Dissertations / Theses on the topic 'FFT solveurs'

La complexité des mécanismes physiques mis en jeu lors de l'interaction laser-plasma à ultra-haute intensité nécessite de recourir à des simulations PIC particulièrement lourdes. Au cœur de ces codes de calcul, les solveurs de Maxwell pseudo-spectraux d'ordre élevé présentent de nombreux avantages en termes de précision numérique. Néanmoins, ces solveurs ont un coût élevé en termes de ressources nécessaires. En effet, les techniques de parallélisation existantes pour ces solveurs sont peu performantes au-delà de quelques milliers de coeurs, ou induisent un important usage mémoire, ce qui limite leur scalabilité à large échelle. Dans cette thèse, nous avons développé une toute nouvelle approche de parallélisation qui combine les avantages des méthodes existantes. Cette méthode a été testée à très large échelle et montre un scaling significativement meilleur que les précédentes techniques, tout en garantissant un usage mémoire réduit.En capitalisant sur ce travail numérique, nous avons réalisé une étude numérique/théorique approfondie dans le cadre de la génération d'harmoniques d'ordres élevés sur cible solide. Lorsqu'une impulsion laser ultra-intense (I>10¹⁶W.cm⁻² ) et ultra-courte (de quelques dizaines de femtosecondes) est focalisée sur une cible solide, elle génère un plasma sur-dense, appelé miroir plasma, qui réfléchit non-linéairement le laser incident. La réflexion de l'impulsion laser est accompagnée par l'émission cohérente d'harmoniques d'ordres élevées, sous forme d'impulsions X-UV attosecondes (1 attosecond = 10⁻¹⁸s). Pour des intensités laser relativistes (I>10¹⁹ W.cm⁻²), la surface du plasma est incurvée sous l'effet de la pression de radiation du laser. De ce fait, les harmoniques rayonnées par la surface du plasma sont focalisées. Dans cette thèse, j'ai étudié la possibilité de produire des impulsions attosecondes isolées en régime relativiste sur miroir plasma, grâce au mécanisme de phare attoseconde. Celui-ci consiste à introduire une rotation des fronts d'onde du laser incident de façon à séparer angulairement les différentes impulsions attosecondes produites à chaque cycle optique. En régime relativiste, la courbure du miroir plasma augmente considérablement la divergence du faisceau harmonique, ce qui rend le mécanisme phare attoseconde inefficace. Pour y remédier, j'ai développé deux techniques de réduction de divergence harmonique afin de mitiger l'effet de focalisation induit par la courbure du miroir plasma et permettre de générer des impulsions attosecondes isolées à partir d’harmoniques Doppler. Ces deux techniques sont basées sur la mise en forme en amplitude et en phase du faisceau laser. Par ailleurs, j'ai développé un modèle théorique pour déterminer les régimes optimaux d'interaction afin de maximiser la séparation angulaire des impulsions attosecondes. Ce modèle a été validé par des simulations numériques PIC en géométries 2D et 3D et sur une large gamme de paramètres laser et plasma. Finalement, on montre qu'en ajustant des paramètres laser et plasma réalistes, il est possible de séparer efficacement les impulsions attosecondes en régime relativiste
The complexity of the physical mechanisms involved in ultra-high intensity laser-plasma interaction requires the use of particularly heavy PIC simulations. At the heart of these computational codes, high-order pseudo-spectral Maxwell solvers have many advantages in terms of numerical accuracy. This numerical approach comes however with an expensive computational cost. Indeed, existing parallelization methods for pseudo-spectral solvers are only scalable to few tens of thousands of cores, or induce an important memory footprint, which also hinders the scaling of the method at large scales. In this thesis, we developed a novel, arbitrarily scalable, parallelization strategy for pseudo-spectral Maxwell's equations solvers which combines the advantages of existing parallelization techniques. This method proved to be more scalable than previously proposed approaches, while ensuring a significant drop in the total memory use.By capitalizing on this computational work, we conducted an extensive numerical and theoretical study in the field of high order harmonics generation on solid targets. In this context, when an ultra-intense (I>10¹⁶W.cm⁻²) ultra-short (few tens of femtoseconds) laser pulse irradiates a solid target, a reflective overdense plasma mirror is formed at the target-vacuum interface. The subsequent laser pulse non linear reflection is accompanied with the emission of coherent high order laser harmonics, in the form of attosecond X-UV light pulses (1 attosecond = 10⁻¹⁸s). For relativistic laser intensities (I>10¹⁹ W.cm⁻²), the plasma surface is curved under the laser radiation pressure. And the plasma mirror acts as a focusing optics for the radiated harmonic beam. In this thesis, we investigated feasible ways for producing isolated attosecond light pulses from relativistic plasma-mirror harmonics, with the so called attosecond lighthouse effect. This effect relies introducing a wavefront rotation on the driving laser pulse in order to send attosecond pulses emitted during different laser optical cycles along different directions. In the case of high order harmonics generated in the relativistic regime, the plasma mirror curvature significantly increases the attosecond pulses divergence and prevents their separation with the attosecond lighthouse scheme. For this matter, we developed two harmonic divergence reduction techniques, based on tailoring the laser pulse phase or amplitude profiles in order to significantly inhibit the plasma mirror focusing effect and allow for a clear separation of attosecond light pulses by reducing the harmonic beam divergence. Furthermore, we developed an analytical model to predict optimal interaction conditions favoring attosecond pulses separation. This model was fully validated with 2D and 3D PIC simulations over a broad range of laser and plasma parameters. In the end, we show that under realistic laser and plasma conditions, it is possible to produce isolated attosecond pulses from Doppler harmonics

Les polycristaux irradiés sont connus pour être le siège d’une intense localisation de la déformation plastique à l’échelle du grain, causant une diminution de leur ductilité ainsi qu’une sensibilité accrue à la corrosion sous contrainte. Cette thèse met à profit les performances offertes par le développement des solveurs FFT massivement parallèles pour améliorer la modélisation de ce phénomène crucial. Nous avons mis au point des méthodes de traitement permettant l’analyse systématique de la nature des bandes de localisation, ainsi que leur caractérisation quantitative, à partir des champs issus de la simulation haute résolution de cellules polycristallines. Elles ont permis de mettre en évidence les limites fondamentales de la plasticité cristalline classique, fondement des modèles de métaux irradiés actuels, quant à la prédiction des modes de localisation intra granulaire du glissement plastique. Pour y remédier, nous avons étudié en détail les prévisions analytiques et numériques d’un modèle de plasticité à gradient, en étendant l’implémentation du solveur AMITEX_FFTP à la résolution de problèmes non locaux. Nous avons pu montrer qu’il constitue un cadre prometteur pour une modélisation physiquement fidèle des modes de localisation intra-granulaires dans les polycristaux adoucissants, donc a fortiori pour les métaux irradiés. Par ailleurs, nous avons également abordé ce problème par la modélisation explicite des bandes de glissement. Nous avons amélioré ses performances grâce au développement de modèles de voxels composites génériques, et montré que cette approche constitue une alternative efficace pour simuler les conséquences de la localisation de la déformation, comme la modification de la distribution de contraintes aux joints de grains, ou l’augmentation de l’écrouissage cinématique
Irradiated polycrystals are known to exhibit an intense localization of plastic deformation at the grain scale, responsible for a severe loss of ductility and increased sensitivity to intergranular stress corrosion cracking. This thesis takes advantage of the performances offered by the recent progresses of highly parallel FFT-based solvers, to improve the modeling of this crucial phenomenon. We developed field processing methods to produce a systematic analysis of the nature and quantitative characterization of localization bands, from high resolution polycrystalline simulation results. They allowed to evidence a fundamental shortcoming of classical crystal plasticity, cornerstone of all irradiated metals models, in the prediction of intragranular localization modes. To overcome this issue, we extended the scope of our FFT solver, AMITEX_FFTP, to nonlocal mechanics. We used it to extensively study the analytical and numerical predictions of a strain gradient plasticity model, showing that it is a promising way to achieve an accurate modeling of plastic slip localization modes in softening polycrystals, and a fortiori for irradiated metals. Additionally, we explored the explicit modeling of slip bands with FFT-based solvers. We developed generic composite voxel models allowing to strongly reduce its computational cost. We show that this approach provides an efficient way to simulate the consequences of strain localization, such as the evolution of the grain boundary stress distribution or the increased kinematic hardening

Cette thèse porte sur la prédiction des propriétés mécaniques effectives de matériaux hétérogènes composés de constituants viscoélastiques fractional, au moyen d'une approche incrémentale variationnelle. Nous appliquons la méthode Effective Internal Variable (EIV) développée par Lahellec and Suquet (2007), particulièrement attrayante pour le traitement de comportements viscoélastiques (Tressou et al., 2016). Contrairement aux méthodes d'homogénéisation communément utilisées qui reposent sur le principe de correspondance et pour lesquelles les fluctuations des champs ne sont pas accessibles, cette approche incrémentale permet de calculer les propriétés effectives dans le domaine direct au moyen des méthodes variationalles de Ponte Castañeda (1991 et 2002) qui prennent en compte les seconds-moments des champs mécaniques. La méthode EIV s'inscrit dans le cadre des Matériaux Standards Généralisés (MSG), dans lequel le comportement des matériaux dissipatifs est décrit par deux potentiels thermodynamiques convexes. Nous considérons des constituants viscoélastiques fractionnaires, dont la loi constitutive est décrite par des équations différentielles linéaires avec des dérivées fractionnaires. En accord avec des observations expérimentales, ce formalisme prend en compte des effets de mémoire longue à travers la superposition de plusieurs temps caractéristiques (Caputo et Mainardi, 1971). La distribution de ces derniers est donnée explicitement par l'expression du spectre en loi puissance. Les potentiels thermodynamiques des matériaux viscoélastiques fractionnaires sont définis en cohérence avec le cadre des MSG. Cette cohérence s'appuie sur l'interprétation rhéologique de l'élément fractionnaire comme un Maxwell généralisé (Lion, 1997). Ainsi, nous tirons parti de l'extension de la méthode EIV à plusieurs variables internes développée par Tressou et al. (2023) afin d'homogénéiser des matériaux composites contenant des constituants viscoélastiques fractionnaires. De plus, les temps caractéristiques sont adéquatement choisis à partir de la discrétisation du spectre. Cette discrétisation est réalisée avec la procédure de Papoulia et al. (2010), basée sur une méthode des trapèzes améliorée. Plus précisément, nous appliquons cette méthode à la fonction de Mittag-Leffler impliquée dans la définition des spectres de relaxation. Nous abordons deux problèmes hétérogènes différents au moyen de la méthode EIV. Nous considérons d'abord un composite de type matrice-inclusions sous chargement harmonique, pour lequel nous rencontrons des difficultés numériques. Nous évaluons ensuite la méthode EIV sur un polycristal de glace soumis à un essai de fluage
This PhD thesis deals with the prediction of the mechanical effective properties of composite materials with linear fractional viscoelastic constituents by means of an incremental variational approach. We make use of the Effective Internal Variable (EIV) method developed by Lahellec and Suquet (2007), which is particularly attractive for viscoelasticity (Tressou et al., 2016). Contrary to the common homogenization methods that rely on the correspondence principle and where the fluctuations are not accessible, this incremental method evaluates the effective properties into the direct domain through the variational methods of Ponte Castañeda (1991 and 2002) that take into account the second-moments of the fields. The EIV method is based on the Generalized Standard Materials framework, in which the dissipative materials are described by means of two convex thermodynamic potentials. We consider local fractional viscoelastic constituents, of which the constitutive behaviours follow linear differential equations with fractional derivative operators. In accordance with experimental observations, this formalism takes into account long-memory effects through the superposition of several characteristic times (Caputo and Mainardi, 1971). Their distribution is provided by the explicit expression of the spectrum as a power law. The potentials of fractional viscoelastic constituents are consistently defined in the GSM framework through the rheological interpretation of the fractional damping element as a generalized Maxwell model (Lion, 1997). Therefore, we take advantage of the extension of the EIV method to several internal variables, developed by Tressou et al. (2023) for the homogenization of composites with local fractional viscoelastic behaviours. Besides, the characteristic times are appropriately chosen by discretizing the spectrum. This is done using the midpoint-based procedure developed by Papoulia et al. (2010). More specifically, we apply their method to the Mittag-Leffler function involved in the definition of the relaxation spectrum. We use the EIV method to tackle two different heterogeneous problems. We consider a matrix-inclusion composite under harmonic loading, for which we come accros numerical issues. We then evaluate the EIV method for a polycrystal subject to a monotonous creep loading

Efficiency is one of the key issues in numerical simulation of large-scale problems with complex 3-D geometry. Traditional domain based methods, such as finite element methods, may not be suitable for these problems due to, for example, the complexity of mesh generation. The Boundary Element Method (BEM), based on boundary integral formulations (BIE), offers one possible solution to this issue by discretizing only the surface of the domain. However, to date, successful applications of the BEM are mostly limited to linear and continuum problems. The challenges in the extension of the BEM to nonlinear problems or problems with non-continuum boundary conditions (BC) include, but are not limited to, the lack of appropriate BIE and the difficulties in the treatment of the volume integrals that result from the nonlinear terms. In this thesis work, new approaches and techniques based on the BEM have been developed for 3-D nonlinear problems and Stokes problems with slip BC. For nonlinear problems, a major difficulty in applying the BEM is the treatment of the volume integrals in the BIE. An efficient approach, based on the precorrected-FFT technique, is developed to evaluate the volume integrals. In this approach, the 3-D uniform grid constructed initially to accelerate surface integration is used as the baseline mesh to evaluate volume integrals. The cubes enclosing part of the boundary are partitioned using surface panels. No volume discretization of the interior cubes is necessary. This grid is also used to accelerate volume integration. Based on this approach, accelerated BEM solvers for non-homogeneous and nonlinear problems are developed and tested. Good agreement is achieved between simulation results and analytical results. Qualitative comparison is made with current approaches. Stokes problems with slip BC are of particular importance in micro gas flows such as those encountered in MEMS devices. An efficient approach based on the BEM combined with the precorrected-FFT technique has been proposed and various techniques have been developed to solve these problems. As the applications of the developed method, drag forces on oscillating objects immersed in an unbounded slip flow are calculated and validated with either analytic solutions or experimental results.

Extracellular neuroelectronic interfacing has important applications in the fields of neural prosthetics, biological computation and whole-cell biosensing for drug screening and toxin detection. While the field of neuroelectronic interfacing holds great promise, the recording of high-fidelity signals from extracellular devices has long suffered from the problem of low signal-to-noise ratios and changes in signal shapes due to the presence of highly dispersive dielectric medium in the neuron-microelectrode cleft. This has made it difficult to correlate the extracellularly recorded signals with the intracellular signals recorded using conventional patch-clamp electrophysiology. For bringing about an improvement in the signal-to-noise ratio of the signals recorded on the extracellular microelectrodes and to explore strategies for engineering the neuron-electrode interface there exists a need to model, simulate and characterize the cell-sensor interface to better understand the mechanism of signal transduction across the interface. Efforts to date for modeling the neuron-electrode interface have primarily focused on the use of point or area contact linear equivalent circuit models for a description of the interface with an assumption of passive linearity for the dynamics of the interfacial medium in the cell-electrode cleft. In this dissertation, results are presented from a nonlinear dynamic characterization of the neuroelectronic junction based on Volterra-Wiener modeling which showed that the process of signal transduction at the interface may have nonlinear contributions from the interfacial medium. An optimization based study of linear equivalent circuit models for representing signals recorded at the neuron-electrode interface subsequently proved conclusively that the process of signal transduction across the interface is indeed nonlinear. Following this a theoretical framework for the extraction of the complex nonlinear material parameters of the interfacial medium like the dielectric permittivity, conductivity and diffusivity tensors based on dynamic nonlinear Volterra-Wiener modeling was developed. Within this framework, the use of Gaussian bandlimited white noise for nonlinear impedance spectroscopy was shown to offer considerable advantages over the use of sinusoidal inputs for nonlinear harmonic analysis currently employed in impedance characterization of nonlinear electrochemical systems. Signal transduction at the neuron-microelectrode interface is mediated by the interfacial medium confined to a thin cleft with thickness on the scale of 20-110 nm giving rise to Knudsen numbers (ratio of mean free path to characteristic system length) in the range of 0.015 and 0.003 for ionic electrodiffusion. At these Knudsen numbers, the continuum assumptions made in the use of Poisson-Nernst-Planck system of equations for modeling ionic electrodiffusion are not valid. Therefore, a lattice Boltzmann method (LBM) based multiphysics solver suitable for modeling ionic electrodiffusion at the mesoscale neuron-microelectrode interface was developed. Additionally, a molecular speed dependent relaxation time was proposed for use in the lattice Boltzmann equation. Such a relaxation time holds promise for enhancing the numerical stability of lattice Boltzmann algorithms as it helped recover a physically correct description of microscopic phenomena related to particle collisions governed by their local density on the lattice. Next, using this multiphysics solver simulations were carried out for the charge relaxation dynamics of an electrolytic nanocapacitor with the intention of ultimately employing it for a simulation of the capacitive coupling between the neuron and the planar microelectrode on a microelectrode array (MEA). Simulations of the charge relaxation dynamics for a step potential applied at t = 0 to the capacitor electrodes were carried out for varying conditions of electric double layer (EDL) overlap, solvent viscosity, electrode spacing and ratio of cation to anion diffusivity. For a large EDL overlap, an anomalous plasma-like collective behavior of oscillating ions at a frequency much lower than the plasma frequency of the electrolyte was observed and as such it appears to be purely an effect of nanoscale confinement. Results from these simulations are then discussed in the context of the dynamics of the interfacial medium in the neuron-microelectrode cleft. In conclusion, a synergistic approach to engineering the neuron-microelectrode interface is outlined through a use of the nonlinear dynamic modeling, simulation and characterization tools developed as part of this dissertation research.
Ph.D.
Doctorate
Physics
Sciences
Physics

Novel integral-equation methods for efficiently solving electromagnetic problems that involve more than a single length scale of interest in complex backgrounds are presented. Such multi-scale electromagnetic problems arise because of the interplay of two distinct factors: the structure under study and the background medium. Both can contain material properties (wavelengths/skin depths) and geometrical features at different length scales, which gives rise to four types of multi-scale problems: (1) twoscale, (2) multi-scale structure, (3) multi-scale background, and (4) multi-scale-squared problems, where a single-scale structure resides in a different single-scale background, a multi-scale structure resides in a single-scale background, a single-scale structure resides in a multi-scale background, and a multi-scale structure resides in a multi-scale background, respectively. Electromagnetic problems can be further categorized in terms of the relative values of the length scales that characterize the structure and the background medium as (a) high-frequency, (b) low-frequency, and (c) mixed-frequency problems, where the wavelengths/skin depths in the background medium, the structure’s geometrical features or internal wavelengths/skin depths, and a combination of these three factors dictate the field variations on/in the structure, respectively. This dissertation presents several problems arising from geophysical exploration and microwave chemistry that demonstrate the different types of multi-scale problems encountered in electromagnetic analysis and the computational challenges they pose. It also presents novel frequency-domain integral-equation methods with proper Green function kernels for solving these multi-scale problems. These methods avoid meshing the background medium and finding fields in an extended computational domain outside the structure, thereby resolving important complications encountered in type 3 and 4 multi-scale problems that limit alternative methods. Nevertheless, they have been of limited practical use because of their high computational costs and because most of the existing ‘fast integral-equation algorithms’ are not applicable to complex Green function kernels. This dissertation introduces novel FFT, multigrid, and FFT-truncated multigrid algorithms that reduce the computational costs of frequency-domain integral-equation methods for complex backgrounds and enable the solution of unprecedented type 3 and 4 multi-scale problems. The proposed algorithms are formulated in detail, their computational costs are analyzed theoretically, and their features are demonstrated by solving benchmark and challenging multi-scale problems.
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Thesis (M.S.)--University of Wisconsin--Madison, 1994.
Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 87-96).

In this paper a precorrected FFT-Fast Multipole Tree (pFFT-FMT) method for solving the potential flow around arbitrary three dimensional bodies is presented. The method takes advantage of the efficiency of the pFFT and FMT algorithms to facilitate more demanding computations such as automatic wake generation and hands-off steady and unsteady aerodynamic simulations. The velocity potential on the body surfaces and in the domain is determined using a pFFT Boundary Element Method (BEM) approach based on the Green’s Theorem Boundary Integral Equation. The vorticity trailing all lifting surfaces in the domain is represented using a Fast Multipole Tree, time advected, vortex participle method. Some simple steady state flow solutions are performed to demonstrate the basic capabilities of the solver. Although this paper focuses primarily on steady state solutions, it should be noted that this approach is designed to be a robust and efficient unsteady potential flow simulation tool, useful for rapid computational prototyping.
Singapore-MIT Alliance (SMA)

Thesis (M.S.)--State University of New York at Buffalo, 2006.
Title from PDF title page (viewed on July. 20, 2006) Available through UMI ProQuest Digital Dissertations. Thesis adviser: Patra, Abani K.

Combustion instability, a complex phenomenon observed in combustion chambers is due to the coupling between heat release and other unsteady flow processes. Combustion instability has long been a topic of interest to rocket scientists and has been extensively investigated experimentally and computationally. However, to date, there is no computational tool that can accurately predict the combustion instabilities in full-size combustors because of the amount of computational power required to perform a high-fidelity simulation of a multi-element chamber. Hence, the focus is shifted to reduced fidelity computational tools which may accurately predict the instability by using the information available from the high-fidelity simulations or experiments of single or few-element combustors. One way of developing reduced fidelity computational tools involves using a reduced fidelity solver together with the flame transfer functions that carry important information about the flame behavior from a high-fidelity simulation or experiment to a reduced fidelity simulation.

To date, research has been focused mainly on premixed flames and using acoustic solvers together with the global flame transfer functions that were obtained by integrating over a region. However, in the case of rockets, the flame is non-premixed and distributed in space and time. Further, the mixing of propellants is impacted by the level of flow fluctuations and can lead to non-uniform mean properties and hence, there is a need for reduced fidelity solver that can capture the gas dynamics, nonlinearities and steep-fronted waves accurately. Nonlinear Euler equations have all the required capabilities and are at the bottom of the list in terms of the computational cost among the solvers that can solve for mean flow and allow multi-dimensional modeling of combustion instabilities. Hence, in the current work, nonlinear Euler solver together with the spatially distributed local flame transfer functions that capture the coupling between flame, acoustics, and hydrodynamics is explored.

In this thesis, the approach to extract flame transfer functions from high-fidelity simulations and their integration with nonlinear Euler solver is presented. The dynamic mode decomposition (DMD) was used to extract spatially distributed flame transfer function (FTF) from high fidelity simulation of a single element non-premixed flame. Once extracted, the FTF was integrated with nonlinear Euler equations as a fluctuating source term of the energy equation. The time-averaged species destruction rates from the high-fidelity simulation were used as the mean source terms of the species equations. Following a variable gain approach, the local species destruction rates were modified to account for local cell constituents and maintain correct mean conditions at every time step of the nonlinear Euler simulation. The proposed reduced fidelity model was verified using a Rijke tube test case and to further assess the capabilities of the proposed model it was applied to a single element model rocket combustor, the Continuously Variable Resonance Combustor (CVRC), that exhibited self-excited combustion instabilities that are on the order of 10% of the mean pressure. The results showed that the proposed model could reproduce the unsteady behavior of the CVRC predicted by the high-fidelity simulation reasonably well. The effects of control parameters such as the number of modes included in the FTF, the number of sampling points used in the Fourier transform of the unsteady heat release, and mesh size are also studied. The reduced fidelity model could reproduce the limit cycle amplitude within a few percent of the mean pressure. The successful constraints on the model include good spatial resolution and FTF with all modes up to at least one dominant frequency higher than the frequencies of interest. Furthermore, the reduced fidelity model reproduced consistent mode shapes and linear growth rates that reasonably matched the experimental observations, although the apparent ability to match growth rates needs to be better understood. However, the presence of significant heat release near a pressure node of a higher harmonic mode was found to be an issue. This issue was rectified by expanding the pressure node of the higher frequency mode. Analysis of two-dimensional effects and coupling between the local pressure and heat release fluctuations showed that it may be necessary to use two dimensional spatially distributed local FTFs for accurate prediction of combustion instabilities in high energy devices such as rocket combustors. Hybrid RANS/LES-FTF simulation of the CVRC revealed that it might be necessary to use Flame Describing Function (FDF) to capture the growth of pressure fluctuations to limit cycle when Navier-Stokes solver is used.

The main objectives of this thesis are:

1. Extraction of spatially distributed local flame transfer function from the high fidelity simulation using dynamic mode decomposition and its integration with nonlinear Euler solver

2. Verification of the proposed approach and its application to the Continuously Variable Resonance Combustor (CVRC).

3. Sensitivity analysis of the reduced fidelity model to control parameters such as the number of modes included in the FTF, the number of sampling points used in the Fourier transform of the unsteady heat release, and mesh size.

The goal of this thesis is to contribute towards a reduced fidelity computational tool which can accurately predict the combustion instabilities in practical systems using flame transfer functions, by providing a path way for reduced fidelity multi-element simulation, and by defining the limitations associated with using flame transfer functions and nonlinear Euler equations for non-premixed flames.