Les générateurs thermoélectriques (TEG), associant des modules thermoélectriques à des échangeurs de chaleur adaptés, permettent de produire de l’électricité à partir d’une source chaude et d’une source froide. Leur utilisation, réservée actuellement à des applications de niche, va s’avérer judicieuse pour différentes applications industrielles ou domestiques en raison de la disponibilité imminente de nouveaux matériaux thermoélectriques permettant des rendements améliorés et des coûts moindres. Pour rendre plus attractive l’utilisation des TEG et améliorer le rendement global des futures installations, une conception et une utilisation optimisées sont indispensables.La conception de TEG performants nécessite le développement de modèles numériques intégrant tous les éléments de la chaîne énergétique (source chaude, source froide, échangeurs, convertisseurs électriques). L’objectif de la thèse est de créer un outil de simulation du fonctionnement des générateurs sur l’ensemble du cycle de production de chaleur et donc sur des fonctionnements réels dépendant du temps. Le modèle développé en 3D pour les transferts de chaleur prend en compte la dépendance à la température des propriétés des matériaux et l’effet Thomson pour le modèle thermoélectrique.La validation de cet outil de simulation a nécessité la comparaison des prédictions du modèle à des résultats expérimentaux. Un dispositif expérimental a été complété et amélioré afin de mieux répondre aux attentes des études en régime instationnaire. Ce banc d'essai permet d'effectuer des tests avec différentes configurations de générateur thermoélectrique et différentes conditions de fonctionnement. Le modèle a montré une estimation correcte des températures du système et de la production électrique du TEG. Le modèle numérique est validé et peut être utilisé pour la prédiction du fonctionnement d’un TEG dans diverses conditions. / Thermoelectric generators (TEG), combine thermoelectric modules with heat exchangers, making it possible to produce electricity from a hot source and a cold source. Their use, which is currently reserved for niche applications, will prove useful for various industrial or domestic applications due to the imminent availability of new thermoelectric materials allowing improved yields and lower costs. To make the use of TEGs more attractive and to improve the overall efficiency of future installations, optimized design and use are essential.The high-performance TEG design requires the development of numerical models integrating all the elements of the energy chain (hot source, cold source, exchangers, electric converters).The aim of the thesis is to create a tool for simulating the operation of generators over the entire heat production cycle and thus on real time-dependent operations. The model developed in 3D for heat transfer takes into account the temperature dependence of the properties of the materials and the Thomson effect for the thermoelectric model.The validation of this simulation tool required the comparison of model predictions with experimental results. An experimental device has been completed and improved to match better the expectations of unsteady studies. This test bench allows testing with different thermoelectric generator configurations and different operating conditions.The model showed a correct estimation of system temperatures and electrical output of TEG. The numerical model is validated and can be used to predict the operation of a TEG under various conditions.

Cette étude vise à caractériser en soufflerie les mécanismes aérodynamiques à l’origine de la génération puis la transmission des fluctuations de bruit dans un modèle d’habitacle automobile. Le banc d’essai conçu en soufflerie anéchoïque consiste en un écoulement dont la vitesse incidente est modulée par un volet mobile, et qui par interaction avec une marche montante rayonne un bruit aéroacoustique transmis à travers une vitre dans un caisson anéchoïque. L’approche retenue consiste, pendant le temps de maniement du volet, à mesurer et relier le champ de vitesse externe mesuré à l’aide de la technique de vélocimétrie laser par images de particules (TR-PIV échantillonnée à 20 kHz) à la pression pariétale d’une part, puis au champ acoustique interne obtenu par transmission d’autre part. Des outils de corrélation spatio-temporelle sont alors utilisés pour mettre en évidence les zones de l’écoulement les plus corrélées avec les fluctuations d’énergie de la pression pariétale et celles du niveau de bruit intérieur. La fluctuation du chargement aérodynamique de la vitre sous la bulle de recirculation est logiquement liée à l’activité instationnaire de cette dernière, puis plus en aval, au lâcher tourbillonnaire. Quant au bruit transmis dans le modèle d’habitacle, il semble principalement lié aux fluctuations de vitesse dans la couche de cisaillement. Enfin, une procédure spécifique a permis d’évaluer le caractère quasi-stationnaire des variations temporelles des quantités fluctuantes ainsi que la réponse acoustique de la vitre. / This study aims at characterizing in a wind tunnel the aerodynamic mechanisms contributing to the generation and transmission of the noise fluctuations into a car interior model. The test bench designed in anechoic wind tunnel consists of a flow whose incoming flow velocity is modulated by a mobile flap, and which by interaction with a forward-facing step radiates an aeroacoustic noise transmitted through a glass into an anechoic box. The adopted approach consists, during the flap handling time, in measuring and connecting the external velocity field measured using the Time-Resolved laser Particle Image Velocimetry technique (TR-PIV at sampling frequency 20 kHz) to the wall pressure on the one hand, and then to the internal acoustic field obtained by transmission on the other hand. Spatio-temporal correlation tools are then used to highlight the flow areas that are the most correlated with the energy fluctuations of the wall pressure and with those of the internal noise level. The fluctuation of the aerodynamic loading of the window under the recirculation bubble is logically related to the unsteady activity of the latter, then further downstream to the vortex stream. As for the noise transmitted into the cabin model, it seems mainly related to the speed fluctuations in the shear layer. Finally, a specific procedure allows to evaluate the quasi-steady nature of the temporal variations of the fluctuating quantities, as well as the acoustic response of the window.

Biofuels produced from lignocellulosic biomass via the fermentation platform are sustainable energy alternatives to fossil fuels. Process Systems Engineering (PSE) uses computer-based tools and methods to design, simulate and optimize processes. Application of PSE tools to the design of economic biorefinery processes requires the development of simulation approaches that can be integrated with existing, mature PSE tools used to optimize traditional refineries, such as Aspen Plus. Current unit operation models lack the ability to describe unsteady state fermentation processes, link unsteady state fermentation with in situ separations, and optimize these processes for competing factors (e.g., yield and productivity). This work applies a novel architecture of commercial PSE tools, Aspen Plus and MATLAB, to develop techniques to simulate time-dependent fermentation without and with in situ separations for process design, analyses and optimization of the operating conditions. Traditional batch fermentation simulations with in situ separations decouple these interdependent steps in a separate “steady state” reactor followed by an equilibrium separation of the final fermentation broth. A typical mechanistic system of ordinary differential equations (ODEs) describing a batch fermentation does not fit the standard built-in power law reaction kinetics model in Aspen Plus. To circumvent this challenge, a novel platform that links the batch reactor to a FORTRAN user kinetics subroutine (incorporates the ODEs) combined with component substitution (to simulate non-databank components) is utilized to simulate an unsteady state batch and in situ gas stripping process. The resulting model system predicts the product profile to be sensitive to the gas flow rate unlike previous “steady state” simulations. This demonstrates the importance of linking a time-dependent fermentation model to the fermentation environment for the design and analyses of fermentation processes. A novel platform linking the genetic algorithm multi-objective and single-objective optimizations in MATLAB to the unsteady state batch fermentation simulation in Aspen Plus through a component object module communication platform is utilized to optimize the operating conditions of a typical batch fermentation process. Two major contributions are: prior concentration of sugars from a typical lignocellulosic hydrolysate may be needed and with a higher initial sugar concentration, the fermentation process must be integrated with an in situ separation process to optimize the performance of fermentation processes. With this framework, fermentation experimentalists can use the full suite of PSE tools and methods to integrate biorefineries and refineries and as a decision-support tool to guide the design, analyses and optimization of fermentation-based biorefineries.

The helicopter possesses the unrivaled capacity for vertical takeoff and landing which has made the helicopter suitable for numerous tasks such as carrying passengers and equipment, providing air medical services, firefighting, and other military and civil tasks. The nature of the aerodynamic environment surrounding the helicopter gives rise to a significant amount of vibration to its whole body. Among different sources of vibrations, the main rotor blade is the major contributor. The dynamic characteristics of the hingeless rotor consisting of elastic blades are of particular interest because of the strongly coupled equations of motion. The elastic rotor blades are subjected to coupled flapping, lead-lag, and torsional (triply coupled) deflections. Once these deflections exceed the maximum allowable level, the structural integrity of the rotor blade is affected leading to the ultimate failure. The maximum deflection that a blade can undergo for a specific operating condition needs to be estimated. Therefore, in this study, the triply coupled free and forced response of the Bo 105 hingeless, composite helicopter rotor blade is investigated at hovering and forward flights. At first, a model of the composite cross-section of the rotor blade is proposed for which a semi-analytical procedure is developed to estimate the sectional properties. These properties are used in the mathematical model of the free vibration of the rotor blade having the proposed cross-section to solve for the natural frequencies and the mode shapes. The aerodynamic loadings from the strip theory are used to estimate the time-varying forced response of the rotor blade for hovering and forward flights. The large flapping and inflow angles are introduced in the mathematical model of the forward flight and the corresponding nonlinear mathematical model requires a numerical solution technique. Therefore, a generalization of the method of lines is performed to develop a robust numerical solution in terms of time-varying deflections and velocities. The effect of the unsteady aerodynamics at the forward flight is included in the mathematical model to estimate the corresponding dynamic response. Both the analytical and the numerical models are validated by finite element results and the convergence study for the free vibration is performed.

An obvious reason for studying unsteady flows is the prediction of the effect of unsteady aerodynamic forces on a flight vehicle, since these effects tend to increase the likelihood of aeroelastic instabilities. This is a major concern in aerodynamic design of aircraft that operate in transonic regime, where the flows are characterised by the presence of adjacent regions of subsonic and supersonic flow, usually accompanied by weak shocks. It has been a common expectation that the numerical approach as an alternative to wind tunnel experiments would become more economical as computers became less expensive and more powerful. However even with all the expected future advances in computer technology, the cost of a numerical flutter analysis (computational aeroelasticity) for a transonic flight remains prohibitively high. Hence it is vitally important to develop an efficient, cheaper (in the sense of computational cost) and physically accurate flutter simulation tech nique which is capable of reproducing the data, which would otherwise be obtained from wind tunnel tests, at least to some acceptable engineering accuracy, and that it is essentially appropriate for industrial applications. This need motivated the present research work on exploring and developing efficient and physically accurate computational techniques for steady, unsteady and time-linearised calculations of transonic flows over an aircraft wing with moving shocks. This dissertation is subdivided into eight chapters, seven appendices and a bibliography listing all the reference materials used in the research work. The research work initially starts with a literature survey in unsteady transonic flow theory and calculations, in which emphasis is placed upon the developments in these areas in the last three decades. Chapter 3 presents the small disturbance theory for potential flows in the subsonic, transonic and supersonic regimes, including the required boundary conditions and shock jump conditions. The flow is assumed irrotational and inviscid, so that the equation of state, continuity equation and Bernoulli's equation formulated in Appendices A and B can be employed to formulate the governing fluid equation in terms of total velocity potential. Furthermore for transonic flow with free-stream Mach number close to unity, we show in Appendix C that the shocks that appear are weak enough to allow us to neglect the flow rotationality. The formulations are based on the main assumption that aerofoil slopes are everywhere small, and the flow quantities are small perturbations about their free-stream values. In Chapter 4, we developed an improved approximate factorisation algorithm that solves the two-dimensional steady subsonic small disturbance equation with nonreflecting far-field boundary conditions. The finite difference formulation for the improved algorithm is presented in Appendix D, with the description of the solver used for solving the system of difference equations described in Appendix E. The calculation of steady and unsteady nonlinear transonic flows over a realistic aerofoil are considered in Chapter 5. Numerical solution methods, based on the finite difference approach, for solving the two-dimensional steady and unsteady, general-frequency transonic small disturbance equations are presented, with the corresponding finite difference formulation described in Appendix F. The theories and solution methods for the time-linearised calculations, in the frequency and time domains, for the problem of unsteady transonic flow over a thin planar wing undergoing harmonic oscillation are presented in Chapters 6 and 7, respectively. The time-linearised calculations include the periodic shock motion via the shock jump correction procedure. This procedure corrects the solution values behind the shock, to accommodate the effect of shock motion, and consequently, the solution method will produce a more accurate time-linearised solution for supercritical flow. Appendix G presents the finite difference formulation of these time-linearised solution methods. The aim is to develop an efficient computational method for calculating oscillatory transonic aerodynamic quantities efficiently for use in flutter analyses of both two- and three-dimensional wings with lifting surfaces. Chapter 8 closes the dissertation with concluding remarks and future prospects on the current research work.

L'étude porte sur le contrôle actif du phénomène de tremblement transsonique sur une voilure supercritique par l'utilisation de deux stratégies de contrôle : thermique et pneumatique. Des simulations numériques de l'écoulement naturel obtenues par résolution des équations de Navier-Stokes moyennées ont permis la restitution des différents régimes (avec ou sans tremblement) en bonne cohérence avec les données expérimentales. Les observations des champs moyens, des champs turbulents et des signaux de pression permettent d'établir le principe de fonctionnement et les performances des actionneurs. Le tremblement transsonique est alors soit repoussé soit supprimé autorisant ainsi l'élargissement du domaine de vol des aéronefs. L'étude paramétrique des deux actionneurs est réalisée aussi bien en mode de fonctionnement continu que rétroactif. Une campagne d'essai consolide et approfondie les résultats obtenues avec la stratégie pneumatique.

These thesis review some recent results on the construction of very high order multidimensional upwind schemes for the solution of steady and unsteady conservation laws on unstructured triangular grids. We also consider the extension to the approximation of solutions to conservation laws containing second order dissipative terms. To build this high order schemes we use a sub-triangulation of the triangular Pk elements where we apply the distribution used for a P1 element. This manuscript is divided in two parts. The first part is dedicated to the design of the high order schemes for scalar equations and focus more on the theoretical design of the schemes. The second part deals with the extension to system of equations, in particular we will compare the performances of 2nd, 3rd and 4th order schemes. The first part is subdivided in four chapters: The aim of the second chapter is to present the multidimensional upwind residual distributive schmes and to explain what was the status of their development at the beginning of this work. The third chapter is dedicated to the first contribution: the design of 3rd and 4th order quasi non-oscillatory schemes. The fourth chapter is composed of two parts: We start by understanding the non-uniformity of the accuracy of the 2nd order schemes for advection-diffusion problem. To solve this issue we use a Finite Element hybridisation. This deep study of the 2nd order scheme is used as a basis to design a 3rd order scheme for advection-diffusion. Finally, in the fifth chapter we extend the high order quasi non-oscillatory schemes to unsteady problems. In the second part, we extend the schemes of the first part to systems of equations as follows: The sixth chapter deals with the extension to steady systems of hyperbolic equations. In particular, we discuss how to solve some issues such as boundary conditions and the discretisation of curved geometries. Then, we look at the performance of 2nd and 3rd order schemes on viscous flow. Finally, we test the space-time schemes on several test cases. In particular, we will test the monotonicity of the space-time non-oscillatory schemes and we apply residual distributive schemes to acoustic problems.

The continuous trend in gas turbine design towards lighter, more powerful and more reliable engines on one side and use of alternative fuels on the other side renders flutter problems as one of the paramount challenges in engine design. Flutter denotes a self-excited and self-sustained aeroelastic instability phenomenon that can lead to material fatigue and eventually damage of structure in a short period of time unless properly damped. The design for flutter safety involves the prediction of unsteady aerodynamics as well as structural dynamics that is mostly based on in-house developed numerical tools. While high confidence has been gained on the structural side unanticipated flutter occurrences during engine design, testing and operation evidence a need for enhanced validation of aerodynamic models despite the degree of sophistication attained. The continuous development of these models can only be based on the deepened understanding of underlying physical mechanisms from test data. As a matter of fact most flutter test cases treat the turbomachine flow in two-dimensional manner indicating that the problem is solved as plane representation at a certain radius rather than representing the complex annular geometry of a real engine. Such considerations do consequently not capture effects that are due to variations in the third dimension, i.e. in radial direction. In this light the present thesis has been formulated to study three-dimensional effects during flutter in the annular environment of a low-pressure turbine blade row and to describe the importance on prediction of flutter stability. The work has been conceived as compound experimental and computational work employing a new annular sector cascade test facility. The aeroelastic response phenomenon is studied in the influence coefficient domain having one blade oscillating in various three-dimensional rigid-body modes and measuring the unsteady response on several blades and at various radial positions. On the computational side a state-of-the-art industrial numerical prediction tool has been used that allowed for two-dimensional and three-dimensional linearized unsteady Euler analyses. The results suggest that considerable three-dimensional effects are present, which are harming prediction accuracy for flutter stability when employing a two-dimensional plane model. These effects are mainly apparent as radial gradient in unsteady response magnitude from tip to hub indicating that the sections closer to the hub experience higher aeroelastic response than their equivalent plane representatives. Other effects are due to turbomachinery-typical three-dimensional flow features such as hub endwall and tip leakage vortices, which considerably affect aeroelastic prediction accuracy. Both effects are of the same order of magnitude as effects of design parameters such as reduced frequency, flow velocity level and incidence. Although the overall behavior is captured fairly well when using two-dimensional simulations notable improvement has been demonstrated when modeling fully three-dimensional and including tip clearance.

The design parameters axial gap and stator count of highpressure turbine stages are evaluated numerically towards theirinfluence on the unsteady aerodynamic excitation of rotorblades. Of particular interest is if and how unsteadyaerodynamic considerations in the design could reduce the riskofhigh cycle fatigue (HCF) failures of the turbine rotor. A well-documented 2D/Q3D non-linear unsteady code (UNSFLO)is chosen to perform the stage flow analyses. The evaluatedresults are interpreted as aerodynamic excitation mechanisms onstream sheets neglecting 3D effects. Mesh studies andvalidations against measurements and 3D computations provideconfidence in the unsteady results. Three test cases areanalysed. First, a typical aero-engine high pressure turbinestage is studied at subsonic and transonic flow conditions,with four axial gaps (37% - 52% of cax,rotor) and two statorconfigurations (43 and 70 NGV). Operating conditions areaccording to the resonant conditions of the blades used inaccompanied experiments. Second, a subsonic high pressureturbine intended to drive the turbopump of a rocket engine isinvestigated. Four axial gap variations (10% - 29% ofcax,rotor) and three stator geometry variations are analysed toextend and generalise the findings made on the first study.Third, a transonic low pressure turbine rotor, known as theInternational Standard Configuration 11, has been modelled tocompute the unsteady flow due to blade vibration and comparedto available experimental data. Excitation mechanisms due to shock, potential waves andwakes are described and related to the work found in the openliterature. The strength of shock excitation leads to increasedpressure excitation levels by a factor 2 to 3 compared tosubsonic cases. Potential excitations are of a typical wavetype in all cases, differences in the propagation direction ofthe waves and the wave reflection pattern in the rotor passagelead to modifications in the time and space resolved unsteadypressures on the blade surface. The significant influence ofoperating conditions, axial gap and stator size on the wavepropagation is discussed on chosen cases. The wake influence onthe rotorblade unsteady pressure is small in the presentevaluations, which is explicitly demonstrated on the turbopumpturbine by a parametric study of wake and potentialexcitations. A reduction in stator size (towards R≈1)reduces the potential excitation part so that wake andpotential excitation approach in their magnitude. Potentials to reduce the risk of HCF excitation in transonicflow are the decrease of stator exit Mach number and themodification of temporal relations between shock and potentialexcitation events. A similar temporal tuning of wake excitationto shock excitation appears not efficient because of the smallwake excitation contribution. The increase of axial gap doesnot necessarily decrease the shock excitation strength neitherdoes the decrease of vane size because the shock excitation mayremain strong even behind a smaller stator. The evaluation ofthe aerodynamic excitation towards a HCF risk reduction shouldonly be done with regard to the excited mode shape, asdemonstrated with parametric studies of the mode shapeinfluence on excitability. <b>Keywords:</b>Aeroelasticity, Aerodynamics, Stator-RotorInteraction, Excitation Mechanism, Unsteady Flow Computation,Forced Response, High Cycle Fatigue, Turbomachinery,Gas-Turbine, High-Pressure Turbine, Turbopump, CFD, Design

The thesis deals with the development of a new residual error estimator and adaptive algorithms based on the error estimator for steady and unsteady fluid flows in a finite volume framework. The aposteriori residual error estimator referred to as R--parameter, is a measure of the local truncation error and is derived from the imbalance arising from the use of an exact operator on the numerical solution for conservation laws. A detailed and systematic study of the R--parameter on linear and non--linear hyperbolic problems, involving continuous flows and discontinuities is performed. Simple theoretical analysis and extensive numerical experiments are performed to establish the fact that the R--parameter is a valid estimator at limiter--free continuous flow regions, but is rendered inconsistent at discontinuities and with limiting. The R--parameter is demonstrated to work equally well on different mesh topologies and detects the sources of error, making it an ideal choice to drive adaptive strategies. The theory of the error estimation is also extended for unsteady flows, both on static and moving meshes. The R--parameter can be computed with a low computational overhead and is easily incorporated into existing finite volume codes with minimal effort. Adaptive refinement algorithms for steady flows are devised employing the residual error estimator. For continuous flows devoid of limiters, a purely R--parameter based adaptive algorithm is designed. A threshold length scale derived from the estimator determines the refinement/derefinement criterion, leading to a self--evolving adaptive algorithm devoid of heuristic parameters. On the other hand, for compressible flows involving discontinuities and limiting, a hybrid adaptive algorithm is proposed. In this hybrid algorithm, error indicators are used to flag regions for refinement, while regions of derefinement are detected using the R--parameter. Two variants of these algorithms, which differ in the computation of the threshold length scale are proposed. The disparate behaviour of the R--parameter for continuous and discontinuous flows is exploited to design a simple and effective discontinuity detector for compressible flows. For time--dependent flow problems, a two--step methodology is proposed for adaptive grid refinement. In the first step, the ``best" mesh at any given time instant is determined. The second step involves predicting the evolution of flow phenomena over a period of time and refines regions into which the flow features would progress into. The latter step is implemented using a geometric--based ``Refinement Level Projection" strategy which guarantees that the flow features remain in adapted zones between successive adaptive cycles and hence uniform solution accuracy. Several numerical experiments involving inviscid and viscous flows on different grid topologies are performed to illustrate the success of the proposed adaptive algorithms. Appendix 1 Candidate's response to the comments/queries of the examiners The author would like to thank the reviewers for their appreciation of the work embodied in the thesis and for their comments. The clarifications to the comments and queries posed in the reviews are summarized below. Referee 1 Q: The example of mesh refinement for RANS solution with shock was performed with isotropic mesh, while the author claims that it is appropriate with anisotropic mesh. If this is the case, why did he not demonstrate that ? As the author knows well, in the case of full 3--D configuration, isotropic adaptation will lead to substantial grid points. The large mesh will hamper timely turnaround time of simulation. Therefore it would be a significant contribution to the aero community if this point is investigated at a later date. Response: The author is of the view that for most practical situations, a pragmatic approach to mesh adaptation for RANS computations would merely involve generating a viscous padding of adequate fineness around the body and allowing for grid adaptation only in the outer potential region. Of course, this method would allow for grid adaptation in the outer layers of viscous padding only to the extent the smoothness criterion is satisfied while adapting the grids in the potential region. This completely obviates point addition to the wall (CAD surface) and there by avoids all complexities (like loss in automation) resulting from the interaction with the surface modeler while adding point on the wall. This method is expected to do well for attached flows and mildly separated flows. This method is expected to do well even for problems involving shock - boundary layer interaction, owing to the fact that the shock is normal to the wall surface (recall, a flow aligned grid is ideal to capture such shocks), as long as the interaction does not result in a massive separation. This approach has already been demonstrated in section 4.5.3 where in adaptive high-lift computations have been performed. Isotropic adaptation retains the goodness of the zero level grid and therefore the robustness of the solver does not suffer through successive levels of grid adaptation. This procedure may result in large number of volumes. On the other hand, the anisotropic refinement may result in significantly less number of volumes, but the mesh quality may have badly degenerated during successive levels of adaptation leading to difficulties in convergence. Therefore, the choice of either of these strategies is effectively dictated by requirements on grid quality and grid size. Also, it is generally understood that building tools for anisotropic adaptation are more complicated as compared to those required for isotropic adaptation, while anisotropic refinement may not require point addition on the wall. Considering these facts, in the view of the author, this issue is an open issue and his personal preference would be to use isotropic refinement or a hybrid strategy employing a combination of these methodologies, particularly considering aspects of solution quality. Finally, in both the examples cited by the reviewer (sections 6.4.5 & 6.4.6) the objective was to demonstrate the efficacy of the new adaptive algorithm (using error indicators and the residual estimator), rather than evaluating the pros & cons of isotropic and anisotropic refinement strategies. In the sections cited above, the author has merely highlighted the advantages of the refinement strategies in specific context of the problem considered and these statements need not be considered as general. Referee 2 Q: For convection problems, a good error estimator must be able to distinguish between locally generated error and convected error. The thesis says the residual error estimator is able to do this and some numerical evidence is presented, but can the candidate comment how the estimator is able to achieve this ? Response: The ultimate aim of any AMR strategy is to reduce the global error. The residual error estimator proposed in this work measures the local truncation error. It has been shown in the context of a linear convective equation that the global error in a cell consists of two parts--the locally generated error in the cell (which is the R--parameter) and the local error transported from other cells in the domain. Either of these errors are dependent on the local error itself and any algorithm that reduces the local truncation error (sources of error) will reduce the global error in the domain. This conclusion is supported by the test case of isentropic flow past an airfoil (Chapter 3, C, Pg 79), where refinement based on the R--parameter leads to lower global error levels than a global error based refinement itself. Q: While analysing the R--parameter in Section 3.3, the operator δ2 is missing. Response: The analysis in Section 3.3 is based on Eq.(3.3) (Pg 58) which provides the local truncation error. As can be seen from Eq.(3.14), the LHS represents the discrete operator acting on the numerical solution (which is zero) and the first term on the RHS is the exact operator acting on the numerical solution (which is I[u]). Consequently the truncation terms T1 and T2 contribute to the truncation error R1 . However, from the viewpoint of computing the error estimate on a discretised domain, we need to replace the exact operator I by a higher order discrete operator δ2 . This gives the R-parameter, which has contributions from R1 as well as discretisation errors due to the higher order operator, R2 . When the latter is negligible compared to the former, the R--parameter is an estimate of the local truncation error. The truncation error depends on the accuracy of the reconstruction procedure used in obtaining the numerical solution and hence on the discrete operator δ1. On very similar lines, it can be shown that operator δ2 leads to a formal second order accuracy and this operator is only required in computing the residual error estimate. Q: What does the phrase "exact derivatives of the numerical solution" mean ? Response: This statement exemplifies the fact that the numerical solution is the exact solution to the modified partial differential equation and that the truncation terms T1 and T2 that constitute the R--parameter are functions of the derivatives of this numerical solution. Q: For the operator δ2 quadratic reconstruction is employed. Is the exact or numerical flux function used ? Response: The operator δ2 is a higher order discrete approximation to the exact operator I. Therefore, a quadratic polynomial with a three--point Gauss quadrature has been used in the error estimation procedure. Error estimation does not involve issues with convergence associated with the flow solver and therefore an exact flux function has been employed with the δ2 operator. Nevertheless, it is also possible to use the same numerical flux function as employed in the flow solver for error estimation also. Q: The same stencil of grid points is used for the solution update and the error estimation. Does this not lead to an increased stencil size ? Response: In comparison to reconstruction using higher degree polynomials such as cubic and quartic reconstruction, quadratic reconstruction involves only a smaller stencil of points consisting of the node--sharing neighbours of a cell. The use of such a support stencil is sufficient for linear reconstruction also and adds to the robustness of the flow solver, although a linear reconstruction can, in principle, work with a smaller support stencil. A possible alternative to using quadratic reconstruction (and hence a slightly larger stencil) is to adopt a Defect Correction strategy to obtain derivatives to higher order accuracy and needs to be explored in detail. Q: How is the R--parameter computed for viscous flows ? Response: The computation of the R--parameter for viscous flows is on the same lines as for inviscid flows. The gradients needed for viscous flux computation at the face centers are obtained using quadratic reconstruction. The procedure for calculation of the R--parameter for steady flows (both inviscid and viscous) is the step--by--step algorithm in Section 3.5. Q: In some cases, regions ahead of the shock show no coarsening. Response: The adaptive algorithm proposed in this work does not allow for coarsening of the initial mesh, and regions ahead of the shock remain unaffected (because of uniform flow) at all levels of refinement. Q: Do adaptation strategies terminate automatically atleast for steady flows ? Response: The adaptation strategies (RAS and HAS) must, in principle by virtue of construction of the algorithm, automatically terminate for steady flows. In the HAS algorithms though, there are certain heuristic criteria for termination of refinement especially at shocks/turbulent boundary layers. In this work, a maximum of four cycles of refinement/derefinement have only been carried out and therefore an automatic termination of the adaptive strategies were no studied. Q: How do residual--based adaptive strategies compare and contrast with adjoint--based approaches which are now becoming popular for goal--oriented adaptation ? Adjoint--based methods involve solution to the adjoint problem in addition to solving the primal problem, which represents a substantial computational cost. A timing study for a typical 3D problem[2] indicates that the solution of the adjoint problem (which needs the computation of the Jacobian and sensitivities of the functional) could require as much as one--half of the total time needed to compute the flow solution. On the contrary, R--parameter based refinement involves no additional information than that required by the flow solver and is roughly equivalent to one explicit iteration of the flow solver (Section 3.5.1). For practical 3--D applications, adjoint--based approaches will lead to a prohibitively high cost, and more so for dynamic adaptation. This is also exemplified by the fact that there has been only few recent works on 3D adaptive computations based on adjoint error estimation (which consider only inviscid flows)[1,2]. Goal--oriented adaptation involves reducing the error in some functional of interest. This can be achieved within the framework of R--parameter based adaptation, by introducing additional termination criteria based on integrated quantities. Within an automated adaptation loop, such an algorithm would terminate when the integrated quantities do not change appreciably with refinement levels. This is in contrast to the adjoint--based approach which strives to reduce the error in the functional below a certain threshold. Considering the fact that reducing the residual leads to reducing the global error itself, the R--parameter based adaptive algorithm would also lead to accurate estimates of the integrated quantities (which depend on the numerical solution). This is also reflected in the fact that the R--parameter based adaptation for the three--element NHLP configuration predicts the lift and drag coefficients to reasonable accuracy, as shown in Section 4.5.3. The author is of the belief that the R--parameter based adaptive algorithm holds huge promise for adaptive simulations of flow past complex geometries, both in terms of computational cost and solution accuracy. This is exemplified by successful adaptive simulations of inviscid flow past ONERA M6 wing as well as a conventional missile configuration[3]. A more concrete comparison of the R--parameter based and adjoint--based approaches would involve systematically solving a set of problems by both approaches and has not been considered in this thesis. [1] Nemec and Aftosmis,``Adjoint error estimation and adaptive refinement for embedded--boundary cartesian meshes", AIAA Paper 2007--4187, 2007. [2] Wintzer, Nemec and Aftosmis,``Adjoint--based adaptive mesh refinement for sonic boom prediction", AIAA Paper 2008--6593, 2008. [3] Nikhil Shende, ``A general purpose flow solver for Euler equations", Ph.D. Thesis, Dept. of Aerospace Engg., Indian Institute of Science, 2005.