Dissertations / Theses: 'High-order modeling'

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Charous, Aaron( Aaron Solomon). "High-order retractions for reduced-order modeling and uncertainty quantification." Thesis, Massachusetts Institute of Technology, 2006. https://hdl.handle.net/1721.1/130904.

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Thesis: S.M., Massachusetts Institute of Technology, Center for Computational Science & Engineering, February, 2021
Cataloged from the official PDF version of thesis.
Includes bibliographical references (pages 145-151).
Though computing power continues to grow quickly, our appetite to solve larger and larger problems grows just as fast. As a consequence, reduced-order modeling has become an essential technique in the computational scientist's toolbox. By reducing the dimensionality of a system, we are able to obtain approximate solutions to otherwise intractable problems. And because the methodology we develop is sufficiently general, we may agnostically apply it to a plethora of problems, whether the high dimensionality arises due to the sheer size of the computational domain, the fine resolution we require, or stochasticity of the dynamics. In this thesis, we develop time integration schemes, called retractions, to efficiently evolve the dynamics of a system's low-rank approximation. Through the study of differential geometry, we are able to analyze the error incurred at each time step. A novel, explicit, computationally inexpensive set of algorithms, which we call perturbative retractions, are proposed that converge to an ideal retraction that projects exactly to the manifold of fixed-rank matrices. Furthermore, each perturbative retraction itself exhibits high-order convergence to the best low-rank approximation of the full-rank solution. We show that these high-order retractions significantly reduce the numerical error incurred over time when compared to a naive Euler forward retraction. Through test cases, we demonstrate their efficacy in the cases of matrix addition, real-time data compression, and deterministic and stochastic differential equations.
by Aaron Charous.
S.M.
S.M. Massachusetts Institute of Technology, Center for Computational Science & Engineering

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Charous, Aaron (Aaron Solomon). "High-order retractions for reduced-order modeling and uncertainty quantification." Thesis, Massachusetts Institute of Technology, 2021. https://hdl.handle.net/1721.1/130904.

Full text

Abstract:

Thesis: S.M., Massachusetts Institute of Technology, Center for Computational Science & Engineering, February, 2021
Cataloged from the official PDF version of thesis.
Includes bibliographical references (pages 145-151).
Though computing power continues to grow quickly, our appetite to solve larger and larger problems grows just as fast. As a consequence, reduced-order modeling has become an essential technique in the computational scientist's toolbox. By reducing the dimensionality of a system, we are able to obtain approximate solutions to otherwise intractable problems. And because the methodology we develop is sufficiently general, we may agnostically apply it to a plethora of problems, whether the high dimensionality arises due to the sheer size of the computational domain, the fine resolution we require, or stochasticity of the dynamics. In this thesis, we develop time integration schemes, called retractions, to efficiently evolve the dynamics of a system's low-rank approximation. Through the study of differential geometry, we are able to analyze the error incurred at each time step. A novel, explicit, computationally inexpensive set of algorithms, which we call perturbative retractions, are proposed that converge to an ideal retraction that projects exactly to the manifold of fixed-rank matrices. Furthermore, each perturbative retraction itself exhibits high-order convergence to the best low-rank approximation of the full-rank solution. We show that these high-order retractions significantly reduce the numerical error incurred over time when compared to a naive Euler forward retraction. Through test cases, we demonstrate their efficacy in the cases of matrix addition, real-time data compression, and deterministic and stochastic differential equations.
by Aaron Charous.
S.M.
S.M. Massachusetts Institute of Technology, Center for Computational Science & Engineering

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3

Velechovsky, Jan. "High-order numerical methods for laser plasma modeling." Thesis, Bordeaux, 2015. http://www.theses.fr/2015BORD0098/document.

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Cette thèse présente le développement d’une méthode ALE pour la modélisation del’interaction laser–plasma. La particularité de cette méthode est l’utilisation d’une étape de projectiond’ordre élevé. Cette étape de projection consiste en une interpolation conservative des quantitésconservatives du maillage Lagrangien sur un maillage régularisé. Afin d’éviter les oscillationsnumériques non-physiques, les flux numériques d’ordre élevé sont combinés avec des fluxnumériques d’ordre moins élevé. Ces flux numériques sont obtenu en considérant les quantitésconservatives constantes par morceaux. Cette méthode pour la discrétisation cellule–centrée consisteà préserver les maximums locaux pour la densité, la vitesse et l’énergie interne. Aspects particuliersde la méthode sont appliquées pour la projection la quantité de mouvement pour la discrétisation’staggered’. Nous l’utilisons ici dans le cadre de la projection sous la forme de la méthode FluxCorrection Remapping (FCR). Dans cette thèse le volet applicatif concerne la modélisation del’interaction d’un laser énergétique avec de plasma et des matériaux microstructures. Un intérêtparticulier est porté à la modélisation de l’absorption du laser par une mousse de faible densité.L’absorption se fait à deux échelles spatiales simultanément. Ce modèle d’absorption laser à deuxéchelles est mis en oeuvre dans le code PALE hydrodynamique. Les simulations numériques de lavitesse de pénétration du laser dans une mousse à faible densité sont en bon accord avec lesdonnées expérimentales
This thesis presents the overview and the original contributions to a high–orderArbitrary Lagrangian–Eulerian (ALE) method applicable for the laser–generated plasma modeling withthe focus to a remapping step of the ALE method. The remap is the conservative interpolation of theconservative quantities from a low–quality Lagrangian grid onto a better, smoothed one. To avoidnon–physical numerical oscillations, the high–order numerical fluxes of the reconstruction arecombined with the low–order (first–order) numerical fluxes produced by a standard donor remappingmethod. The proposed method for a cell–centered discretization preserves bounds for the density,velocity and specific internal energy by its construction. Particular symmetry–preserving aspects of themethod are applied for a staggered momentum remap. The application part of the thesis is devoted tothe laser radiation absorption modeling in plasmas and microstructures materials with the particularinterest in the laser absorption in low–density foams. The absorption is modeled on two spatial scalessimultaneously. This two–scale laser absorption model is implemented in the hydrodynamic codePALE. The numerical simulations of the velocity of laser penetration in a low–density foam are in agood agreement with the experimental data

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Heidkamp, Holger [Verfasser]. "Modeling Localization and Failure with High-Order Finite Elements / Holger Heidkamp." Aachen : Shaker, 2008. http://d-nb.info/1164341642/34.

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Beisiegel, Nicole [Verfasser], and Jörn [Akademischer Betreuer] Behrens. "High-order Adaptive Discontinuous Galerkin Inundation Modeling / Nicole Beisiegel. Betreuer: Jörn Behrens." Hamburg : Staats- und Universitätsbibliothek Hamburg, 2014. http://d-nb.info/1060484749/34.

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Beisiegel, Nicole Verfasser], and Jörn [Akademischer Betreuer] [Behrens. "High-order Adaptive Discontinuous Galerkin Inundation Modeling / Nicole Beisiegel. Betreuer: Jörn Behrens." Hamburg : Staats- und Universitätsbibliothek Hamburg, 2014. http://nbn-resolving.de/urn:nbn:de:gbv:18-70360.

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Tong, Oisin. "Development of a Three-Dimensional High-Order Strand-Grids Approach." DigitalCommons@USU, 2016. https://digitalcommons.usu.edu/etd/4711.

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Development of a novel high-order flux correction method on strand grids is presented. The method uses a combination of flux correction in the unstructured plane and summation-by-parts operators in the strand direction to achieve high-fidelity solutions. Low-order truncation errors are cancelled with accurate flux and solution gradients in the flux correction method, thereby achieving a formal order of accuracy of 3, although higher orders are often obtained, especially for highly viscous flows. In this work, the scheme is extended to high-Reynolds number computations in both two and three dimensions. Turbulence closure is achieved with a robust version of the Spalart-Allmaras turbulence model that accommodates negative values of the turbulence working variable, and the Menter SST turbulence model, which blends the k-ε and k-ω turbulence models for better accuracy. A major advantage of this high-order formulation is the ability to implement traditional finite volume-like limiters to cleanly capture shocked and discontinuous flow. In this work, this approach is explored via a symmetric limited positive (SLIP) limiter. Extensive verification and validation is conducted in two and three dimensions to determine the accuracy and fidelity of the scheme for a number of different cases. Verification studies show that the scheme achieves better than third order accuracy for low and high-Reynolds number flow. Cost studies show that in three-dimensions, the third-order flux correction scheme requires only 30% more walltime than a traditional second-order scheme on strand grids to achieve the same level of convergence. In order to overcome meshing issues at sharp corners and other small-scale features, a unique approach to traditional geometry, coined "asymptotic geometry," is explored. Asymptotic geometry is achieved by filtering out small-scale features in a level set domain through min/max flow. This approach is combined with a curvature based strand shortening strategy in order to qualitatively improve strand grid mesh quality.

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Ye, Fei. "Developing Efficient High-Order Transport Schemes for Cross-Scale Coupled Estuary-Ocean Modeling." W&M ScholarWorks, 2017. https://scholarworks.wm.edu/etd/1516639591.

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Geophysical fluid dynamics (GFD) models have progressed greatly in simulating the world’s oceans and estuaries in the past three decades, thanks to the development of novel numerical algorithms and the advent of massively parallel high-performance computing platforms. Study of inter-related processes on multi-scales (e.g., between large-scale (remote) processes and small-scale (local) processes) has always been an important theme for GFD modeling. For this purpose, models based on unstructured-grid (UG) have shown great potential because of their superior abilities in enabling multi-resolution and in fitting geometry and boundary. Despite UG models’ successful applications on coastal systems, significant obstacles still exist that have so far prevented UG models from realizing their full cross-scale capability. The pressing issues include the computation overhead resulting from large contrasts in the spatial resolutions, and the relative lack of skill for UG model in the eddying regime. Specifically for our own implicit UG model (SCHISM), the transport solver often emerges as a major bottleneck for both accuracy and efficiency. The overall goal of this dissertation is two-fold. The first goal is to address the challenges in tracer transport by developing efficient high-order schemes for the transport processes and test them in the framework of a community supported modeling system (SCHISM: Semi-implicit Cross-scale Hydroscience Integrated System Model) for cross-scale processes. The second goal is to utilize the new schemes developed in this dissertation and elsewhere to build a bona fide cross-scale Chesapeake Bay model and use it to address some key knowledge gaps in the physical processes in this system and to better assist decision makers of coastal resource management. The work on numerical scheme development has resulted in two new high-order transport solvers. The first solver tackles the vertical transport that often imposes the most stringent constraint on model efficiency (Chapter 2). With an implicit method and two flux limiters in both space and time, the new TVD2 solver leads to a speed-up of 1.6-6.0 in various cross-scale applications as compared to traditional explicit methods, while achieving 2nd-order accuracy in both space and time. Together with a flexible vertical gridding system, the flow over steep slopes can be faithfully simulated efficiently and accurately without altering the underlying bathymetry. The second scheme aims at improving the model skill in the eddying ocean (Chapter 4). UG coastal models tend to under-resolve features like meso-scale eddies and meanders, and this issue is partially attributed to the numerical diffusion in the transport schemes that are originally developed for estuarine applications. to address this issue, a 3rd-order transport scheme based on WENO formulation is developed, and is demonstrated to improve the meso-scale features. The new solvers are then tested in the Chesapeake Bay and adjacent Atlantic Ocean on small, medium and large domains respectively, corresponding to the three main chapters of this dissertation (Chapter 2-4), with an ultimate goal of achieving a seamless cross-scale model from the Gulf Stream to the shallow regions in the Bay tributaries and sub-tributaries. We highlight the dominant role played by the bathymetry in nearshore systems and the detrimental effects of bathymetric smoothing commonly used in many coastal models (Chapter 3). With the new methods developed in this dissertation and elsewhere, the model has enabled the analyses on some important processes that are hard to quantify with traditional techniques, e.g., the effect of channel-shoal contrast on lateral circulation and salinity distribution, hypoxia volume, the influence of realistic bathymetry on the freshwater plume etc. Potential topics for future research are also discussed at the end. In addition, the new solvers have also been successfully exported to many other oceanic and nearshore systems around the world via user groups of our community modeling system (cf. ‘Publications’ under ‘schism.wiki’).

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Collins, Justin A. Valentine Jerry. "Higher-order thinking in the high-stakes accountability era linking student engagement and test performance /." Diss., Columbia, Mo. : University of Missouri-Columbia, 2009. http://hdl.handle.net/10355/6769.

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The entire thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file; a non-technical public abstract appears in the public.pdf file. Title from PDF of title page (University of Missouri--Columbia, viewed on March 25, 2010). Thesis advisor: Dr. Jerry W. Valentine. Vita. Includes bibliographical references.

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Powers, Sean W. "Analysis of Stresses in Metal Sheathed Thermocouples in High-Temperature, Hypersonic Flows." Thesis, Virginia Tech, 2020. http://hdl.handle.net/10919/98000.

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Flow temperature sensing remains important for many hypersonic aerodynamics and propulsion applications. Flight test applications, in particular, demand robust and accurate sensing, making thermocouple sensors attractive. Even for these extremely well-developed sensors, the prediction of stresses (hoop, radial, and axial) within thermocouple sheaths for custom-configured probes remains a topic of great concern for ensuring adequate lifetime of sensors. In contemporary practice, high-fidelity simulations must be run to prove if a new design will work at all, albeit at significant time and expense. Given the time and money it takes to run high-fidelity simulations, rapid optimization of sensor configurations is often impossible, or at a minimum, impractical. The developments presented in this Thesis address the need for hypersonic flow temperature sensor structural predictions which are compatible with rapid design iteration. The derivation and implementation of a new analytical, low-order model to predict stresses (hoop, radial, and axial) within the sheath of a thermocouple are provided. The analytical model is compared to high-fidelity ANSYS mechanical simulations as well as simplified experimental data. The predictions using the newly developed structural low-order model are in excellent agreement with the numerically simulated results and experimental results with an absolute maximum percent error of approximately 4% and 9.5%, respectively, thus validating the model. A MATLAB GUI composed of the combination of a thermal low-order model outlined in additional references [1] through [6] and the new structural low-order model for thermocouples was developed. This code is capable of solving a highly generalized version of the 1-D pin fin equation, allowing for the solution of the temperature distribution in a sensor taking into account conduction, convection, and radiation heat transfer which is not possible with other existing analytical solutions. This temperature distribution is then used in the analytical structural low-order model. This combination allows for the thermal and structural performance of a thermocouple to be found analytically and compared quickly with other designs.
M.S.
Thermocouples are a device for measuring temperature, consisting of two wires of different metals connected at two different points. This configuration produces a temperature-dependent voltage as a result of the thermoelectric effect. Preexisting curves are used to relate the voltage to temperature. Thermocouples are extensively used in high-temperature high-stress environments such as in rockets, jet engines, or any high-corrosive environment. Accurately predicting the stresses within the sheath of a metal-clad thermocouple in extreme conditions is required for many research areas including hypersonic aerodynamics and various propulsion applications. Even for these extremely well-developed and widely used sensors, the accurate prediction of stresses within the metal sheath remains a topic of great concern for ensuring the sensor’s survivability in these extreme conditions. Current engineering practice is to use high-fidelity numerical simulations (Finite Element Analysis) to predict the stresses within the sheath. Perhaps the biggest drawback to this approach is the time it takes to model, mesh, and set-up these simulations. Comparative studies between different designs using numerical simulations are almost impossible due to the time requirement. This Thesis will present an analytically derived quasi-3D solution to find the stresses within the sheath. These equations were implemented into a low-order model that can handle varying temperature, geometry, and material inputs. This model was validated against both high-fidelity numerical simulations (ANSYS Mechanical) and a simplified experiment. The predictions using this newly developed structural low-order model are in excellent agreement with the numerically simulated results and experimental results.

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Cohan, Daniel Shepherd. "Photochemical Formation and Cost-Efficient Abatement of Ozone: High-Order Sensitivity Analysis." Diss., Available online, Georgia Institute of Technology, 2004:, 2004. http://etd.gatech.edu/theses/available/etd-09152004-150617/unrestricted/cohan%5Fdaniel%5Fs%5F200412%5Fphd.pdf.

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Thesis (Ph. D.)--Earth and Atmospheric Sciences, Georgia Institute of Technology, 2005.
Russell, Armistead G., Committee Chair ; Chameides, William L., Committee Member ; Wang, Yuhang, Committee Member ; Noonan, Douglas, Committee Member ; Chang, Michael E., Committee Member. Vita. Includes bibliographical references.

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Rambo, Jeffrey D. "Reduced-Order Modeling of Multiscale Turbulent Convection: Application to Data Center Thermal Management." Diss., Available online, Georgia Institute of Technology, 2006, 2006. http://etd.gatech.edu/theses/available/etd-03272006-080024/.

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Thesis (Ph. D.)--Mechanical Engineering, Georgia Institute of Technology, 2006.
Marc Smith, Committee Member ; P.K. Yeung, Committee Member ; Benjamin Shapiro, Committee Member ; Sheldon Jeter, Committee Member ; Yogendra Joshi, Committee Chair.

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Gopalan, Harish. "Numerical Modeling of Aerodynamics of Airfoils of Micro Air Vehicles in Gusty Environment." University of Akron / OhioLINK, 2008. http://rave.ohiolink.edu/etdc/view?acc_num=akron1221497568.

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Pasha, Soheila. "Electromagnetic Modeling of High-Speed Interconnects with Frequency Dependent Conductor Losses, Compatible with Passive Model Order Reduction Techniques." Diss., The University of Arizona, 2012. http://hdl.handle.net/10150/268354.

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A computationally efficient, discrete model is presented for transmission line analysis and passive model order reduction of high-speed interconnect systems. The development of this model was motivated by the on-going efforts in chip/package co-design to route a major portion of the on-chip clock and high-speed data buses through the package in order to overcome the bandwidth reduction and delay caused by the high ohmic loss of on-chip wiring. The geometric complexity of the resulting interconnections is such that model order reduction is essential for rapid and accurate signal integrity assessment to support pre-layout design iteration and optimization. The modal network theory of the skin effect in conjunction with the theory of compact differences is used for the development of discrete models for dispersive, multi-conductor interconnects compatible with passive model order reduction algorithms. The passive reduced-order interconnect modeling algorithm, PRIMA, is then used on the resulting discrete model to generate a low-order, multi-port macromodel for interconnect networks. Numerical examples are used to demonstrate the validity and efficiency of the proposed model.

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Torberntsson, Kim, and Vidar Stiernström. "A High Order Finite Difference Method for Simulating Earthquake Sequences in a Poroelastic Medium." Thesis, Uppsala universitet, Avdelningen för beräkningsvetenskap, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-298414.

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Induced seismicity (earthquakes caused by injection or extraction of fluids in Earth's subsurface) is a major, new hazard in the United States, the Netherlands, and other countries, with vast economic consequences if not properly managed. Addressing this problem requires development of predictive simulations of how fluid-saturated solids containing frictional faults respond to fluid injection/extraction. Here we present a numerical method for linear poroelasticity with rate-and-state friction faults. A numerical method for approximating the fully coupled linear poroelastic equations is derived using the summation-by-parts-simultaneous-approximation-term (SBP-SAT) framework. Well-posedness is shown for a set of physical boundary conditions in 1D and in 2D. The SBP-SAT technique is used to discretize the governing equations and show semi-discrete stability and the correctness of the implementation is verified by rigorous convergence tests using the method of manufactured solutions, which shows that the expected convergence rates are obtained for a problem with spatially variable material parameters. Mandel's problem and a line source problem are studied, where simulation results and convergence studies show satisfactory numerical properties. Furthermore, two problem setups involving fault dynamics and slip on faults triggered by fluid injection are studied, where the simulation results show that fluid injection can trigger earthquakes, having implications for induced seismicity. In addition, the results show that the scheme used for solving the fully coupled problem, captures dynamics that would not be seen in an uncoupled model. Future improvements involve imposing Dirichlet boundary conditions using a different technique, extending the scheme to handle curvilinear coordinates and three spatial dimensions, as well as improving the high-performance code and extending the study of the fault dynamics.

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Rodríguez, Fernández Jhan Ignacio [Verfasser], and András [Akademischer Betreuer] Bárdossy. "High order interactions among environmental variables : diagnostics and initial steps towards modeling / Jhan Ignacio Rodríguez Fernández. Betreuer: András Bárdossy." Stuttgart : Universitätsbibliothek der Universität Stuttgart, 2014. http://d-nb.info/1046564404/34.

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Laurent, Charlelie. "Low-order modeling and high-fidelity simulations for the prediction of combustion instabilities in liquid rocket engines and gas turbines." Thesis, Toulouse, INPT, 2020. http://www.theses.fr/2020INPT0038.

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Au cours des dernières décennies, les instabilités de combustion ont constitué un important défi pour de nombreux projets industriels, en particulier dans la conception de moteurs-fusées à ergols liquide et de turbines à gaz. L'atténuation de leurs effets nécessite une solide compréhension scientifique de l'interaction complexe entre la dynamique de flamme et les ondes acoustiques qu'elles impliquent. Au cours de cette thèse, plusieurs directions ont été explorées pour fournir une meilleure compréhension de la dynamique des flammes dans les moteurs-fusées cryogéniques, ainsi que des méthodes numériques plus efficaces et robustes pour la prédiction des instabilités thermoacoustiques dans les chambres de combustion à géométries complexes. La première facette de ce travail a consisté en la résolution de modes thermoacoustiques dans les chambres de combustion complexes comportant à injecteurs multiples, une tâche qui nécessite souvent des simplifications pour être abordable en termes de coût de calcul. Ces hypothèses physiques nécessaires ont conduit à la popularité croissante des modèles bas-ordre acoustiques, parmi lesquels ceux utilisant l'expansion de Galerkin ont démontré une efficacité prometteuse tout en conservant une précision satisfaisante. Ceux-ci sont cependant limités à des géométries simples qui n'intègrent pas les caractéristiques complexes des systèmes industriels. Une grande partie de ce travail a donc consisté tout d'abord à identifier clairement les limitations mathématiques de l'expansion classique de Galerkin, puis à concevoir un nouveau type d'expansion modale, appelé expansion sur frame, qui ne souffre pas des mêmes restrictions. En particulier, l'expansion sur frame est capable de représenter avec précision le champ de vitesse acoustique près des parois de la chambre de combustion autres que des murs rigides, une capacité cruciale qui manque à la méthode Galerkin. Dans ce travail, le concept d'expansion modale de surface a également été introduit pour modéliser des frontières topologiquement complexes, comme les plaques multi-perforées rencontrées dans les turbines à gaz. Ces nouvelles méthodes numériques ont été combinées avec le formalisme state-space pour construire des réseaux acoustiques de systèmes complexes. Le modèle obtenu a été implémenté dans le code STORM (State-space Thermoacoustic low-ORder Model), qui permet la modélisation bas-ordre des instabilités thermoacoustiques dans des géométries arbitrairement complexes. Le deuxième ingrédient de la prédiction des instabilités thermoacoustiques est la modélisation de la dynamique de flamme. Ce travail a traité de ce point, dans le cas spécifique d'une flamme-jet cryogénique caractéristique d'un moteur-fusée à ergols liquides. Les phénomènes contrôlant la dynamique de flamme ont été identifiés grâce à des Simulations aux Grandes Échelles (SGE) du banc d'essai expérimental Mascotte, où les deux réactifs (CH4 et O2) sont injectés dans des conditions transcritiques. Une première simulation donne un aperçu détaillé de la dynamique intrinsèque de la flamme. Plusieurs SGE avec modulation harmonique de l'injection de carburant, à différentes fréquences et amplitudes, ont été effectués afin d'évaluer la réponse de la flamme aux oscillations acoustiques et de calculer une Fonction de Transfert de Flamme (FTF). La réponse non-linéaire de la flamme, notamment les interactions entre les oscillations intrinsèques et forcées, a également été étudiée. Enfin, la stabilisation de cette flamme dans la région proche de l'injecteur, qui est d'une importance primordiale sur la dynamique globale de la flamme, a été étudiée grâce à une simulation directe multi-physique, où un problème couplé de transfert de chaleur est résolu au niveau de la lèvre de l'injecteur
Over the last decades, combustion instabilities have been a major concern for a number of industrial projects, especially in the design of Liquid Rocket Engines (LREs) and gas turbines. Mitigating their effects requires a solid scientific understanding of the intricate interplay between flame dynamics and acoustic waves that they involve. During this PhD work, several directions were explored to provide a better comprehension of flame dynamics in cryogenic rocket engines, as well as more efficient and robust numerical methods for the prediction of thermoacoustic instabilities in complex combustors. The first facet of this work consisted in the resolution of unstable thermoacoustic modes in complex multi-injectors combustors, a task that often requires a number of simplifications to be computationally affordable. These necessary physics-based assumptions led to the growing popularity of acoustic Low-Order Models (LOMs), among which Galerkin expansion LOMs have displayed a promising efficiency while retaining a satisfactory accuracy. Those are however limited to simple geometries that do not incorporate the complex features of industrial systems. A major part of this work therefore consisted first in clearly identifying the mathematical limitations of the classical Galerkin expansion, and then in designing a novel type of modal expansion, named a frame expansion, that does not suffer from the same restrictions. In particular, the frame expansion is able to accurately represent the acoustic velocity field, near non-rigid-wall boundaries of the combustor, a crucial ability that the Galerkin method lacks. In this work, the concept of surface modal expansion is also introduced to model topologically complex boundaries, such as multi-perforated liners encountered in gas turbines. These novel numerical methods were combined with the state-space formalism to build acoustic networks of complex systems. The resulting LOM framework was implemented in the code STORM (State-space Thermoacoustic low-ORder Model), which enables the low-order modeling of thermoacoustic instabilities in arbitrarily complex geometries. The second ingredient in the prediction of thermoacoustic instabilities is the flame dynamics modeling. This work dealt with this problem, in the specific case of a cryogenic coaxial jet-flame characteristic of a LRE. Flame dynamics driving phenomena were identified thanks to three-dimensional Large Eddy Simulations (LES) of the Mascotte experimental test rig where both reactants (CH4 and O2) are injected in transcritical conditions. A first simulation provides a detailed insight into the flame intrinsic dynamics. Several LES with harmonic modulation of the fuel inflow at various frequencies and amplitudes were performed in order to evaluate the flame response to acoustic oscillations and compute a Flame Transfer Function (FTF). The flame nonlinear response, including interactions between intrinsic and forced oscillations, were also investigated. Finally, the stabilization of this flame in the near-injector region, which is of primary importance on the overall flame dynamics, was investigated thanks to muulti-physics two-dimensional Direct Numerical Simulations (DNS), where a conjugate heat transfer problem is resolved at the injector lip

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Crowell, Andrew R. "Model Reduction of Computational Aerothermodynamics for Multi-Discipline Analysis in High Speed Flows." The Ohio State University, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=osu1366204830.

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Dreyer, Emily Rose. "Assessment of Reduced Fidelity Modeling of a Maneuvering Hypersonic Vehicle." The Ohio State University, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=osu1610018486409227.

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20

Zhang, Wenxian. "Direct sensitivity techniques in regional air quality models: development and application." Diss., Georgia Institute of Technology, 2013. http://hdl.handle.net/1853/52941.

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Sensitivity analysis based on a chemical transport model (CTM) serves as an important approach towards better understanding the relationship between trace contaminant levels in the atmosphere and emissions, chemical and physical processes. Previous studies on ozone control identified the high-order Decoupled Direct Method (HDDM) as an efficient tool to conduct sensitivity analysis. Given the growing recognition of the adverse health effects of fine particulate matter (i.e., particles with an aerodynamic diameter less than 2.5 micrometers (PM2.5)), this dissertation presents the development of a HDDM sensitivity technique for particulate matter and its implementation it in a widely used CTM, CMAQ. Compared to previous studies, two new features of the implementation are 1) including sensitivities of aerosol water content and activity coefficients, and 2) tracking the chemical regimes of the embedded thermodynamic model. The new features provide more accurate sensitivities especially for nitrate and ammonium. Results compare well with brute force sensitivities and are shown to be more stable and computationally efficient. Next, this dissertation explores the applications of HDDM. Source apportionment analysis for the Houston region in September 2006 indicates that nonlinear responses accounted for 3.5% to 33.7% of daily average PM2.5, and that PM2.5 formed rapidly during night especially in the presence of abundant ozone and under stagnant conditions. Uncertainty analysis based on the HDDM found that on average, uncertainties in the emissions rates led to 36% uncertainty in simulated daily average PM2.5 and could explain much, but not all, of the difference between simulated and observed PM2.5 concentrations at two observations sites. HDDM is then applied to assess the impact of flare VOC emissions with temporally variable combustion efficiency. Detailed study of flare emissions using the 2006 Texas special inventory indicates that daily maximum 8-hour ozone at a monitoring site can increase by 2.9 ppb when combustion is significantly decreased. The last application in this dissertation integrates the reduced form model into an electricity generation planning model, and enables representation of geospatial dependence of air quality-related health costs in the optimization process to seek the least cost planning for power generation. The integrated model can provide useful advice on selecting fuel types and locations for power plants.

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Ruan, Kangping. "NUMERICAL AND EXPERIMENTAL TECHNIQUES FOR ASSESSING THE ACOUSTIC PERFORMANCE OF DUCT SYSTEMS ABOVE THE PLANE WAVE CUTOFF FREQUENCY." UKnowledge, 2018. https://uknowledge.uky.edu/me_etds/120.

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This research deals with determining the acoustic attenuation of heating, ventilation, and air conditioning (HVAC) ductwork. A finite element approach was developed for calculating insertion loss and breakout transmission loss. Procedures for simulating the source and receiving rooms were developed and the effect of structureborne flanking was included. Simulation results have been compared with measurements from the literature and the agreement is very good. With a good model in place, the work was extended in three ways. 1) Since measurements on full-scale equipment are difficult, scale modeling rules were developed and validated. 2) Two different numerical approaches were developed for evaluating the transmission loss of silencers taking into account the effect of higher order modes. 3) A power transfer matrix approach was developed to assess the acoustic performance of several duct components connected in series.

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Moglan, Raluca. "Modeling and numerical simulation of flow and heat phenomena in a telecommunication heat cabinet." Rouen, 2013. http://www.theses.fr/2013ROUES060.

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Nous proposons dans cette étude une nouvelle approche 3D pour la résolution des équations de Navier-Stokes incompressibles sous l’approximation de Boussinesq. La nouveauté du code développé est l’utilisation des méthodes d’ordre élevé pour l’intégration en temps (schéma de Runge-Kutta à l’ordre trois) et pour la discrétisation spatiale (schéma aux différences finies à l’ordre six). Une étude de l’ordre de la méthode numérique a été faite, suivie par une validation détaillée pour plusieurs cas de convection naturelle. Une méthode d’éléments finis été développée pour le même problème, codée avec FreeFem++, et validée pour les mêmes cas de convection naturelle. Nous avons considéré ensuite le cas d’une armoire de télécommunications, modélisée sous la forme d’un domaine rectangulaire, avec des objets (obstacles) intérieurs, représentés par une méthode de type frontière immergée. Cette méthode a été validée par rapport aux cas existants dans la littérature et par rapport aux résultats obtenus avec le code éléments finis (qui représente exactement les obstacles). Nous présentons des résultats pour plusieurs configurations, avec des obstacles chauffants placés différemment à l’intérieur de la cavité. Une comparaison avec les mesures expérimentales effectuées dans une armoire avec deux composantes dissipant de la chaleur est aussi effectuée. Le code de type éléments finis est finalement développé et testé pour simuler des matériaux à changement de phase
In this thesis we present a new 3D approach for solving the incompressible Navier-Stokes equations under the Boussinesq approximation. The advantage of the developed numerical code is the use of high order methods for time integration (3rd order Runge-Kutta method) and spatial discretization (6th order finite difference schemes). A study of the order of the numerical method was made, followed by an extensive validation for several cases of natural convection. A finite element simulation code for the same problem was developed using FreeFem++, and was validated with respect to the same cases of natural convection. The case of a telecommunication cabinet was treated by modelling interior obstacles generating heat using an immersed boundary method. This method was validated with respect to the finite element simulation, and many other cases from the literature. We present the results for different 2D and 3D configurations, with obstacles differently placed inside the cavity. Results are also presented for the comparison with experimental measurements in a cabinet with two components dissipating heat. The finite element code is finally extended and tested to simulate phase change materials that could serve as passive cooling devices

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Ferrer, Esteban. "A high order Discontinuous Galerkin - Fourier incompressible 3D Navier-Stokes solver with rotating sliding meshes for simulating cross-flow turbines." Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:db8fe6e3-25d0-4f6a-be1b-6cde7832296d.

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This thesis details the development, verification and validation of an unsteady unstructured high order (≥ 3) h/p Discontinuous Galerkin - Fourier solver for the incompressible Navier-Stokes equations on static and rotating meshes in two and three dimensions. This general purpose solver is used to provide insight into cross-flow (wind or tidal) turbine physical phenomena. Simulation of this type of turbine for renewable energy generation needs to account for the rotational motion of the blades with respect to the fixed environment. This rotational motion implies azimuthal changes in blade aero/hydro-dynamics that result in complex flow phenomena such as stalled flows, vortex shedding and blade-vortex interactions. Simulation of these flow features necessitates the use of a high order code exhibiting low numerical errors. This thesis presents the development of such a high order solver, which has been conceived and implemented from scratch by the author during his doctoral work. To account for the relative mesh motion, the incompressible Navier-Stokes equations are written in arbitrary Lagrangian-Eulerian form and a non-conformal Discontinuous Galerkin (DG) formulation (i.e. Symmetric Interior Penalty Galerkin) is used for spatial discretisation. The DG method, together with a novel sliding mesh technique, allows direct linking of rotating and static meshes through the numerical fluxes. This technique shows spectral accuracy and no degradation of temporal convergence rates if rotational motion is applied to a region of the mesh. In addition, analytical mappings are introduced to account for curved external boundaries representing circular shapes and NACA foils. To simulate 3D flows, the 2D DG solver is parallelised and extended using Fourier series. This extension allows for laminar and turbulent regimes to be simulated through Direct Numerical Simulation and Large Eddy Simulation (LES) type approaches. Two LES methodologies are proposed. Various 2D and 3D cases are presented for laminar and turbulent regimes. Among others, solutions for: Stokes flows, the Taylor vortex problem, flows around square and circular cylinders, flows around static and rotating NACA foils and flows through rotating cross-flow turbines, are presented.

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Legrand, Nicolas. "Numerical and modeling methods for multi-level large eddy simulations of turbulent flows in complex geometries." Thesis, Normandie, 2017. http://www.theses.fr/2017NORMIR16/document.

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La simulation aux grandes échelles est devenue un outil d’analyse incontournable pour l’étude des écoulements turbulents dans des géométries complexes. Cependant, à cause de l’augmentation constante des ressources de calcul, le traitement des grandes quantités de données générées par les simulations hautement résolues est devenu un véritable défi qu’il n’est plus possible de relever avec des outils traditionnels. En mécanique des fluides numérique, cette problématique émergente soulève les mêmes questions que celles communément rencontrées en informatique avec des données massives. A ce sujet, certaines méthodes ont déjà été développées telles que le partitionnement et l’ordonnancement des données ou bien encore le traitement en parallèle mais restent insuffisantes pour les simulations numériques modernes. Ainsi, l’objectif de cette thèse est de proposer de nouveaux formalismes permettant de contourner le problème de volume de données en vue des futurs calculs exaflopiques que l’informatique devrait atteindre en 2020. A cette fin, une méthode massivement parallèle de co-traitement, adaptée au formalisme non-structuré, a été développée afin d’extraire les grandes structures des écoulements turbulents. Son principe consiste à introduire une série de grilles de plus en plus grossières réduisant ainsi la quantité de données à traiter tout en gardant intactes les structures cohérentes d’intérêt. Les données sont transférées d’une grille à une autre grâce à l’utilisation de filtres et de méthodes d’interpolation d’ordre élevé. L’efficacité de cette méthodologie a pu être démontrée en appliquant des techniques de décomposition modale lors de la simulation 3D d’une pale de turbine turbulente sur une grille de plusieurs milliards d’éléments. En outre, cette capacité à pouvoir gérer plusieurs niveaux de grilles au sein d’une simulation a été utilisée par la suite pour la mise en place de calculs basés sur une stratégie multi-niveaux. L’objectif de cette méthode est d’évaluer au cours du calcul les erreurs numériques et celles liées à la modélisation en simulant simultanément la même configuration pour deux résolutions différentes. Cette estimation de l’erreur est précieuse car elle permet de générer des grilles optimisées à travers la construction d’une mesure objective de la qualité des grilles. Ainsi, cette méthodologie de multi-résolution tente de limiter le coût de calcul de la simulation en minimisant les erreurs de modélisation en sous-maille, et a été appliquée avec succès à la simulation d’un écoulement turbulent autour d’un cylindre
Large-Eddy Simulation (LES) has become a major tool for the analysis of highly turbulent flows in complex geometries. However, due to the steadily increase of computational resources, the amount of data generated by well-resolved numerical simulations is such that it has become very challenging to manage them with traditional data processing tools. In Computational Fluid Dynamics (CFD), this emerging problematic leads to the same "Big Data" challenges as in the computer science field. Some techniques have already been developed such as data partitioning and ordering or parallel processing but still remain insufficient for modern numerical simulations. Hence, the objective of this work is to propose new processing formalisms to circumvent the data volume issue for the future 2020 exa-scale computing objectives. To this aim, a massively parallel co-processing method, suited for complex geometries, was developed in order to extract large-scale features in turbulent flows. The principle of the method is to introduce a series of coarser nested grids to reduce the amount of data while keeping the large scales of interest. Data is transferred from one grid level to another using high-order filters and accurate interpolation techniques. This method enabled to apply modal decomposition techniques to a billion-cell LES of a 3D turbulent turbine blade, thus demonstrating its effectiveness. The capability of performing calculations on several embedded grid levels was then used to devise the multi-resolution LES (MR-LES). The aim of the method is to evaluate the modeling and numerical errors during an LES by conducting the same simulation on two different mesh resolutions, simultaneously. This error estimation is highly valuable as it allows to generate optimal grids through the building of an objective grid quality measure. MR-LES intents to limit the computational cost of the simulation while minimizing the sub-grid scale modeling errors. This novel framework was applied successfully to the simulation of a turbulent flow around a 3D cylinder

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Ueckermann, Mattheus Percy. "High order hybrid discontinuous Galerkin regional ocean modelling." Thesis, Massachusetts Institute of Technology, 2014. http://hdl.handle.net/1721.1/87984.

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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mechanical Engineering, 2014.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 343-357).
Accurate modeling of physical and biogeochemical dynamics in coastal ocean regions is required for multiple scientific and societal applications, covering a wide range of time and space scales. However, in light of the strong nonlinearities observed in coastal regions and in biological processes, such modeling is challenging. An important subject that has been largely overlooked is the numerical requirements for regional ocean simulation studies. Major objectives of this thesis are to address such computational questions for non-hydrostatic multiscale flows and for biogeochemical interactions, and to derive and develop numerical schemes that meet these requirements, utilizing the latest advances in computational fluid dynamics. We are interested in studying nonlinear, transient, and multiscale ocean dynamics over complex geometries with steep bathymetry and intricate coastlines, from sub-mesoscales to basin-scales. These dynamical interests, when combined with our requirements for accurate, efficient and flexible ocean modeling, led us to develop new variable resolution, higher-order and non-hydrostatic ocean modeling schemes. Specifically, we derived, developed and applied new numerical schemes based on the novel hybrid discontinuous Galerkin (HDG) method in combination with projection methods. The new numerical schemes are first derived for the Navier-Stokes equations. To ensure mass conservation, we define numerical fluxes that are consistent with the discrete divergence equation. To improve stability and accuracy, we derive a consistent HDG stability parameter for the pressure-correction equation. We also apply a new boundary condition for the pressure-corrector, and show the form and origin of the projection method's time-splitting error for a case with implicit diffusion and explicit advection. Our scheme is implemented for arbitrary, mixed-element unstructured grids using a novel quadrature-free integration method for a nodal basis, which is consistent with the HDG method. To prevent numerical oscillations, we design a selective high-order nodal limiter. We demonstrate the correctness of our new schemes using a tracer advection benchmark, a manufactured solution for the steady diffusion and stokes equations, and the 2D lock-exchange problem. These numerical schemes are then extended for non-hydrostatic, free-surface, variable-density regional ocean dynamics. The time-splitting procedure using projection methods is derived for non-hydrostatic or hydrostatic, and nonlinear free-surface or rigid-lid, versions of the model. We also derive consistent HDG stability parameters for the free-surface and non-hydrostatic pressure-corrector equations to ensure stability and accuracy. New boundary conditions for the free-surface-corrector and pressure-corrector are also introduced. We prove that these conditions lead to consistent boundary conditions for the free-surface and pressure proper. To ensure discrete mass conservation with a moving free-surface, we use an arbitrary Lagrangian- Eulerian (ALE) moving mesh algorithm. These schemes are again verified, this time using a tidal flow problem with analytical solutions and a 3D lock-exchange benchmark. We apply our new numerical schemes to evaluate the numerical requirements of the coupled biological-physical dynamics. We find that higher-order schemes are more accurate at the same efficiency compared to lower-order (e.g. second-order) accurate schemes when modeling a biological patch. Due to decreased numerical dissipation, the higher-order schemes are capable of modeling biological patchiness over a sustained duration, while the lower-order schemes can lose significant biomass after a few non-dimensional times and can thus solve erroneous nonlinear dynamics. Finally, inspired by Stellwagen Bank in Massachusetts Bay, we study the effect of non-hydrostatic physics on biological productivity and phytoplankton fields for tidally-driven flows over an idealized bank. We find that the non-hydrostatic pressure and flows are important for biological dynamics, especially when flows are supercritical. That is, when the slope of the topography is larger than the slope of internal wave rays at the tidal frequency. The non-hydrostatic effects increase with increasing nonlinearity, both when the internal Froude number and criticality parameter increase. Even in cases where the instantaneous biological productivity is not largely modified, we find that the total biomass, spatial variability and patchiness of phytoplankton can be significantly altered by non-hydrostatic processes. Our ultimate dynamics motivation is to allow quantitative simulation studies of fundamental nonlinear biological-physical dynamics in coastal regions with complex bathymetric features such as straits, sills, ridges and shelfbreaks. This thesis develops the necessary numerical schemes that meet the stringent accuracy requirements for these types of flows and dynamics.
by Mattheus Percy Ueckermann.
Ph. D.

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Schmidt, Kersten. "High-order numerical modelling of highly conductive thin sheets /." Zürich : ETH, 2008. http://e-collection.ethbib.ethz.ch/show?type=diss&nr=17903.

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Mifsud, Michael. "Reduced-order modelling for high-speed aerial weapon aerodynamics." Thesis, Cranfield University, 2008. http://hdl.handle.net/1826/3511.

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In this work a high-fidelity low-cost surrogate of a computational fluid dynamics analysis tool was developed. This computational tool is composed of general and physics- based approximation methods by which three dimensional high-speed aerodynamic flow- field predictions are made with high efficiency and an accuracy which is comparable with that of CFD. The tool makes use of reduced-basis methods that are suitable for both linear and non-linear problems, whereby the basis vectors are computed via the proper orthogonal decomposition (POD) of a training dataset or a set of observations. The surrogate model was applied to two flow problems related to high-speed weapon aerodynamics. Comparisons of surrogate model predictions with high-fidelity CFD simulations suggest that POD-based reduced-order modelling together with response surface methods provide a reliable and robust approach for efficient and accurate predictions. In contrast to the many modelling efforts reported in the literature, this surrogate model provides access to information about the whole flow-field. In an attempt to reduce the up-front cost necessary to generate the training dataset from which the surrogate model is subsequently developed, a variable-fidelity POD- based reduced-order modelling method is proposed in this work for the first time. In this model, the scalar coefficients which are obtained by projecting the solution vectors onto the basis vectors, are mapped between spaces of low and high fidelities, to achieve high- fidelity predictions with complete flow-field information. In general, this technique offers an automatic way of fusing variable-fidelity data through interpolation and extrapolation schemes together with reduced-order modelling (ROM). Furthermore, a study was undertaken to investigate the possibility of modelling the transonic flow over an aerofoil using a kernel POD–based reduced-order modelling method. By using this type of ROM it was noticed that the weak non-linear features of the transonic flow are accurately modelled using a small number of basis vectors. The strong non-linear features are only modelled accurately by using a large number of basis vectors.

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Zachariadis, Zacharias Ioannis. "High resolution and high order methods for RANS modelling and aerodynamic optimization." Thesis, Cranfield University, 2008. http://hdl.handle.net/1826/3806.

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With the optimisation of fixed aerodynamic shapes reaching its limits, the active flow control concept increasingly attracts attention of both academia and industry. Adaptive wing technology, and shape morphing airfoils in particular, represents a promising way forward. The aerodynamic performance of the morphing profiles is an important issue affecting the overall aerodynamic performance of an adaptive wing. A new concept of active flow, the Active Camber concept has been investigated. The actuator is integrated into the aerofoil and aerofoil morphing is realized via camber deformation. In order to identify the most aerodynamically efficient designs, an optimisation study has been performed using high resolution methods in conjunction with a two equation eddy viscosity model. Several different types of previously proposed compressible filters, including monotone upstream-centered schemes for conservation laws (MUSCL) and weighted essential non-oscillatory (WENO) filters, are incorporated and investigated in the present research. The newly developed CFD solver is validated and the effect that high resolution methods have on turbulent flow simulations is highlighted. The outermost goal is the development of a robust high resolution CFD method that will efficiently and accurately simulate various phenomena, such as shock/boundary layer interaction, flow separation and turbulence and thus provide the numerical framework for analysis and aerodynamic aerofoil design. With respect to the latter a multi-objective integrated design system (MOBID) has been developed that incorporates the CFD solver and a state-of-the-art heuristic optimisation algorithm, along with an efficient parametrization technique and a fast and robust method of propagating geometric displacements. The methodologies in the MOBID system resulted in the identification of the design vectors that revealed aerodynamic performance gains over the datum aerofoil design. The Pareto front provided a clear picture of the achievable trade-offs between the competing objectives. Furthermore, the implementation of different numerical schemes led to significant differences in the optimised airfoil shape, thus highlighting the need for high-resolution methods in aerodynamic optimisation.

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Brandi, Analice Costacurta. "Estratégias "upwind" e modelagem k-epsilon para simulação numérica de escoamentos com superfícies livres em altos números de Reynolds." Universidade de São Paulo, 2005. http://www.teses.usp.br/teses/disponiveis/55/55134/tde-01122005-170110/.

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Este trabalho é dedicado à análise e implementação de esquemas "upwind" de alta ordem modernos e o modelo de turbulência k-epsilon padrão no Freeflow-2D; um ambiente integrado para simulação numérica em diferenças finitas de problemas de escoamentos incompressíveis com superfícies livres. O propósito do estudo é a simulação de escoamentos de fluidos newtonianos incompressíveis, bidimensionais, confinados e/ou com superfícies livres e a altos valores do número de Reynolds. O desempenho do código Freeflow-2D atual é avaliada na simulação do escoamento numa expansão brusca e de um jato livre incidindo perpendicularmente sobre uma superfície rígida impermeável. O código é então aplicado na simulação de um jato planar turbulento em uma porção de fluido com superfície livre e estacionário. Os resultados numéricos obtidos são comparados com dados experimentais, soluções analíticas e soluções numéricas de outros trabalhos.
This work is devoted to the analysis and implementation of modern high-order upwind schemes and the standard k-epsilon turbulence model into the Freeflow-2D; a finite difference integrated environment for the numerical simulation of incompressible free surface flow problems. The purpose of this study is the two-dimensional simulation of high-Reynolds incompressible newtonian confined and/or free surface flows. The performance of the current Freeflow-2D code is assessed by applying it to the simulation of flow over a backward facing step and of an impinging free jet onto an impermeable rigid surface. The code is then applied to a turbulent planar jet into a pool. The numerical results are compared with experimental data, analytical solution, and numerical simulations of other works.

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Mosedale, Andrew Daniel. "Modelling shock-induced instabilities, transition and turbulent mixing using high-order methods." Thesis, Cranfield University, 2008. http://hdl.handle.net/1826/3791.

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High-order numerical methods have been considered and implemented in order to assess their applicability in a range of complex ows centering on shockinduced turbulent mixing. Speci cally, Weighted Essentially Non-Oscillatory (WENO) variable reconstruction schemes of fth and ninth order accuracy have been investigated within the context of a nite volume Godunov solver. In addition to this there have been further numerical developments to assess the HLLC Riemann solver and various quasi-conservative multi-component models in conjunction with the high-order methods. Understanding the physics of fundamental ow instabilities and turbulence is increasingly necessary to the development of a vast range of engineering applications with relation to uid dynamics. It is desirable to develop numerical methods that possess su cient accuracy to capture the detail of such ows while remaining robust and viable in terms of cost. The WENO schemes have been tested on a number of cases in comparison with more traditional second-order MUSCL schemes. These include two and three dimensional, single and multi mode Richtmyer-Meshkov instabilities with differing initial perturbations, a cube of homogeneous decaying turbulence and two hypersonic geometry cases were simulated. The results from this research were consistent. The higher-order methods provided measurably greater resolution of small scale uctuations. By conducting grid convergence studies it was seen that the e ect of the higher-order methods was comparable to the e ect of increasing the number of grid points. The cost analysis repeatedly showed that despite the additional cost of using a higher-order method they were much better value as they could resolve ow features on a signi cantly coarser grid. The high-order methods were not only validated for a range of ow problems but shown to o er great value for their additional cost; they could potentially help advance understanding and development in a wide range of elds much faster than is currently the case.

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Botti, Michele. "Advanced polyhedral discretization methods for poromechanical modelling." Thesis, Montpellier, 2018. http://www.theses.fr/2018MONTS041/document.

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Dans cette thèse, on s’intéresse à de nouveaux schémas de discrétisation afin de résoudre les équations couplées de la poroélasticité et nous présentons des résultats analytiques et numériques concernant des problèmes issus de la poromécanique. Nous proposons de résoudre ces problèmes en utilisant les méthodes Hybrid High-Order (HHO), une nouvelle classe de méthodes de discrétisation polyédriques d’ordre arbitraire. Cette thèse a été conjointement financée par le Bureau de Recherches Géologiques et Minières (BRGM) et le LabEx NUMEV. Le couplage entre l’écoulement souterrain et la déformation géomécanique est un sujet de recherche crucial pour les deux institutions de cofinancement
In this manuscript we focus on novel discretization schemes for solving the coupled equations of poroelasticity and we present analytical and numerical results for poromechanics problems relevant to geoscience applications. We propose to solve these problems using Hybrid High-Order (HHO) methods, a new class of nonconforming high-order methods supporting general polyhedral meshes. This Ph.D. thesis was conjointly founded by the Bureau de recherches géologiques et minières (BRGM) and LabEx NUMEV. The coupling between subsurface flow and geomechanical deformation is a crucial research topic for both cofunding institutions

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From, Christopher. "High-order lattice Boltzmann for nonideal fluid mixtures." Thesis, Queensland University of Technology, 2020. https://eprints.qut.edu.au/200190/1/Christopher_From_Thesis.pdf.

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Nonideal fluid mixtures are ubiquitous in nature and the study of their fundamental dynamics is important in many areas of modern science, such as miniaturized flow processes for portable small-scale medical diagnostic tools. However, numerical simulations of such flows face a formidable multi-scale challenge due to the competing nonideal interactions. This thesis presents a novel numerical model for simulating nonideal fluid mixtures based on high-order lattice Boltzmann methods. A solution to gauge the physical interpretations of nonideal interactions is proposed and with this, previously unknown transport properties are derived, including, the equation of state, interface tension, diffusion coefficient, and contact angle.

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Mall, Suneeta. "Modelling the interpretation of digital mammography using high order statistics and deep machine learning." Thesis, The University of Sydney, 2018. http://hdl.handle.net/2123/19987.

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Visual search is an inhomogeneous, yet efficient sampling process accomplished by the saccades and the central (foveal) vision. Areas that attract the central vision have been studied for errors in interpretation of medical images. In this study, we extend existing visual search studies to understand features of areas that receive direct visual attention and elicit a mark by the radiologist (True and False Positive decisions) from those that elicit a mark but were captured by the peripheral vision. We also investigate if there are any differences between these areas and those that are never fixated by radiologists. Extending these investigations, we further explore the possibility of modelling radiologists’ search behavior and their interpretation of mammograms using deep machine learning techniques. We demonstrated that energy profiles of foveated (FC), peripherally fixated (PC), and never fixated (NFC) areas are distinct. It was shown that FCs are selected on the basis of being most informative. Never fixated regions were found to be least informative. Evidences that energy profiles and dwell time of these areas influence radiologists’ decisions (and confidence in such decisions) were also shown. High-order features provided additional information to the radiologists, however their effect on decision (and confidence in such decision) was not significant. We also showed that deep-convolution neural network can successfully be used to model radiologists’ attentional level, decisions and confidence in their decisions. High accuracy and high agreement (between true and predicted values) in such predictions can be achieved in modelling attentional level (accuracy: 0.90, kappa: 0.82) and decisions (accuracy: 0.92, kappa: 0.86) of radiologists. Our results indicated that an ensembled model for radiologist’s search behavior and decision can successfully be built. Convolution networks failed to model missed cancers however.

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Canestrelli, Alberto. "Numerical Modelling of Alluvial Rivers by Shock Capturing Methods." Doctoral thesis, Università degli studi di Padova, 2009. http://hdl.handle.net/11577/3421764.

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The problem of modelling both the unsteady hydrodynamics and the bed morphological variations in natural channels is generally performed by solving the De Saint Venant balance equations for the liquid phase together with the Exner continuity equation for the sediments carried as bed-load. This thesis focuses on the development of an high-order accurate centred scheme of the finite volume type for the numerical solution of the coupled De Saint Venant-Exner system. A new scheme, called PRICE-C, is proposed. It solves the system of equations in a non-conservative form, however it has the important characteristic of reducing automatically to a conservative scheme if the underlying PDE system is a conservation law. It is applied to the shallow water equations in the presence of either a fix or a movable bed. The scheme is first introduced in a one-dimensional framework, and it is then extended to the two-dimensional case. The extension is not straightforward in the case of an unstructured mesh, since averages over suitable edge-based control volumes have to be performed. The scheme is extended to high order of accuracy in space and time via the ADER-WENO and MUSCL technique respectively for the one- and twodimensional case. The well-balanced property of the scheme is proven, i.e. the ability to reach steady states also in the presence of discontinuous water surface or discontinuous bottom profile. The scheme can deal with subcritical and supercritical flows, as well as transcritical situations. Moreover the proposed approach leads to a correct estimate of the celerity of surface discontinuities as well sediment bores and small bottom perturbations. The main characteristic of the scheme is its simplicity: it is based on a simple centred approach, that means that the knowledge of the eigenvalues of the matrix of the system is not required. This is important since the interaction between sediment transport and water flow not always admits detailed knowledge of the eigenstructure. Hence this scheme can be useful to engineers since they need simple numerical tools that can be easily used without entering in the mathematical detail of the differential hyperbolic system under consideration. Moreover the centred strategy gives generality to the scheme: in fact, it can be applied without modification to any kind of hyperbolic equations with non-conservative terms.
La modellazione dell’idrodinamica e delle variazioni orfologiche in canali naturali `e generalmente effettuata risolvendo numericamente le equazioni delle onde lunghe in acque basse, che regolano il moto della fase fluida, assieme all’equazione di Exner, che descrive l’evoluzione del fondo. L’argomento della presente tesi consiste nello sviluppo di un schema ai volumi finiti di tipo ”centrato” per la soluzione accoppiata di tale sistema di equazioni. Un nuovo schema, denominato PRICE-C, `e qui introdotto: esso risolve le equazioni in forma conconservativa, ma ha l’importante propriet`a di degenerare in uno schema conservativo se il sottostante sistema di equazioni ammette una forma conservativa. Lo schema `e applicato alle equazioni delle onde lunghe in acque basse sia nel caso di fondo fisso che di fondo mobile, dapprima in un ambito unidimensionale e successivamente in quello bidimensionale. L’estensione non `e immediata nel caso in cui il reticolo di calcolo sia non-strutturato, dal momento che le equazioni differenziali devono essere mediate su opportuni volumi di controllo. Lo schema `e poi esteso ad alti ordini di accuratezza nello spazio e nel tempo attraverso le procedure ADER-WENO e MUSCL rispettivamente per il caso unidimensionale e bidimensionale. Inoltre si dimostra come lo schema proposto verifichi la ”well-balanced property”, che consiste nella capacit`a di raggiungere soluzioni stazionarie, anche in presenza di discontinuit`a della superficie libera e del fondo. Condizioni di corrente lenta e rapida, come pure condizioni di tipo transcritico vengono correttamente risolte. Inoltre lo schema in grado di riprodurre le celerit`a di propagazione di discontinuit`a della superficie e fronti di sedimenti al fondo, cos`? come la celerit`a di propagazione di piccoli disturbi del fondo. Caratteristica principale dello schema `e la sua semplicit`a: `e basato su un semplice approccio di tipo centrato, cio`e non necessita la conoscenza degli autovalori della matrice del sistema. Questa `e un’importante caratteristica dal momento che non sempre autovalori e autovettori sono calcolabili analiticamente, in particolare nel caso di complesse formule di chiusura per il trasporto al fondo. Quindi questo schema pu`o rivelarsi utile per l’ingegnere che spesso necessita di un semplice strumento numerico che possa essere applicato ad un sistema di equazioni differenziali di tipo iperbolico senza dover entrare nel dettaglio delle propriet`a atematiche del sistema stesso. Data la sua generalit`a, infatti, lo schema pu`o essere applicato ad ogni tipo di sistema iperbolico contenente termini non-conservativi.

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35

Burton, Ludovic Nicolas. "Multi-Scale Thermal Modeling Methodology for High Power-Electronic Cabinets." Thesis, Georgia Institute of Technology, 2007. http://hdl.handle.net/1853/19808.

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Future generation of all-electric ships will be highly dependent on electric power, since every single system aboard such as the drive propulsion, the weapon system, the communication and navigation systems will be electrically powered. Power conversion modules (PCM) will be used to transform and distribute the power as desired in various zone within the ships. As power densities increase at both components and systems-levels, high-fidelity thermal models of those PCMs are indispensable to reach high performance and energy efficient designs. Efficient systems-level thermal management requires modeling and analysis of complex turbulent fluid flow and heat transfer processes across several decades of length scales. In this thesis, a methodology for thermal modeling of complex PCM cabinets used in naval applications is offered. High fidelity computational fluid dynamics and heat transfer (CFD/HT) models are created in order to analyze the heat dissipation from the chip to the multi-cabinet level and optimize turbulent convection cooling inside the cabinet enclosure. Conventional CFD/HT modeling techniques for such complex and multi-scale systems are severely limited as a design or optimization tool. The large size of such models and the complex physics involved result in extremely slow processing time. A multi-scale approach has been developed to predict accurately the overall airflow conditions at the cabinet level as well as the airflow around components which dictates the chip temperature in details. Various models of different length scales are linked together by matching the boundary conditions. The advantage is that it allows high fidelity models at each length scale and more detailed simulations are obtained than what could have been accomplished with a single model methodology. It was found that the power cabinets under the prescribed design parameters, experience operating point airflow rates that are much lower than the design requirements. The flow is unevenly distributed through the various bays. Approximately 90 % of the cold plenum inlet flow rate goes exclusively through Bay 1 and Bay 2. Re-circulation and reverse flow are observed in regions experiencing a lack of flow motion. As a result high temperature of the air flow and consequently high component temperatures are also experienced in the upper bays of the cabinet. A proper orthogonal decomposition (POD) methodology has been performed to develop reduced-order compact models of the PCM cabinets. The reduced-order modeling approach based on POD reduces the numerical models containing 35 x 109 DOF down to less than 20 DOF, while still retaining a great accuracy. The reduced-order models developed yields prediction of the full-field 3-D cabinet within 30 seconds as opposed to the CFD/HT simulations that take more than 3 hours using a high power computer cluster. The reduced-order modeling methodology developed could be a useful tool to quickly and accurately characterize the thermal behavior of any electronics system and provides a good basis for thermal design and optimization purposes.

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36

Le, Touzé David. "Méthodes spectrales pour la modélisation non-linéaire d'écoulements à surface libre instationnaires." Phd thesis, Ecole centrale de nantes - ECN, 2003. http://tel.archives-ouvertes.fr/tel-00370200.

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Les méthodes spectrales sont connues pour leurs propriétés de convergence rapide et de précision. Cependant, leur application à l'hydrodynamique navale reste encore aujourd'hui peu étendue. Le but de ce doctorat est d'étudier les possibilités de leur application à la génération et propagation de houle, dans le cadre de la théorie des écoulements potentiels.
Un bilan des différentes approches spectrales employées jusqu'à présent en hydrodynamique navale est d'abord dressé, étayant le choix des techniques développées au cours de ce travail. L'étude des propriétés de ces techniques est ensuite réalisée sur le ‘noyau' de la méthode, i.e. une cuve tri-dimensionnelle de géométrie figée. En particulier, différentes techniques High-Order Spectral sont comparées entre elles et à la méthode directe, et une nouvelle variante est proposée. Des validations sur des cas de lâchers de surface libre et d'oscillations forcées de surface libre sont présentées et confrontées à diverses méthodes.
L'approche est ensuite étendue, à partir de ce ‘noyau' et au moyen de stratégies de ‘potentiel additionnel', donnant lieu au développement de divers modèles. Ainsi, des houles non-linéaires sont modélisées à l'aide de doublets tournants instationnaires spécifiquement développés. Des cas de reproduction de signaux temporels cibles à une distance, et de génération et propagation de houle irrégulière sont présentés. De plus, une caractéristique avantageuse d'une telle approche spectrale est exploitée pour proposer des modèles originaux de diffraction autour de corps. Ceux-ci allient une génération de houle par méthode spectrale à des modèles de diffraction en fluide parfait ou visqueux, formulés en changement de variable. Des exemples illustratifs de diffraction de cette houle autour de corps bi- ou tri-dimensionnels sont proposés.
Enfin, un modèle original de simulation complète, au second-ordre, du processus de génération et propagation en bassin de houle tri-dimensionnel est réalisé. Il inclut la modélisation de différents batteurs, ainsi qu'un modèle d'absorption, permettant notamment de reproduire les caractéristiques complètes du nouveau bassin de houle de l'École Centrale de Nantes. Ce modèle est validé par comparaison à une solution analytique en régime établi et ses propriétés numériques sont étudiées. L'investigation des ondes libres et leur suppression, ainsi que la caractérisation de zones utiles sont proposées à titre d'application.

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37

Thomas, Gregory Robert. "A combined high-order spectral and boundary integral equation method for modelling wave interactions with submerged bodies." Thesis, Monterey, California. Naval Postgraduate School, 1996. http://hdl.handle.net/10945/8098.

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Thomas, Gregory Robert. "A combined high-order spectral and boundary integral equation method for modelling wave interactions with submerged bodies." Thesis, Massachusetts Institute of Technology, 1997. http://hdl.handle.net/1721.1/17432.

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39

D'Alessio, Giuseppe. "Data-driven models for reacting flows simulations: reduced-order modelling, chemistry acceleration and analysis of high-fidelity data." Doctoral thesis, Universite Libre de Bruxelles, 2021. https://dipot.ulb.ac.be/dspace/bitstream/2013/328064/5/contratGA.pdf.

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Combustion science must necessarily go through a deep process of innovation, as only improving the energy efficiency and the fuel flexibility it will be possible to mitigate the impact of the anthropogenic activities on the climate and the environment. Because of the strong relation that is observed in chemically reacting flows between the fluid-dynamic conditions and the chemical kinetics, the use of Computational Fluid Dynamics (CFD) simulations with detailed kinetic mechanisms represents the best tool to optimize and develop novel combustion systems. In fact, while the CFD provides for the possibility to retrieve information that cannot be extracted by using experimental means (such as the turbulence-chemistry interaction and the local straining rates) and it avoids the costs associated to the scale-up process from laboratory scale experiments, the use of detailed kinetic mechanisms offers the possibility to correctly describe process conditions which are relevant from an industrial point of view (i.e. in which the chemical and mixing time scales are comparable), as well as to predict the formation of complex chemical species, such as the pollutants. Nevertheless, the use of detailed kinetic mechanisms in numerical simulations adds a considerable number of differential equations to be solved (because of the large number of species which are taken into account), and therefore increases the computational complexity of the CFD model. Thus, Machine Learning (ML) algorithms and Reduced-Order Models (ROMs) can be effectively included in the numerical description of chemically reacting flows. In fact, they can be used either to reduce the computational cost associated to the large number of equations in CFD simulations carried out with detailed chemistry, or to leverage the detailed information which can be found in massive, high-fidelity, data obtained from Direct Numerical Simulations (DNS), for model development and validation. In this Thesis, unsupervised and supervised learning algorithms were employed to design a novel adaptive-chemistry approach: the Sample-Partitioning Adaptive Reduced Chemistry (SPARC). This framework can be used to reduce the computational effort required by detailed CFD simulations thanks to a kinetic reduction accomplished in light of the local conditions of the thermochemical field. Several machine-learning algorithms, such as the Principal Component Analysis (PCA), the Local Principal Component Analysis (LPCA), and Artificial Neural Networks (ANNs) were coupled with the Direct Relation Graph with Error Propagation (DRGEP), a graph-based tool for the automatic reduction of kinetic mechanisms. The aforementioned algorithms were compared to achieve the optimal formulation of the adaptive approach, such that the best performances, in terms of accuracy and computational speed-up with respect to the CFD simulation carried out with detailed kinetics, could be obtained. Finally, PCA-based algorithms were proposed and tested to perform feature extraction and local feature selection from high-fidelity data, which were obtained by means of a DNS of a n-heptane jet reacting in air. The PCA, as well as two formulations of LPCA, and the Procrustes analysis were employed and compared with the aim to extract the main features of the turbulent reacting jet in an unsupervised fashion (i.e. to perform data mining tasks), as well as to aid the formulation of local optimized ROMs. All the codes employed to perform the unsupervised and supervised machine learning tasks in the current work were also included in an open-source Python framework, called OpenMORe, designed to perform reduction, clustering and data analysis, and specifically conceived for reacting flows. In fact, although many open-source Python software are already available, they often cannot be adapted to the user’s specific needs, unlike OpenMORe. In addition, many features such as the PCA-based clustering algorithm, or the local feature selection via PCA, are not yet available on any commercial or open-source software, to the best of the author’s knowledge.
Doctorat en Sciences de l'ingénieur et technologie
This thesis is submitted to the Université Libre de Bruxelles (ULB) and to the Politecnico di Milano for the degree of philosophy doctor. This doctoral work has been performed at the Université Libre de Bruxelles, École polytechnique de Bruxelles, Aero-Thermo-Mechanics Laboratory, Bruxelles, Belgium with Professor Alessandro Parente and at the Politecnico di Milano, CRECK Modelling Lab, Department of Chemistry, Materials and Chemical Engineering, Milan, Italy with Professor Alberto Cuoci.
info:eu-repo/semantics/nonPublished

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40

Sim, Min Kyu. "Empirical findings in asset price dynamics revealed by quantitative modelling." Diss., Georgia Institute of Technology, 2014. http://hdl.handle.net/1853/54302.

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This dissertation addresses the fundamental question of what factors drive equity prices and investigates the mechanisms through which the drivers influence the price dynamics. The studies are based on the two different frequency levels of financial data. The first part aims to identify what systematic risk factors affect the expected return of stocks based on historical data with frequency being daily or monthly. The second part aims to explain how the hidden supply-demand of a stock affects the stock price dynamics based on market data observed at frequency levels generally between a millisecond and a second. With more and more financial market data becoming available, it greatly facilitates quantitative approaches for analyzing asset price dynamics and market microstructure problems. In the first part, we propose an econometric measure, terms as modularity, for characterizing the cluster structure in a universe of stocks. A high level of modularity implies that the cluster structure of the universe of stocks is highly evident, and low modularity implies a blurred cluster structure. The modularity measure is shown to be related to the cycle of the economy. In addition, individual stock's sensitivity to the modularity measure is shown to be related to its expected return. From 1992 to 2011, the average annual return of stocks with the lowest sensitivity exceeds that of the stocks with highest sensitivities by approximately 7.6%. Considerations of modularity as an asset pricing factor expand the investment opportunity set to passive investors. In the second part, we analyze the effect of hidden demands/supplies in equity trading market on the stock price dynamics. We propose a statistical estimation model for average hidden liquidity based on the limit orderbook data. Not only the estimated hidden liquidity explains the probabilistic property in market microstructure better, it also refines the existing price impact model and achieves higher explanation powers. Our enhanced price impact model offers a base for devising optimal order execution strategies. After we develop an optimal execution strategy based on the price impact function, the advantage of this strategy over benchmark strategies is tested on a simulated stock trading model calibrated by historical data. Simulation tests indicate that our strategy yields significant savings in transaction cost over the benchmark strategies.

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41

Shafieipour, Mohammad. "Efficient Error-Controllable High-Order Electromagnetic Modelling of Scattering on Electrically Large Targets with the Locally Corrected Nyström Method." IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, 2014. http://hdl.handle.net/1993/31181.

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This dissertation is about efficient computation of the electromagnetic fields with the locally corrected Nyström (LCN) method as a point-based boundary element method (BEM). The concept of surface integral equations is discussed and the electric field integral equation (EFIE) is derived from the Maxwell’s equations. Due to its point-based nature, the LCN discretization of the EFIE has some advantages over discretizing the EFIE by the method-of-moments (MoM) which is an element-based BEM. On the other hand, due to maturity of the MoM, a large body of work is available to resolve the numerical issues arising in MoM while there has been less work related to the relatively new LCN. To combine the benefits of the LCN method and the classical Rao-Wilton-Glisson MoM, equivalence between these BEMs are established and their exact relationships are derived. Both the vector-potential EFIE and the mixed-potential EFIE are covered. Various aspects of achieving HO convergence to the correct answer using high-order (HO) LCN method are discussed. In particular, the patch size limitation, predicting the optimal degrees of freedom, and the effect of dynamic range in the solution are discussed both analytically and numerically to provide concrete motivations towards HO LCN. The benefits of an HO BEM can not be realized unless an HO geometry representation is used in conjunction with the BEM. Non-uniform rational b-spline (NURBS) surfaces are the most widely adopted HO geometry modelling technique in various disciplines due to their many advantages. However, a typical mesh created out of NURBS surfaces contain both triangular and quadrilateral elements while formulating LCN based on Gaussian quadrature rules on triangular elements have limitations. As a result, the LCN community has mostly adopted LCN based on curvilinear quadrilateral modelling of the geometry. A new class of Newton-Cotes quadrature rules for triangles is proposed to facilitate incorporating NURBS surfaces into the HO LCN.
May 2016

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42

Quint, Karsten [Verfasser]. "Thermomechanically coupled processes for functionally graded materials : experiments, modelling, and finite element analysis using high-order DIRK-methods / Karsten Quint." Clausthal-Zellerfeld : Universitätsbibliothek Clausthal, 2012. http://d-nb.info/1024717844/34.

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43

Ducrozet, Guillaume. "Modélisation des processus non-linéaires de génération et de propagation d'états de mer par une approche spectrale." Phd thesis, Université de Nantes, 2007. http://tel.archives-ouvertes.fr/tel-00263596.

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L'analyse des processus non-linéaires de génération et de propagation de la houle a constitué le cadre de cette thèse. Afin d'améliorer la compréhension de ces phénomènes, une méthode numérique dite High-Order Spectral (HOS), résolvant le problème de façon non-linéaire, a été développée. Cette méthode, avec une formulation surfacique et résolue de manière spectrale, associe précision et efficacité.

Un traitement original de la génération de houle non-linéaire est proposé. Il permet l'accès à des simulations de champs de vagues tridimensionnels complexes, fortement cambrés, dans un bassin de houle. Diverses comparaisons avec des expériences menées dans le bassin du Laboratoire de Mécanique des Fluides de l'ECN sont présentées.

Des simulations océaniques, en milieu ouvert, sont également proposées. Un intérêt particulier est porté à l'étude de l'apparition des vagues scélérates au sein de l'océan. L'importance des effets non-linéaires est pointée ainsi que l'aptitude de la méthode à modéliser de tels phénomènes. Des comparaisons avec les méthodes classiquement employées dans ce genre de problématique indiquent l'intérêt de l'approche utilisée ici.

La résolution du problème de tenue à la mer est également envisagée. L'utilisation de la méthode HOS dans les codes couplés, développés au Laboratoire de Mécanique des Fluides (potentiel, RANS, SPH), est envisagée. Elle permettra la description précise de la houle incidente ; le couplage est mis en place et validé sur un certain nombre de cas d'application.

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44

Steiert, Christoph, Juliane Weber, Alexander Galant, Janine Glänzel, and Jürgen Weber. "Fluid-thermal co-simulation for a high performance concrete machine frame." Technische Universität Dresden, 2020. https://tud.qucosa.de/id/qucosa%3A71161.

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Thermo-elastic errors are one of the main drivers for reduced quality of workpieces in machining. Cooling systems can prevent these errors and improve quality. The paper describes a simulation method that takes into account both the temperature field of a machine tool frame and the fluid cooling system. Such simulations can help to improve the thermal stability of the machine tool frame.

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Saliba, Pamela. "High-frequency trading : statistical analysis, modelling and regulation." Thesis, Université Paris-Saclay (ComUE), 2019. http://www.theses.fr/2019SACLX044.

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Cette thèse est constituée de deux parties liées l’une à l’autre. Dans la première, nous étudions empiriquement le comportement des traders haute fréquence sur les marchés financiers européens. Nous utilisons les résultats obtenus afin de construire dans la seconde partie de nouveaux modèles multi-agents. L’objectif principal de ces modèles est de fournir aux régulateurs et plateformes de négociation des outils innovants leur permettant de mettre en place des règles pertinentes pour la microstructure et de quantifier l’impact des divers participants sur la qualité du marché.Dans la première partie, nous effectuons deux études empiriques sur des données uniques fournies par le régulateur français. Nous avons accès à l’ensemble des ordres et transactions des actifs du CAC 40, à l’échelle de la microseconde, avec par ailleurs les identités des acteurs impliqués. Nous commençons par comparer le comportement des traders haute fréquence à celui des autres intervenants, notamment pendant les périodes de stress, en termes de provision de liquidité et d’activité de négociation. Nous approfondissons ensuite notre analyse en nous focalisant sur les ordres consommant la liquidité. Nous étudions leur impact sur le processus de formation des prix et leur contenu informationnel selon les différentes catégories de flux : traders haute fréquence, participants agissant pour compte client et participants agissant pour compte propre.Dans la seconde partie, nous proposons trois modèles multi-agents. À l’aide d’une approche à la Glosten-Milgrom, nous parvenons avec notre premier modèle à construire l’ensemble du carnet d’ordres (spread et volume disponible à chaque prix) à partir des interactions entre trois types d’agents : un agent informé, un agent non informé et des teneurs de marché. Ce modèle nous permet par ailleurs de développer une méthodologie de prédiction du spread en cas de modification du pas de cotation et de quantifier la valeur de la priorité dans la file d’attente. Afin de se concentrer sur une échelle individuelle, nous proposons une deuxième approche où les dynamiques spécifiques des agents sont modélisées par des processus de type Hawkes non linéaires et dépendants de l’état du carnet d’ordres. Dans ce cadre, nous sommes en mesure de calculer en fonction des flux individuels plusieurs indicateurs pertinents relatifs à la microstructure. Il est notamment possible de classer les teneurs de marché selon leur contribution propre à la volatilité. Enfin, nous introduisons un modèle où les fournisseurs de liquidité optimisent leurs meilleurs prix à l’achat et à la vente en fonction du profit qu’ils peuvent générer et du risque d’inventaire auquel ils sont confrontés. Nous mettons alors en évidence théoriquement et empiriquement une nouvelle relation importante entre inventaire et volatilité
This thesis is made of two related parts. In the first one, we study the empirical behaviour of high-frequency traders on European financial markets. We use the obtained results to build in the second part new agent-based models for market dynamics. The main purpose of these models is to provide innovative tools for regulators and exchanges allowing them to design suitable rules at the microstructure level and to assess the impact of the various participants on market quality.In the first part, we conduct two empirical studies on unique data sets provided by the French regulator. It covers the trades and orders of the CAC 40 securities, with microseconds accuracy and labelled by the market participants identities. We begin by investigating the behaviour of high-frequency traders compared to the rest of the market, notably during periods of stress, in terms of liquidity provision and trading activity. We work both at the day-to-day scale and at the intra-day level. We then deepen our analysis by focusing on liquidity consuming orders. We give some evidence concerning their impact on the price formation process and their information content according to the different order flow categories: high-frequency traders, agency participants and proprietary participants.In the second part, we propose three different agent-based models. Using a Glosten-Milgrom type approach, the first model enables us to deduce the whole limit order book (bid-ask spread and volume available at each price) from the interactions between three kinds of agents: an informed trader, a noise trader and several market makers. It also allows us to build a spread forecasting methodology in case of a tick size change and to quantify the queue priority value. To work at the individual agent level, we propose a second approach where market participants specific dynamics are modelled by non-linear and state dependent Hawkes type processes. In this setting, we are able to compute several relevant microstructural indicators in terms of the individual flows. It is notably possible to rank market makers according to their own contribution to volatility. Finally, we introduce a model where market makers optimise their best bid and ask according to the profit they can generate from them and the inventory risk they face. We then establish theoretically and empirically a new important relationship between inventory and volatility

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Larat, Adam. "Conception et Analyse de Schémas Distribuant le Résidu d'Ordre Très Élevé. Application à la Mécanique des Fluides." Phd thesis, Université Sciences et Technologies - Bordeaux I, 2009. http://tel.archives-ouvertes.fr/tel-00502429.

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La simulation numérique est aujourd'hui un outils majeur dans la conception des objets aérodynamiques, que ce soit dans l'aéronautique, l'automobile, l'industrie navale, etc... Un des défis majeurs pour repousser les limites des codes de simulation est d'améliorer leur précision, tout en utilisant une quantité fixe de ressources (puissance et/ou temps de calcul). Cet objectif peut être atteint par deux approches différentes, soit en construisant une discrétisation fournissant sur un maillage donné une solution d'ordre très élevé, soit en construisant un schéma compact et massivement parallélisable, de manière à minimiser le temps de calcul en distribuant le problème sur un grand nombre de processeurs. Dans cette thèse, nous tentons de rassembler ces deux approches par le développement et l'implémentation de Schéma Distribuant le Résidu (RDS) d'ordre très élevé et de compacité maximale. Ce manuscrit commence par un rappel des principaux résultats mathématiques concernant les Lois de Conservation hyperboliques (CLs). Le but de cette première partie est de mettre en évidence les propriétés des solutions analytiques que nous cherchons à approcher, de manière à injecter ces propriétés dans celles de la solution discrète recherchée. Nous décrivons ensuite les trois étapes principales de la construction d'un schéma RD d'ordre très élevé : \begin{itemize} \item la représentation polynomiale d'ordre très élevé de la solution sur des polygones et des polyèdres; \item la description de méthodes distribuant le résidu de faible ordre, compactes et conservatives, consistantes avec une représentation polynomiale des données de très haut degré. Parmi elles, une attention particulière est donnée à la plus simple, issue d'une généralisation du schéma de Lax-Friedrichs (LxF); \item la mise en place d'une procédure préservant la positivité qui transforme tout schéma stable et linéaire, en un schéma non linéaire d'ordre très élevé, capturant les chocs de manière non oscillante. \end{itemize} Dans le manuscrit, nous montrons que les schémas obtenus par cette procédure sont consistants avec la CL considérée, qu'ils sont stables en norme $\L^{\infty}$ et qu'ils ont la bonne erreur de troncature. Même si tous ces développements théoriques ne sont démontrés que dans le cas de CL scalaires, des remarques au sujet des problèmes vectoriels sont faites dès que cela est possible. Malheureusement, lorsqu'on considère le schéma LxF, le problème algébrique non linéaire associé à la recherche de la solution stationnaire est en général mal posé. En particulier, on observe l'apparition de modes parasites de haute fréquence dans les régions de faible gradient. Ceux-ci sont éliminés grâce à un terme supplémentaire de stabilisation dont les effets et l'évaluation numérique sont précisément détaillés. Enfin, nous nous intéressons à une discrétisation correcte des conditions limites pour le schéma d'ordre élevé proposé. Cette théorie est ensuite illustrée sur des cas test scalaires bidimensionnels simples. Afin de montrer la généralité de notre approche, des maillages composés uniquement de triangles et des maillages hybrides, composés de triangles et de quadrangles, sont utilisés. Les résultats obtenus par ces tests confirment ce qui est attendu par la théorie et mettent en avant certains avantages des maillages hybrides. Nous considérons ensuite des solutions bidimensionnelles des équations d'Euler de la dynamique des gaz. Les résultats sont assez bons, mais on perd les pentes de convergence attendues dès que des conditions limite de paroi sont utilisées. Ce problème nécessite encore d'être étudié. Nous présentons alors l'implémentation parallèle du schéma. Celle-ci est analysée et illustrée à travers des cas test tridimensionnel de grande taille. Du fait de la relative nouveauté et de la complexité des problèmes tridimensionels, seuls des remarques qualitatives sont faites pour ces cas test : le comportement global semble être bon, mais plus de travail est encore nécessaire pour définir les propriétés du schémas en trois dimensions. Enfin, nous présentons une extension possible du schéma aux équations de Navier-Stokes dans laquelle les termes visqueux sont traités par une formulation de type Galerkin. La consistance de cette formulation avec les équations de Navier-Stokes est démontrée et quelques remarques au sujet de la précision du schéma sont soulevées. La méthode est validé sur une couche limite de Blasius pour laquelle nous obtenons des résultats satisfaisants. Ce travail offre une meilleure compréhension des propriétés générales des schémas RD d'ordre très élevé et soulève de nouvelles questions pour des améliorations futures. Ces améliorations devrait faire des schémas RD une alternative attractive aux discrétisations classiques FV ou ENO/WENO, aussi bien qu'aux schémas Galerkin Discontinu d'ordre très élevé, de plus en plus populaires.

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47

Zebiri, Boubakr. "Étude numérique des interactions onde de choc / couche limite dans les tuyères propulsives Shock-induced flow separation in an overexpanded supersonic planar nozzle A parallel high-order compressible flows solver with domain decomposition method in the generalized curvilinear coordinates system Analysis of shock-wave unsteadiness in conical supersonic nozzles." Thesis, Normandie, 2020. http://www.theses.fr/2020NORMIR06.

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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

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Feng, Tseng Kou, and 曾國峰. "Image Source Modeling Using High-Order Conditional Statistic Criterions." Thesis, 1994. http://ndltd.ncl.edu.tw/handle/36405449605332620422.

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Heidkamp, Holger [Verfasser]. "Modeling localization and failure with high order finite elements / Holger Heidkamp." 2007. http://d-nb.info/985218177/34.

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Kuo, Chia-Hsu T., and 郭家旭. "HIGH-ORDER SOURCE MODELING AND CODING FOR NOISELESS DATA COMPRESSION SYSTEM." Thesis, 1995. http://ndltd.ncl.edu.tw/handle/65481007419117753380.

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博士
國立中央大學
電機工程研究所
83
The modern paradigm for data compression is to separate compression system into source modeling and sequence coding units. In this dissertation, data compression system with applications to texts including Chinese and English and gray scale images is investigated. An optimal modeling technique for Chinese text compression is established. The performance using the nibble symbol based on the higher order (n=3) outperforms that using the byte symbol with order equal to one under the same complexity. An alphabet reduction model, i.e., the bitplanes decomposition, based on different template searching algorithms is proposed to compress the gray scale images in which conditional entropy coding using high-order conditional statistics is involved. For the purpose of further reducing the resulted code rate in the lower significant bitplanes, a bitplane merging algorithm is applied to the alphabet reduction model with bitplanes decomposition owing to the high uncertainty. The compression efficiency even under the lower complexity can beat that of bitplanes decomposition without merging algorithm. We introduce a novel code table reduction with estimated conditional probabilities algorithm applied to bitplanes decomposition technique of alphabet reduction model for high-order conditional entropy coding. The serious problem of high complexity in the data compression system when the high- order conditional entropy coding is applied and the number of conditional states becomes extremely large can be untangled by this technique without the complicated incremental tree extension algorithm. Two new algorithms for repetition finder used with dynamic Huffman coding are proposed to improve the compression efficiency by reducing the redundancy due to string repetitions. The perfect results are presented in our experiments.

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