Systematic selection of analogue redesign method for forward-type digital power converters

This article proposes a systematic approach to determine the most suitable analogue redesign method to be used for forward-type converters under digital voltage mode control. The focus of the method is to achieve the highest phase margin at the particular switching and crossover frequencies chosen by the designer. It is shown that at high crossover frequencies with respect to switching frequency, controllers designed using backward integration have the largest phase margin; whereas at low crossover frequencies with respect to switching frequency, controllers designed using bilinear integration with pre-warping have the largest phase margins. An algorithm has been developed to determine the frequency of the crossing point where the recommended discretisation method changes. An accurate model of the power stage is used for simulation and experimental results from a Buck converter are collected. The performance of the digital controllers is compared to that of the equivalent analogue controller both in simulation and experiment. Excellent closeness between the simulation and experimental results is presented. This work provides a concrete example to allow academics and engineers to systematically choose a discretisation method.

Plane wave discontinuous Galerkin methods: exponential convergence of the hp-version

We consider the two-dimensional Helmholtz equation with constant coefficients on a domain with piecewise analytic boundary, modelling the scattering of acoustic waves at a sound-soft obstacle. Our discretisation relies on the Trefftz-discontinuous Galerkin approach with plane wave basis functions on meshes with very general element shapes, geometrically graded towards domain corners. We prove exponential convergence of the discrete solution in terms of number of unknowns.

Sparse space-time boundary element methods for the heat equation

The goal of this work is the efficient solution of the heat equation with Dirichlet or Neumann boundary conditions using the Boundary Elements Method (BEM). Efficiently solving the heat equation is useful, as it is a simple model problem for other types of parabolic problems. In complicated spatial domains as often found in engineering, BEM can be beneficial since only the boundary of the domain has to be discretised. This makes BEM easier than domain methods such as finite elements and finite differences, conventionally combined with time-stepping schemes to solve this problem. The contribution of this work is to further decrease the complexity of solving the heat equation, leading both to speed gains (in CPU time) as well as requiring smaller amounts of memory to solve the same problem. To do this we will combine the complexity gains of boundary reduction by integral equation formulations with a discretisation using wavelet bases. This reduces the total work to O(h

Noether-type discrete conserved quantities arising from a finite element approximation of a variational problem

In this work, we prove a weak Noether-type Theorem for a class of variational problems that admit broken extremals. We use this result to prove discrete Noether-type conservation laws for a conforming finite element discretisation of a model elliptic problem. In addition, we study how well the finite element scheme satisfies the continuous conservation laws arising from the application of Noether’s first theorem (1918). We summarise extensive numerical tests, illustrating the conservation of the discrete Noether law using the p-Laplacian as an example and derive a geometric-based adaptive algorithm where an appropriate Noether quantity is the goal functional.

Stability theory and numerical analysis of non-autonomous dynamical systems

The development and use of cocycles for analysis of non-autonomous behaviour is a technique that has been known for several years. Initially developed as an extension to semi-group theory for studying rion-autonornous behaviour, it was extensively used in analysing random dynamical systems [2, 9, 10, 12]. Many of the results regarding asymptotic behaviour developed for random dynamical systems, including the concept of cocycle attractors were successfully transferred and reinterpreted for deterministic non-autonomous systems primarily by P. Kloeden and B. Schmalfuss [20, 21, 28, 29]. The theory concerning cocycle attractors was later developed in various contexts specific to particular classes of dynamical systems [6, 7, 13], although a comprehensive understanding of cocycle attractors (redefined as pullback attractors within this thesis) and their role in the stability of non-autonomous dynamical systems was still at this stage incomplete. It was this purpose that motivated Chapters 1-3 to define and formalise the concept of stability within non-autonomous dynamical systems. The approach taken incorporates the elements of classical asymptotic theory, and refines the notion of pullback attraction with further development towards a study of pull-back stability arid pullback asymptotic stability. In a comprehensive manner, it clearly establishes both pullback and forward (classical) stability theory as fundamentally unique and essential components of non-autonomous stability. Many of the introductory theorems and examples highlight the key properties arid differences between pullback and forward stability. The theory also cohesively retains all the properties of classical asymptotic stability theory in an autonomous environment. These chapters are intended as a fundamental framework from which further research in the various fields of non-autonomous dynamical systems may be extended. A preliminary version of a Lyapunov-like theory that characterises pullback attraction is created as a tool for examining non-autonomous behaviour in Chapter 5. The nature of its usefulness however is at this stage restricted to the converse theorem of asymptotic stability. Chapter 7 introduces the theory of Loci Dynamics. A transformation is made to an alternative dynamical system where forward asymptotic (classical asymptotic) behaviour characterises pullback attraction to a particular point in the original dynamical system. This has the advantage in that certain conventional techniques for a forward analysis may be applied. The remainder of the thesis, Chapters 4, 6 and Section 7.3, investigates the effects of perturbations and discretisations on non-autonomous dynamical systems known to possess structures that exhibit some form of stability or attraction. Chapter 4 investigates autonomous systems with semi-group attractors, that have been non-autonomously perturbed, whilst Chapter 6 observes the effects of discretisation on non-autonomous dynamical systems that exhibit properties of forward asymptotic stability. Chapter 7 explores the same problem of discretisation, but for pullback asymptotically stable systems. The theory of Loci Dynamics is used to analyse the nature of the discretisation, but establishment of results directly analogous to those discovered in Chapter 6 is shown to be unachievable. Instead a case by case analysis is provided for specific classes of dynamical systems, for which the results generate a numerical approximation of the pullback attraction in the original continuous dynamical system. The nature of the results regarding discretisation provide a non-autonomous extension to the work initiated by A. Stuart and J. Humphries [34, 35] for the numerical approximation of semi-group attractors within autonomous systems. . Of particular importance is the effect on the system's asymptotic behaviour over non-finite intervals of discretisation.

Computational aspects of the numerical solution of SDEs

In the last 30 to 40 years, many researchers have combined to build the knowledge base of theory and solution techniques that can be applied to the case of differential equations which include the effects of noise. This class of ``noisy'' differential equations is now known as stochastic differential equations (SDEs). Markov diffusion processes are included within the field of SDEs through the drift and diffusion components of the Itô form of an SDE. When these drift and diffusion components are moderately smooth functions, then the processes' transition probability densities satisfy the Fokker-Planck-Kolmogorov (FPK) equation -- an ordinary partial differential equation (PDE). Thus there is a mathematical inter-relationship that allows solutions of SDEs to be determined from the solution of a noise free differential equation which has been extensively studied since the 1920s. The main numerical solution technique employed to solve the FPK equation is the classical Finite Element Method (FEM). The FEM is of particular importance to engineers when used to solve FPK systems that describe noisy oscillators. The FEM is a powerful tool but is limited in that it is cumbersome when applied to multidimensional systems and can lead to large and complex matrix systems with their inherent solution and storage problems. I show in this thesis that the stochastic Taylor series (TS) based time discretisation approach to the solution of SDEs is an efficient and accurate technique that provides transition and steady state solutions to the associated FPK equation. The TS approach to the solution of SDEs has certain advantages over the classical techniques. These advantages include their ability to effectively tackle stiff systems, their simplicity of derivation and their ease of implementation and re-use. Unlike the FEM approach, which is difficult to apply in even only two dimensions, the simplicity of the TS approach is independant of the dimension of the system under investigation. Their main disadvantage, that of requiring a large number of simulations and the associated CPU requirements, is countered by their underlying structure which makes them perfectly suited for use on the now prevalent parallel or distributed processing systems. In summary, l will compare the TS solution of SDEs to the solution of the associated FPK equations using the classical FEM technique. One, two and three dimensional FPK systems that describe noisy oscillators have been chosen for the analysis. As higher dimensional FPK systems are rarely mentioned in the literature, the TS approach will be extended to essentially infinite dimensional systems through the solution of stochastic PDEs. In making these comparisons, the advantages of modern computing tools such as computer algebra systems and simulation software, when used as an adjunct to the solution of SDEs or their associated FPK equations, are demonstrated.

Estudo de campo elétrico em linha de transmissão utilizando o método dos elementos de contorno

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Modelizzazione spazio-temporale delle dinamiche di uso del suolo ed analisi comparativa di differenti approcci predittivi. Uso integrato di SIG e telerilevamento nello studio dei processi di deforestazione nella regione La Joyanca in Peten, Guatemala

L’uso frequente dei modelli predittivi per l’analisi di sistemi complessi, naturali o artificiali, sta cambiando il tradizionale approccio alle problematiche ambientali e di rischio. Il continuo miglioramento delle capacità di elaborazione dei computer facilita l’utilizzo e la risoluzione di metodi numerici basati su una discretizzazione spazio-temporale che permette una modellizzazione predittiva di sistemi reali complessi, riproducendo l’evoluzione dei loro patterns spaziali ed calcolando il grado di precisione della simulazione. In questa tesi presentiamo una applicazione di differenti metodi predittivi (Geomatico, Reti Neurali, Land Cover Modeler e Dinamica EGO) in un’area test del Petén, Guatemala. Durante gli ultimi decenni questa regione, inclusa nella Riserva di Biosfera Maya, ha conosciuto una rapida crescita demografica ed un’incontrollata pressione sulle sue risorse naturali. L’area test puó essere suddivisa in sotto-regioni caratterizzate da differenti dinamiche di uso del suolo. Comprendere e quantificare queste differenze permette una migliore approssimazione del sistema reale; é inoltre necessario integrare tutti i parametri fisici e socio-economici, per una rappresentazione più completa della complessità dell’impatto antropico. Data l’assenza di informazioni dettagliate sull’area di studio, quasi tutti i dati sono stati ricavati dall’elaborazione di 11 immagini ETM+, TM e SPOT; abbiamo poi realizzato un’analisi multitemporale dei cambi uso del suolo passati e costruito l’input per alimentare i modelli predittivi. I dati del 1998 e 2000 sono stati usati per la fase di calibrazione per simulare i cambiamenti nella copertura terrestre del 2003, scelta come data di riferimento per la validazione dei risultati. Quest’ultima permette di evidenziare le qualità ed i limiti per ogni modello nelle differenti sub-regioni.

Entwicklung und Tests von Algorithmen für die Impedanztomographie

Die Elektrische Impedanztomographie soll als kostengünstige und nebenwirkungsfreie Tomographiemethode in der medizinischen Diagnostik, z. B. in der Mammographie dienen. Mit der EIT läßt sich Krebsgewebe von gesundem Gewebe unterscheiden, da es eine signifikant erhöhte Leitfähigkeit aufweist. Damit kann die EIT als Ergänzung zu den klassischen Diagnoseverfahren dienen. So ist z.B. bei jungen Frauen mit einem dichteren Fettgewebe die Identifizierung eines Mammakarzinoms mit der Röntgentomographie nicht immer möglich. Ziel dieser Arbeit war es, einen Prototypen für die Impedanztomographie zu entwickeln und mögliche Anwendungen zu testen. Der Tomograph ist in Zusammenarbeit mit Dr. K.H.Georgi gebaut worden. Der Tomograph erlaubt es niederohmige, Wechselströme an Elektroden auf der Körperoberfläche einzuspeisen. Die Potentiale können an diesen Elektroden programmierbar vorgegeben werden. Weitere hochohmige Elektroden dienen zur Potentialmessung. Um den Hautwiderstand zu überbrücken, werden Wechselstromfrequenzen von 20-100 kHz eingesetzt. Mit der Möglichkeit der Messung von Strom und Potential auf unterschiedlichen Elektroden kann man das Problem des nur ungenau bekannten Hautwiderstandes umgehen. Prinzipiell ist es mit dem Mainzer EIT System möglich, 100 Messungen in der Sekunde durchzuführen. Auf der Basis von mit dem Mainzer EIT gewonnenen Daten sollten unterschiedliche Rekonstruktionsalgorithmen getestet und weiterentwickelt werden. In der Vergangenheit sind verschiedene Rekonstruktionsalgorithmen für das mathematisch schlecht gestellte EIT Problem betrachtet worden. Sie beruhen im Wesentlichen auf zwei Strategien: Die Linearisierung und iterative Lösung des Problems und Gebietserkennungsmethoden. Die iterativen Verfahren wurden von mir dahingehend modifiziert, dass Leitfähigkeitserhöhungen und Leitfähigkeitserniedrigungen gleichberechtigt behandelt werden können. Für den modifizierten Algorithmus wurden zwei verschiedene Rekonstruktionsalgorithmen programmiert und mit synthetischen Daten getestet. Zum einen die Rekonstruktion über die approximative Inverse, zum anderen eine Rekonstruktion mit einer Diskretisierung. Speziell für die Rekonstruktion mittels Diskretisierung wurde eine Methode entwickelt, mit der zusätzliche Informationen in der Rekonstruktion berücksichtigt werden können, was zu einer Verbesserung der Rekonstruktion beiträgt. Der Gebietserkennungsalgorithmus kann diese Zusatzinformationen liefern. In der Arbeit wurde ein neueres Verfahren für die Gebietserkennung derart modifiziert, dass eine Rekonstruktion auch für getrennte Strom- und Spannungselektroden möglich wurde. Mit Hilfe von Differenzdaten lassen sich ausgezeichnete Rekonstruktionen erzielen. Für die medizinischen Anwendungen sind aber Absolutmessungen nötig, d.h. ohne Leermessung. Der erwartende Effekt einer Inhomogenität in der Leitfähigkeit ist sehr klein und als Differenz zweier grosser Zahlen sehr schwierig zu bestimmen. Die entwickelten Algorithmen kommen auch gut mit Absolutdaten zurecht.

Volumenpackungen nach SAE J1100

We present new algorithms to approximate the discrete volume of a polyhedral geometry using boxes defined by the US standard SAE J1100. This problem is NP-hard and has its main application in the car design process. The algorithms produce maximum weighted independent sets on a so-called conflict graph for a discretisation of the geometry. We present a framework to eliminate a large portion of the vertices of a graph without affecting the quality of the optimal solution. Using this framework we are also able to define the conflict graph without the use of a discretisation. For the solution of the maximum weighted independent set problem we designed an enumeration scheme which uses the restrictions of the SAE J1100 standard for an efficient upper bound computation. We evaluate the packing algorithms according to the solution quality compared to manually derived results. Finally, we compare our enumeration scheme to several other exact algorithms in terms of their runtime. Grid-based packings either tend to be not tight or have intersections between boxes. We therefore present an algorithm which can compute box packings with arbitrary placements and fixed orientations. In this algorithm we make use of approximate Minkowski Sums, computed by uniting many axis-oriented equal boxes. We developed an algorithm which computes the union of equal axis-oriented boxes efficiently. This algorithm also maintains the Minkowski Sums throughout the packing process. We also extend these algorithms for packing arbitrary objects in fixed orientations.

Hadronic matrix elements in lattice QCD

The lattice formulation of Quantum ChromoDynamics (QCD) has become a reliable tool providing an ab initio calculation of low-energy quantities. Despite numerous successes, systematic uncertainties, such as discretisation effects, finite-size effects, and contaminations from excited states, are inherent in any lattice calculation. Simulations with controlled systematic uncertainties and close to the physical pion mass have become state-of-the-art. We present such a calculation for various hadronic matrix elements using non-perturbatively O(a)-improved Wilson fermions with two dynamical light quark flavours. The main topics covered in this thesis are the axial charge of the nucleon, the electro-magnetic form factors of the nucleon, and the leading hadronic contributions to the anomalous magnetic moment of the muon. Lattice simulations typically tend to underestimate the axial charge of the nucleon by 5 − 10%. We show that including excited state contaminations using the summed operator insertion method leads to agreement with the experimentally determined value. Further studies of systematic uncertainties reveal only small discretisation effects. For the electro-magnetic form factors of the nucleon, we see a similar contamination from excited states as for the axial charge. The electro-magnetic radii, extracted from a dipole fit to the momentum dependence of the form factors, show no indication of finite-size or cutoff effects. If we include excited states using the summed operator insertion method, we achieve better agreement with the radii from phenomenology. The anomalous magnetic moment of the muon can be measured and predicted to very high precision. The theoretical prediction of the anomalous magnetic moment receives contribution from strong, weak, and electro-magnetic interactions, where the hadronic contributions dominate the uncertainties. A persistent 3σ tension between the experimental determination and the theoretical calculation is found, which is considered to be an indication for physics beyond the Standard Model. We present a calculation of the connected part of the hadronic vacuum polarisation using lattice QCD. Partially twisted boundary conditions lead to a significant improvement of the vacuum polarisation in the region of small momentum transfer, which is crucial in the extraction of the hadronic vacuum polarisation.

Diskontinuierliche Galerkin-Verfahren für die operationelle Wettervorhersage

In dieser Arbeit wird ein neuer Dynamikkern entwickelt und in das bestehendernnumerische Wettervorhersagesystem COSMO integriert. Für die räumlichernDiskretisierung werden diskontinuierliche Galerkin-Verfahren (DG-Verfahren)rnverwendet, für die zeitliche Runge-Kutta-Verfahren. Hierdurch ist ein Verfahrenrnhoher Ordnung einfach zu realisieren und es sind lokale Erhaltungseigenschaftenrnder prognostischen Variablen gegeben. Der hier entwickelte Dynamikkern verwendetrngeländefolgende Koordinaten in Erhaltungsform für die Orographiemodellierung undrnkoppelt das DG-Verfahren mit einem Kessler-Schema für warmen Niederschlag. Dabeirnwird die Fallgeschwindigkeit des Regens, nicht wie üblich implizit imrnKessler-Schema diskretisiert, sondern explizit im Dynamikkern. Hierdurch sindrndie Zeitschritte der Parametrisierung für die Phasenumwandlung des Wassers undrnfür die Dynamik vollständig entkoppelt, wodurch auch sehr große Zeitschritte fürrndie Parametrisierung verwendet werden können. Die Kopplung ist sowohl fürrnOperatoraufteilung, als auch für Prozessaufteilung realisiert.rnrnAnhand idealisierter Testfälle werden die Konvergenz und die globalenrnErhaltungseigenschaften des neu entwickelten Dynamikkerns validiert. Die Massernwird bis auf Maschinengenauigkeit global erhalten. Mittels Bergüberströmungenrnwird die Orographiemodellierung validiert. Die verwendete Kombination ausrnDG-Verfahren und geländefolgenden Koordinaten ermöglicht die Behandlung vonrnsteileren Bergen, als dies mit dem auf Finite-Differenzenverfahren-basierendenrnDynamikkern von COSMO möglich ist. Es wird gezeigt, wann die vollernTensorproduktbasis und wann die Minimalbasis vorteilhaft ist. Die Größe desrnEinflusses auf das Simulationsergebnis der Verfahrensordnung, desrnParametrisierungszeitschritts und der Aufteilungsstrategie wirdrnuntersucht. Zuletzt wird gezeigt dass bei gleichem Zeitschritt die DG-Verfahrenrnaufgrund der besseren Skalierbarkeit in der Laufzeit konkurrenzfähig zurnFinite-Differenzenverfahren sind.

IMEX finite volume methods for the shallow water equations

Die Flachwassergleichungen (SWE) sind ein hyperbolisches System von Bilanzgleichungen, die adäquate Approximationen an groß-skalige Strömungen der Ozeane, Flüsse und der Atmosphäre liefern. Dabei werden Masse und Impuls erhalten. Wir unterscheiden zwei charakteristische Geschwindigkeiten: die Advektionsgeschwindigkeit, d.h. die Geschwindigkeit des Massentransports, und die Geschwindigkeit von Schwerewellen, d.h. die Geschwindigkeit der Oberflächenwellen, die Energie und Impuls tragen. Die Froude-Zahl ist eine Kennzahl und ist durch das Verhältnis der Referenzadvektionsgeschwindigkeit zu der Referenzgeschwindigkeit der Schwerewellen gegeben. Für die oben genannten Anwendungen ist sie typischerweise sehr klein, z.B. 0.01. Zeit-explizite Finite-Volume-Verfahren werden am öftersten zur numerischen Berechnung hyperbolischer Bilanzgleichungen benutzt. Daher muss die CFL-Stabilitätsbedingung eingehalten werden und das Zeitinkrement ist ungefähr proportional zu der Froude-Zahl. Deswegen entsteht bei kleinen Froude-Zahlen, etwa kleiner als 0.2, ein hoher Rechenaufwand. Ferner sind die numerischen Lösungen dissipativ. Es ist allgemein bekannt, dass die Lösungen der SWE gegen die Lösungen der Seegleichungen/ Froude-Zahl Null SWE für Froude-Zahl gegen Null konvergieren, falls adäquate Bedingungen erfüllt sind. In diesem Grenzwertprozess ändern die Gleichungen ihren Typ von hyperbolisch zu hyperbolisch.-elliptisch. Ferner kann bei kleinen Froude-Zahlen die Konvergenzordnung sinken oder das numerische Verfahren zusammenbrechen. Insbesondere wurde bei zeit-expliziten Verfahren falsches asymptotisches Verhalten (bzgl. der Froude-Zahl) beobachtet, das diese Effekte verursachen könnte.Ozeanographische und atmosphärische Strömungen sind typischerweise kleine Störungen eines unterliegenden Equilibriumzustandes. Wir möchten, dass numerische Verfahren für Bilanzgleichungen gewisse Equilibriumzustände exakt erhalten, sonst können künstliche Strömungen vom Verfahren erzeugt werden. Daher ist die Quelltermapproximation essentiell. Numerische Verfahren die Equilibriumzustände erhalten heißen ausbalanciert.rnrnIn der vorliegenden Arbeit spalten wir die SWE in einen steifen, linearen und einen nicht-steifen Teil, um die starke Einschränkung der Zeitschritte durch die CFL-Bedingung zu umgehen. Der steife Teil wird implizit und der nicht-steife explizit approximiert. Dazu verwenden wir IMEX (implicit-explicit) Runge-Kutta und IMEX Mehrschritt-Zeitdiskretisierungen. Die Raumdiskretisierung erfolgt mittels der Finite-Volumen-Methode. Der steife Teil wird mit Hilfe von finiter Differenzen oder au eine acht mehrdimensional Art und Weise approximniert. Zur mehrdimensionalen Approximation verwenden wir approximative Evolutionsoperatoren, die alle unendlich viele Informationsausbreitungsrichtungen berücksichtigen. Die expliziten Terme werden mit gewöhnlichen numerischen Flüssen approximiert. Daher erhalten wir eine Stabilitätsbedingung analog zu einer rein advektiven Strömung, d.h. das Zeitinkrement vergrößert um den Faktor Kehrwert der Froude-Zahl. Die in dieser Arbeit hergeleiteten Verfahren sind asymptotisch erhaltend und ausbalanciert. Die asymptotischer Erhaltung stellt sicher, dass numerische Lösung das "korrekte" asymptotische Verhalten bezüglich kleiner Froude-Zahlen besitzt. Wir präsentieren Verfahren erster und zweiter Ordnung. Numerische Resultate bestätigen die Konvergenzordnung, so wie Stabilität, Ausbalanciertheit und die asymptotische Erhaltung. Insbesondere beobachten wir bei machen Verfahren, dass die Konvergenzordnung fast unabhängig von der Froude-Zahl ist.

Modeling and Vibration Suppression for Telescopic Systems of Structural Members with Clearance

Telescopic systems of structural members with clearance are found in many applications, e.g., mobile cranes, rack feeders, fork lifters, stacker cranes (see Figure 1). Operating these machines, undesirable vibrations may reduce the performance and increase safety problems. Therefore, this contribution has the aim to reduce these harmful vibrations. For a better understanding, the dynamic behaviour of these constructions is analysed. The main interest is the overlapping area of each two sections of the above described systems (see markings in Figure 1) which is investigated by measurements and by computations. A test rig is constructed to determine the dynamic behaviour by measuring fundamental vibrations and higher frequent oscillations, damping coefficients, special appearances and more. For an appropriate physical model, the governing boundary value problem is derived by applying Hamilton’s principle and a classical discretisation procedure is used to generate a coupled system of nonlinear ordinary differential equations as the corresponding truncated mathematical model. On the basis of this model, a controller concept for preventing harmful vibrations is developed.

Numerical Error Prediction and its applications in CFD using tau-estimation

Nowadays, Computational Fluid Dynamics (CFD) solvers are widely used within the industry to model fluid flow phenomenons. Several fluid flow model equations have been employed in the last decades to simulate and predict forces acting, for example, on different aircraft configurations. Computational time and accuracy are strongly dependent on the fluid flow model equation and the spatial dimension of the problem considered. While simple models based on perfect flows, like panel methods or potential flow models can be very fast to solve, they usually suffer from a poor accuracy in order to simulate real flows (transonic, viscous). On the other hand, more complex models such as the full Navier- Stokes equations provide high fidelity predictions but at a much higher computational cost. Thus, a good compromise between accuracy and computational time has to be fixed for engineering applications. A discretisation technique widely used within the industry is the so-called Finite Volume approach on unstructured meshes. This technique spatially discretises the flow motion equations onto a set of elements which form a mesh, a discrete representation of the continuous domain. Using this approach, for a given flow model equation, the accuracy and computational time mainly depend on the distribution of nodes forming the mesh. Therefore, a good compromise between accuracy and computational time might be obtained by carefully defining the mesh. However, defining an optimal mesh for complex flows and geometries requires a very high level expertize in fluid mechanics and numerical analysis, and in most cases a simple guess of regions of the computational domain which might affect the most the accuracy is impossible. Thus, it is desirable to have an automatized remeshing tool, which is more flexible with unstructured meshes than its structured counterpart. However, adaptive methods currently in use still have an opened question: how to efficiently drive the adaptation ? Pioneering sensors based on flow features generally suffer from a lack of reliability, so in the last decade more effort has been made in developing numerical error-based sensors, like for instance the adjoint-based adaptation sensors. While very efficient at adapting meshes for a given functional output, the latter method is very expensive as it requires to solve a dual set of equations and computes the sensor on an embedded mesh. Therefore, it would be desirable to develop a more affordable numerical error estimation method. The current work aims at estimating the truncation error, which arises when discretising a partial differential equation. These are the higher order terms neglected in the construction of the numerical scheme. The truncation error provides very useful information as it is strongly related to the flow model equation and its discretisation. On one hand, it is a very reliable measure of the quality of the mesh, therefore very useful in order to drive a mesh adaptation procedure. On the other hand, it is strongly linked to the flow model equation, so that a careful estimation actually gives information on how well a given equation is solved, which may be useful in the context of _ -extrapolation or zonal modelling. The following work is organized as follows: Chap. 1 contains a short review of mesh adaptation techniques as well as numerical error prediction. In the first section, Sec. 1.1, the basic refinement strategies are reviewed and the main contribution to structured and unstructured mesh adaptation are presented. Sec. 1.2 introduces the definitions of errors encountered when solving Computational Fluid Dynamics problems and reviews the most common approaches to predict them. Chap. 2 is devoted to the mathematical formulation of truncation error estimation in the context of finite volume methodology, as well as a complete verification procedure. Several features are studied, such as the influence of grid non-uniformities, non-linearity, boundary conditions and non-converged numerical solutions. This verification part has been submitted and accepted for publication in the Journal of Computational Physics. Chap. 3 presents a mesh adaptation algorithm based on truncation error estimates and compares the results to a feature-based and an adjoint-based sensor (in collaboration with Jorge Ponsín, INTA). Two- and three-dimensional cases relevant for validation in the aeronautical industry are considered. This part has been submitted and accepted in the AIAA Journal. An extension to Reynolds Averaged Navier- Stokes equations is also included, where _ -estimation-based mesh adaptation and _ -extrapolation are applied to viscous wing profiles. The latter has been submitted in the Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering. Keywords: mesh adaptation, numerical error prediction, finite volume Hoy en día, la Dinámica de Fluidos Computacional (CFD) es ampliamente utilizada dentro de la industria para obtener información sobre fenómenos fluidos. La Dinámica de Fluidos Computacional considera distintas modelizaciones de las ecuaciones fluidas (Potencial, Euler, Navier-Stokes, etc) para simular y predecir las fuerzas que actúan, por ejemplo, sobre una configuración de aeronave. El tiempo de cálculo y la precisión en la solución depende en gran medida de los modelos utilizados, así como de la dimensión espacial del problema considerado. Mientras que modelos simples basados en flujos perfectos, como modelos de flujos potenciales, se pueden resolver rápidamente, por lo general aducen de una baja precisión a la hora de simular flujos reales (viscosos, transónicos, etc). Por otro lado, modelos más complejos tales como el conjunto de ecuaciones de Navier-Stokes proporcionan predicciones de alta fidelidad, a expensas de un coste computacional mucho más elevado. Por lo tanto, en términos de aplicaciones de ingeniería se debe fijar un buen compromiso entre precisión y tiempo de cálculo. Una técnica de discretización ampliamente utilizada en la industria es el método de los Volúmenes Finitos en mallas no estructuradas. Esta técnica discretiza espacialmente las ecuaciones del movimiento del flujo sobre un conjunto de elementos que forman una malla, una representación discreta del dominio continuo. Utilizando este enfoque, para una ecuación de flujo dado, la precisión y el tiempo computacional dependen principalmente de la distribución de los nodos que forman la malla. Por consiguiente, un buen compromiso entre precisión y tiempo de cálculo se podría obtener definiendo cuidadosamente la malla, concentrando sus elementos en aquellas zonas donde sea estrictamente necesario. Sin embargo, la definición de una malla óptima para corrientes y geometrías complejas requiere un nivel muy alto de experiencia en la mecánica de fluidos y el análisis numérico, así como un conocimiento previo de la solución. Aspecto que en la mayoría de los casos no está disponible. Por tanto, es deseable tener una herramienta que permita adaptar los elementos de malla de forma automática, acorde a la solución fluida (remallado). Esta herramienta es generalmente más flexible en mallas no estructuradas que con su homóloga estructurada. No obstante, los métodos de adaptación actualmente en uso todavía dejan una pregunta abierta: cómo conducir de manera eficiente la adaptación. Sensores pioneros basados en las características del flujo en general, adolecen de una falta de fiabilidad, por lo que en la última década se han realizado grandes esfuerzos en el desarrollo numérico de sensores basados en el error, como por ejemplo los sensores basados en el adjunto. A pesar de ser muy eficientes en la adaptación de mallas para un determinado funcional, este último método resulta muy costoso, pues requiere resolver un doble conjunto de ecuaciones: la solución y su adjunta. Por tanto, es deseable desarrollar un método numérico de estimación de error más asequible. El presente trabajo tiene como objetivo estimar el error local de truncación, que aparece cuando se discretiza una ecuación en derivadas parciales. Estos son los términos de orden superior olvidados en la construcción del esquema numérico. El error de truncación proporciona una información muy útil sobre la solución: es una medida muy fiable de la calidad de la malla, obteniendo información que permite llevar a cabo un procedimiento de adaptación de malla. Está fuertemente relacionado al modelo matemático fluido, de modo que una estimación precisa garantiza la idoneidad de dicho modelo en un campo fluido, lo que puede ser útil en el contexto de modelado zonal. Por último, permite mejorar la precisión de la solución resolviendo un nuevo sistema donde el error local actúa como término fuente (_ -extrapolación). El presenta trabajo se organiza de la siguiente manera: Cap. 1 contiene una breve reseña de las técnicas de adaptación de malla, así como de los métodos de predicción de los errores numéricos. En la primera sección, Sec. 1.1, se examinan las estrategias básicas de refinamiento y se presenta la principal contribución a la adaptación de malla estructurada y no estructurada. Sec 1.2 introduce las definiciones de los errores encontrados en la resolución de problemas de Dinámica Computacional de Fluidos y se examinan los enfoques más comunes para predecirlos. Cap. 2 está dedicado a la formulación matemática de la estimación del error de truncación en el contexto de la metodología de Volúmenes Finitos, así como a un procedimiento de verificación completo. Se estudian varias características que influyen en su estimación: la influencia de la falta de uniformidad de la malla, el efecto de las no linealidades del modelo matemático, diferentes condiciones de contorno y soluciones numéricas no convergidas. Esta parte de verificación ha sido presentada y aceptada para su publicación en el Journal of Computational Physics. Cap. 3 presenta un algoritmo de adaptación de malla basado en la estimación del error de truncación y compara los resultados con sensores de featured-based y adjointbased (en colaboración con Jorge Ponsín del INTA). Se consideran casos en dos y tres dimensiones, relevantes para la validación en la industria aeronáutica. Este trabajo ha sido presentado y aceptado en el AIAA Journal. También se incluye una extensión de estos métodos a las ecuaciones RANS (Reynolds Average Navier- Stokes), en donde adaptación de malla basada en _ y _ -extrapolación son aplicados a perfiles con viscosidad de alas. Este último trabajo se ha presentado en los Actas de la Institución de Ingenieros Mecánicos, Parte G: Journal of Aerospace Engineering. Palabras clave: adaptación de malla, predicción del error numérico, volúmenes finitos