. La mediana de edad fue 20 (rango intercuartílico=4) y 63% eran mujeres. De acuerdo al IPAQ, 53,9% realizaban actividad física alta, 35,4%, moderada y 10,7%, leve. Se encontró una correlación muy baja (rs=0,06) entre el puntaje del ORK-10 y la cantidad de equivalentes metabólicos/minuto consumidos por semana, pero no era significativa (p=0,38). Las personas informadas por medios de comunicación y por personal de salud obtuvieron mayores puntajes en el ORK- 10 que quienes se informaron por otras vías (p<0,05). Conclusiones. La correlación entre los conocimientos sobre consecuencias de la obesidad y el grado de actividad física es muy baja. Es necesario utilizar enfoques multidisciplinarios que incluyan todos los determinantes de la realización de actividad física para poder lograr cambios en la conducta de la población.

abstract: The emergence of new technologies as well as a fresh look at analyzing existing processes have given rise to a new type of response characteristic, known as a profile. Profiles are useful when a quality variable is functionally dependent on one or more explanatory, or independent, variables. So, instead of observing a single measurement on each unit or product a set of values is obtained over a range which, when plotted, takes the shape of a curve. Traditional multivariate monitoring schemes are inadequate for monitoring profiles due to high dimensionality and poor use of the information stored in functional form leading to very large variance-covariance matrices. Profile monitoring has become an important area of study in statistical process control and is being actively addressed by researchers across the globe. This research explores the understanding of the area in three parts. A comparative analysis is conducted of two linear profile-monitoring techniques based on probability of false alarm rate and average run length (ARL) under shifts in the model parameters. The two techniques studied are control chart based on classical calibration statistic and a control chart based on the parameters of a linear model. The research demonstrates that a profile characterized by a parametric model is more efficient monitoring scheme than one based on monitoring only the individual features of the profile. A likelihood ratio based changepoint control chart is proposed for detecting a sustained step shift in low order polynomial profiles. The test statistic is plotted on a Shewhart like chart with control limits derived from asymptotic distribution theory. The statistic is factored to reflect the variation due to the parameters in to aid in interpreting an out of control signal. The research also looks at the robust parameter design study of profiles, also referred to as signal response systems. Such experiments are often necessary for understanding and reducing the common cause variation in systems. A split-plot approach is proposed to analyze the profiles. It is demonstrated that an explicit modeling of variance components using generalized linear mixed models approach has more precise point estimates and tighter confidence intervals.
Dissertation/Thesis
Ph.D. Industrial Engineering 2010

The miscible displacement equations provide the mathematical model for simulating the displacement of a mixture of oil and miscible fluid in underground reservoirs during the Enhance Oil Recovery(EOR) process. In this thesis, I propose a stable numerical scheme combining a mixed finite element method and space-time discontinuous Galerkin method for solving miscible displacement equations under low regularity assumption. Convergence of the discrete solution is investigated using a compactness theorem for functions that are discontinuous in space and time. Numerical experiments illustrate that the rate of convergence is improved by using a high order time stepping method. For petroleum engineers, it is essential to compute finely detailed fluid profiles in order to design efficient recovery procedure thereby increase production in the EOR process. The method I propose takes advantage of both high order time approximation and discontinuous Galerkin method in space and is capable of providing accurate numerical solutions to assist in increasing the production rate of the miscible displacement oil recovery process.

碩士
國立臺灣大學
地質科學研究所
102
Since there is no practical method for earthquakes prediction today, the main disaster prevention method is based on the seismic design of buildings. Earthquake early warning (EEW) is another effective way to reduce damage in real-time (Kanamori et al., 1997). Because EEW needs to provide reliable message in a short time, it is important to shorten the reporting time window by the improving of data process. In order to provide location and magnitude after an earthquake just happened, a low cost and high density EEW system has been developed and established by using the Palert seismometers in Taiwan (Wu et al., 2013). Due to the distribution of the stations, which detected the signals at first, is poor. It needs more than eight stations to get reliable information. Thus, it shortens the lead time before strong ground shaking. This study use the arrival-time order location (AOL) method, which introduced by Anderson in 1981, to improve the efficiency of Palert EEW system for earthquake location. At the same time, because of Palert has a relatively low signal-to-noise ratio (S/N) in τc (Kanamori, 2005, Wu and Kanamori, 2005a) determinations. So τc approach does not use in the Palet EEW system (Wu et al., 2013). This study try to use the signals stacking small arrays to enhance S/N ratio and try to use τc for magnitude estimation. Results shows that, AOL method can provide a reliable earthquake location by only using four to five stations. It can improve the EEW efficiency. By stacking the signals from small array can also get more accurate magnitude estimation usingτc. So that more information can be provided in on-site EEW warning purpose.

The solution of the Burgers' equation computed by the standard finite element method is degraded by oscillations, which are the manifestation of the Gibbs phenomenon. In this work we study the following numerical me- thods: Discontinuous Galerkin method, stable low order schemes and the flux corrected technique method in order to prevent the undesired Gibbs phenomenon. The focus is on the reduction of severe overshoots and under- shoots and the preservation of the smoothness of the solution. We consider a simple 1D problem on the interval (0, 1) with different initial conditions to demonstrate the properties of the presented methods. The numerical results of individual methods are provided. 1