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Cao, Xiande. "Volume and Surface Integral Equations for Solving Forward and Inverse Scattering Problems." UKnowledge, 2014. http://uknowledge.uky.edu/ece_etds/65.
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In this dissertation, a hybrid volume and surface integral equation is used to solve scattering problems. It is implemented with RWG basis on the surface and the edge basis in the volume. Numerical results shows the correctness of the hybrid VSIE in inhomogeneous medium. The MLFMM method is also implemented for the new VSIEs.
Further more, a synthetic apature radar imaging method is used in a 2D microwave imaging for complex objects. With the mono-static and bi-static interpolation scheme, a 2D FFT is applied for the imaging with the data simulated with VSIE method. Then we apply a background cancelling scheme to improve the imaging quality for the targets in interest. Numerical results shows the feasibility of applying the background canceling into wider applications.
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Pillain, Axelle. "Line, Surface, and Volume Integral Equations for the Electromagnetic Modelling of the Electroencephalography Forward Problem." Thesis, Télécom Bretagne, 2016. http://www.theses.fr/2016TELB0412/document.
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La reconstruction des sources de l'activité cérébrale à partir des mesures de potentiel fournies par un électroencéphalographie (EEG) nécessite de résoudre le problème connu sous le nom de « problème inverse de l'EEG ». La solution de ce problème dépend de la solution du « problème direct de l'EEG », qui fournit à partir de sources de courant connues, le potentiel mesuré au niveau des électrodes. Pour des modèles de tête réels, ce problème ne peut être résolut que de manière numérique. En particulier, les équations intégrales de surfaces requièrent uniquement la discrétisation des interfaces entre les différents compartiments constituant le milieu cérébral. Cependant, les formulations intégrales existant actuellement ne prennent pas en comptent l'anisotropie du milieu. Le travail présenté dans cette thèse introduit deux nouvelles formulations intégrales permettant de palier à cette faiblesse. Une formulation indirecte capable de prendre en compte l'anisotropie du cerveau est proposée. Elle est discrétisée à l'aide de fonctions conformes aux propriétés spectrales des opérateurs impliqués. L'effet de cette discrétisation de type mixe lors de la reconstruction des sources cérébrales est aussi étudié. La seconde formulation se concentre sur l'anisotropie due à la matière blanche. Calculer rapidement la solution du système numérique obtenu est aussi très désirable. Le travail est ainsi complémenté d'une preuve de l'applicabilité des stratégies de préconditionnement de type Calderon pour les milieux multicouches. Le théorème proposé est appliqué dans le contexte de la résolution du problème direct de l'EEG. Un préconditionneur de type Calderon est aussi introduit pour l'équation intégrale du champ électrique (EFIE) dans le cas de structures unidimensionnelles. Finalement, des résultats préliminaires sur l'impact d'un solveur rapide direct lors de la résolution rapide du problème direct de l'EEG sont présentésElectroencephalography (EEG) is a very useful tool for characterizing epileptic sources. Brain source imaging with EEG necessitates to solve the so-called EEG inverse problem. Its solution depends on the solution of the EEG forward problem that provides from known current sources the potential measured at the electrodes positions. For realistic head shapes, this problem can be solved with different numerical techniques. In particular surface integral equations necessitates to discretize only the interfaces between the brain compartments. However, the existing formulations do not take into account the anisotropy of the media. The work presented in this thesis introduces two new integral formulations to tackle this weakness. An indirect formulation that can handle brain anisotropies is proposed. It is discretized with basis functions conform to the mapping properties of the involved operators. The effect of this mixed discretization on brain source reconstruction is also studied. The second formulation focuses on the white matter fiber anisotropy. Obtaining the solution to the obtained numerical system rapidly is also highly desirable. The work is hence complemented with a proof of the preconditioning effect of Calderon strategies for multilayered media. The proposed theorem is applied in the context of solving the EEG forward problem. A Calderon preconditioner is also introduced for the wire electric field integral equation. Finally, preliminary results on the impact of a fast direct solver in solving the EEG forward problem are presented
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Aas, Rune Øistein. "Electromagnetic Scattering : A Surface Integral Equation Formulation." Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for fysikk, 2012. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-19240.
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A numerical approach to solving the problem of electromagnetic (EM) scattering on a single scatterer is studied. The problem involves calculating the total EM field in arbitrary observation points when a planar EM wave is scattered.The method considered is a surface integral equation (SIE) formulation involving the use of a dyadic Green's function. A theoretical derivation of the magnetic field integral equation (MFIE) and the electric field integral equation (EFIE) from Maxwell's equations are shown. The Method of Weighted Residuals (MWR) and Kirchoff's Approximation (KA) with their respective domains of application are studied as ways of estimating the surface current densities. A parallelized implementation of the SIE method including both the KA and the MWRis written using the FORTRAN language. The implementation is applied in three concrete versions of the scattering problem, all involving a spherical perfectly conducting scatterer, namely the cases of incoming wavelength much larger, much smaller and comparable with the radius of the scatterer. The problems are divided into two separate solution categories, separated by whether or not the KA is assumed valid. A recursive discretization algorithm was found to be superior to a Delaunay triangulationalgorithm due to less spread in element shape and area. The produced resultsfitted well considering the interference pattern and symmetry requirements with relative errors in the order of magnitude $10^{-5}$ and less. The case of having large wavelength compared to the radius was also compared with Rayleigh scattering theory considering the far field dependence on wavelenth, scattering angle and distance from the scatterer. This resulted in relative errors of 2.1 percent and less. The main advantage of the SIE method is only requiring the surface of the scatterer to be discretized thus saving computational time and memory compared to methods requiring discretization of volume. The method is also capable of producing accurate results for observation points arbitrary close to the scatterer surface. A brief discussion on how the program may be modified in order to extend its capabilities is also included.
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HENRY, CLEMENT BERNARD PIERRE. "Volume Integral Equation Methods for Forward and Inverse Bioelectromagnetic Approaches." Doctoral thesis, Politecnico di Torino, 2021. http://hdl.handle.net/11583/2914544.
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Wei, Jiangong. "Surface Integral Equation Methods for Multi-Scale and Wideband Problems." The Ohio State University, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=osu1408653442.
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Rockway, John Dexter. "Integral equation formulation for object scattering above a rough surface /." Thesis, Connect to this title online; UW restricted, 2001. http://hdl.handle.net/1773/5832.
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Caudron, Boris. "Couplages FEM-BEM faibles et optimisés pour des problèmes de diffraction harmoniques en acoustique et en électromagnétisme." Thesis, Université de Lorraine, 2018. http://www.theses.fr/2018LORR0062/document.
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Dans cette thèse, nous proposons de nouvelles méthodes permettant de résoudre numériquement des problèmes de diffraction harmoniques et tridimensionnels, aussi bien acoustiques qu'électromagnétiques, pour lesquels l'objet diffractant est pénétrable et inhomogène. La résolution de tels problèmes est centrale pour des calculs de surfaces équivalentes sonar et radar (SES et SER). Elle est toutefois connue pour être difficile car elle requiert de discrétiser des équations aux dérivées partielles posées dans un domaine extérieur. Étant infini, ce domaine ne peut pas être maillé en vue d'une résolution par la méthode des éléments finis volumiques. Deux approches classiques permettent de contourner cette difficulté. La première consiste à tronquer le domaine extérieur et rend alors possible une résolution par la méthode des éléments finis volumiques. Étant donné qu'elles approximent les problèmes de diffraction au niveau continu, les méthodes de troncature de domaine peuvent toutefois manquer de précision pour des calculs de SES et de SER. Les problèmes de diffraction harmoniques, pénétrables et inhomogènes peuvent également être résolus en couplant une formulation variationnelle volumique associée à l'objet diffractant et des équations intégrales surfaciques rattachées au domaine extérieur. Nous parlons de couplages FEM-BEM (Finite Element Method-Boundary Element Method). L'intérêt de cette approche réside dans le fait qu'elle est exacte au niveau continu. Les couplages FEM-BEM classiques sont dits forts car ils couplent la formulation variationnelle volumique et les équations intégrales surfaciques au sein d'une même formulation. Ils ne sont toutefois pas adaptés à la résolution de problèmes à haute fréquence. Pour pallier cette limitation, d'autres couplages FEM-BEM, dits faibles, ont été proposés. Ils correspondent concrètement à des algorithmes de décomposition de domaine itérant entre l'objet diffractant et le domaine extérieur. Dans cette thèse, nous introduisons de nouveaux couplages faibles FEM-BEM acoustiques et électromagnétiques basés sur des approximations de Padé récemment développées pour les opérateurs Dirichlet-to-Neumann et Magnetic-to-Electric. Le nombre d'itérations nécessaires à la résolution de ces couplages ne dépend que faiblement de la fréquence et du raffinement du maillage. Les couplages faibles FEM-BEM que nous proposons sont donc adaptés pour des calculs précis de SES et de SER à haute fréquenceIn this doctoral dissertation, we propose new methods for solving acoustic and electromagnetic three-dimensional harmonic scattering problems for which the scatterer is penetrable and inhomogeneous. The resolution of such problems is key in the computation of sonar and radar cross sections (SCS and RCS). However, this task is known to be difficult because it requires discretizing partial differential equations set in an exterior domain. Being unbounded, this domain cannot be meshed thus hindering a volume finite element resolution. There are two standard approaches to overcome this difficulty. The first one consists in truncating the exterior domain and renders possible a volume finite element resolution. Given that they approximate the scattering problems at the continuous level, truncation methods may however not be accurate enough for SCS and RCS computations. Inhomogeneous penetrable harmonic scattering problems can also be solved by coupling a volume variational formulation associated with the scatterer and surface integral equations related to the exterior domain. This approach is known as FEM-BEM coupling (Finite Element Method-Boundary Element Method). It is of great interest because it is exact at the continuous level. Classical FEM-BEM couplings are qualified as strong because they couple the volume variational formulation and the surface integral equations within one unique formulation. They are however not suited for solving high-frequency problems. To remedy this drawback, other FEM-BEM couplings, said to be weak, have been proposed. These couplings are actually domain decomposition algorithms iterating between the scatterer and the exterior domain. In this thesis, we introduce new acoustic and electromagnetic weak FEM-BEM couplings based on recently developed Padé approximations of Dirichlet-to-Neumann and Magnetic-to-Electric operators. The number of iterations required to solve these couplings is only slightly dependent on the frequency and the mesh refinement. The weak FEM-BEM couplings that we propose are therefore suited to accurate SCS and RCS computations at high frequencies
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Chen, Yongpin, and 陈涌频. "Surface integral equation method for analyzing electromagnetic scattering in layered medium." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2011. http://hub.hku.hk/bib/B4775283X.
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Surface integral equation (SIE) method with the kernel of layered medium Green's
function (LMGF) is investigated in details from several fundamental aspects. A
novel implementation of discrete complex image method (DCIM) is developed to
accelerate the evaluation of Sommerfeld integrals and especially improve the far
field accuracy of the conventional one. To achieve a broadband simulation of thin
layered structure such as microstrip antennas, the mixed-form thin-stratified
medium fast-multipole algorithm (MF-TSM-FMA) is developed by applying
contour deformation and combining the multipole expansion and plane wave
expansion into a single multilevel tree. The low frequency breakdown of the
integral operator is further studied and remedied by using the loop-tree
decomposition and the augmented electric field integral equation (A-EFIE), both
in the context of layered medium integration kernel. All these methods are based
on the EFIE for the perfect electric conductor (PEC) and hence can be applied in
antenna and circuit applications. To model general dielectric or magnetic objects,
the layered medium Green's function based on pilot vector potential approach is
generalized for both electric and magnetic current sources. The matrix
representation is further derived and the corresponding general SIE is setup.
Finally, this SIE is accelerated with the DCIM and applied in quantum optics,
such as the calculation of spontaneous emission enhancement of a quantum
emitter embedded in a layered structure and in the presence of nano scatterers.published_or_final_version
Electrical and Electronic Engineering
Doctoral
Doctor of Philosophy
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Grandison, Scott. "Boundary integral equation techniques in protein electrostatics and free surface flow problems." Thesis, University of East Anglia, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.410096.
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Hidle, Frederick B. "Application of the integral equation asymptotic phase method to penetrable scatterers." Thesis, Georgia Institute of Technology, 2001. http://hdl.handle.net/1853/15797.
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Zhu, Zhenhai 1970. "Efficient integral equation based algorithms for parasitic extraction of interconnects with smooth or rough surface." Thesis, Massachusetts Institute of Technology, 2004. http://hdl.handle.net/1721.1/28739.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2004.Includes bibliographical references (p. 187-198).
This thesis describes a few efficient parasitic extraction algorithms based on integral equation methods. It has two parts. Part one describes the algorithms used in FastImp, a program for accurate analysis of wide-band electromagnetic effects in very complicated geometries of conductors. The program is based on a recently developed surface integral formulation and a Pre-corrected FFT accelerated iterative method, but includes a new piecewise quadrature panel integration scheme, a new scaling and preconditioning technique as well as a generalized grid interpolation and projection strategy. Computational results are given on a variety of integrated circuit interconnect structures to demonstrate that FastImp is robust and can accurately analyze very complicated geometries of conductors. Part two describes an efficient Stochastic Integral Equation (SIE) Method for computing the mean value and variance of the capacitance of interconnects with random surface roughness in O(Nlog2Ì(N)) time. An ensemble average Green's function is used to account for the surface roughness. A second-order correction scheme is used to improve the accuracy. A sparsification technique based on the Hierarchical Matrix method is proposed to significantly reduce the computational cost. The SIE method avoids the time-consuming Monte Carlo simulations and the discretization of rough surfaces. Numerical experiments show that the results of the new method agree very well with those of Monte Carlo simulations.
by Zhenhai Zhu.
Ph.D.
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Rahman, Mohammed Magfurar. "MAPPING SURFACE SOIL MOISTURE AND ROUGHNESS BY RADAR REMOTE SENSING IN THE SEMI-ARID ENVIRONMENT." Diss., Tucson, Arizona : University of Arizona, 2005. http://etd.library.arizona.edu/etd/GetFileServlet?file=file:///data1/pdf/etd/azu%5Fetd%5F1193%5F1%5Fm.pdf&type=application/pdf.
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Johnson, Jedediah Edward Jensen. "Computationally Modeling the Effects of Surface Roughness on Soft X-Ray Multilayer Reflectors." Diss., CLICK HERE for online access, 2006. http://contentdm.lib.byu.edu/ETD/image/etd1626.pdf.
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Ozdemir, Nilufer A. "The method of moments solution of a nonconformal volume integral equation via the IE-FFT algorithm for electromagnetic scattering from penetrable objects." Columbus, Ohio : Ohio State University, 2007. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1182258230.
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Yu, Chunshui. "Two Dimensional Finite Volume Model for Simulating Unsteady Turbulent Flow and Sediment Transport." Diss., The University of Arizona, 2013. http://hdl.handle.net/10150/301662.
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The two-dimensional depth-averaged shallow water equations have attracted considerable attentions as a practical way to solve flows with free surface. Compared to three-dimensional Navier-Stokes equations, the shallow water equations give essentially the same results at much lower cost. Solving the shallow water equations by the Godunov-type finite volume method is a newly emerging area. The Godunov-type finite volume method is good at capturing the discontinuous fronts in numerical solutions. This makes the method suitable for solving the system of shallow water equations. In this dissertation, both the shallow water equations and the Godunov-type finite volume method are described in detail. A new surface flow routing method is proposed in the dissertation. The method does not limit the shallow water equations to open channels but extends the shallow water equations to the whole domain. Results show that the new routing method is a promising method for prediction of watershed runoff. The method is also applied to turbulence modeling of free surface flow. The κ - ε turbulence model is incorporated into the system of shallow water equations. The outcomes prove that the turbulence modeling is necessary for calculation of free surface flow. At last part of the dissertation, a total load sediment transport model is described and the model is tested against 1D and 2D laboratory experiments. In summary, the proposed numerical method shows good potential in solving free surface flow problems. And future development will be focusing on river meandering simulation, non-equilibrium sediment transport and surface flow - subsurface flow interaction.
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Strydom, Willem Jacobus. "Recovery based error estimation for the Method of Moments." Thesis, Stellenbosch : Stellenbosch University, 2015. http://hdl.handle.net/10019.1/96881.
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Thesis (MEng)--Stellenbosch University, 2015.ENGLISH ABSTRACT: The Method of Moments (MoM) is routinely used for the numerical solution of electromagnetic surface integral equations. Solution errors are inherent to any numerical computational method, and error estimators can be effectively employed to reduce and control these errors. In this thesis, gradient recovery techniques of the Finite Element Method (FEM) are formulated within the MoM context, in order to recover a higher-order charge of a Rao-Wilton-Glisson (RWG) MoM solution. Furthermore, a new recovery procedure, based specifically on the properties of the RWG basis functions, is introduced by the author. These recovered charge distributions are used for a posteriori error estimation of the charge. It was found that the newly proposed charge recovery method has the highest accuracy of the considered recovery methods, and is the most suited for applications within recovery based error estimation. In addition to charge recovery, the possibility of recovery procedures for the MoM solution current are also investigated. A technique is explored whereby a recovered charge is used to find a higher-order divergent current representation. Two newly developed methods for the subsequent recovery of the solenoidal current component, as contained in the RWG solution current, are also introduced by the author. A posteriori error estimation of the MoM current is accomplished through the use of the recovered current distributions. A mixed second-order recovered current, based on a vector recovery procedure, was found to produce the most accurate results. The error estimation techniques developed in this thesis could be incorporated into an adaptive solver scheme to optimise the solution accuracy relative to the computational cost.
AFRIKAANSE OPSOMMING: Die Moment Metode (MoM) vind algemene toepassing in die numeriese oplossing van elektromagnetiese oppervlak integraalvergelykings. Numeriese foute is inherent tot die prosedure: foutberamingstegnieke is dus nodig om die betrokke foute te analiseer en te reduseer. Gradiënt verhalingstegnieke van die Eindige Element Metode word in hierdie tesis in die MoM konteks geformuleer. Hierdie tegnieke word ingespan om die oppervlaklading van 'n Rao-Wilton-Glisson (RWG) MoM oplossing na 'n verbeterde hoër-orde voorstelling te neem. Verder is 'n nuwe lading verhalingstegniek deur die outeur voorgestel wat spesifiek op die eienskappe van die RWG basis funksies gebaseer is. Die verhaalde ladingsverspreidings is geïmplementeer in a posteriori fout beraming van die lading. Die nuut voorgestelde tegniek het die akkuraatste resultate gelewer, uit die groep verhalingstegnieke wat ondersoek is. Addisioneel tot ladingsverhaling, is die moontlikheid van MoM-stroom verhalingstegnieke ook ondersoek. 'n Metode vir die verhaling van 'n hoër-orde divergente stroom komponent, gebaseer op die verhaalde lading, is geïmplementeer. Verder is twee nuwe metodes vir die verhaling van die solenodiale komponent van die RWG stroom deur die outeur voorgestel. A posteriori foutberaming van die MoM-stroom is met behulp van die verhaalde stroom verspreidings gerealiseer, en daar is gevind dat 'n gemengde tweede-orde verhaalde stroom, gebaseer op 'n vektor metode, die beste resultate lewer. Die foutberamingstegnieke wat in hierdie tesis ondersoek is, kan in 'n aanpasbare skema opgeneem word om die akkuraatheid van 'n numeriese oplossing, relatief tot die berekeningskoste, te optimeer.
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Sakly, Hamdi. "Opérateur intégral volumique en théorie de diffraction électromagnétique." Thesis, Rennes 1, 2014. http://www.theses.fr/2014REN1S028.
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Le problème de diffraction électromagnétique gouverné par les équations de Maxwell admet une formulation équivalente par une équation intégrale volumique fortement singulière. Cette thèse a pour but d'examiner l'opérateur intégral qui décrit cette équation. La première partie de ce manuscrit porte sur l'étude de son spectre essentiel. Cette analyse est intéressante en vue d'obtenir les conditions nécessaires et suffisantes pour avoir l'unicité de solutions du problème surtout quand il s'agirait de la diffraction des ondes par des matériaux négatifs où les techniques classiques perdent leurs utilité. Après avoir justifié le bon choix du cadre fonctionnel, nous étudions tout d'abord le cas où les paramètres caractéristiques du milieu à savoir la permittivité électrique et la perméabilité magnétique sont constants par morceaux avec discontinuité au travers du bord de la cible. Dans ce cadre, nous donnons une réponse complète à la question pour les domaines réguliers et Lipschitziens. Ensuite, et à l'aide d'une technique de localisation, nous donnons une extension de ces résultats dans le cas des paramètres réguliers par morceaux pour deux opérateurs intégraux, l'un qui correspond à la version diélectrique du problème et l'autre pour sa version magnétique. Nous terminons cette thèse par l'étude de la dérivée de forme des opérateurs diélectrique et magnétique et nous en déduisons une nouvelle caractérisation de la dérivée de forme des solutions des deux problèmes de diffractionThe electromagnetic diffraction problem which is governed by the Maxwell equations admits an equivalent formulation in terms of a strongly singular volume integral equation. This thesis aims to examine the integral operator that describes this equation. The first part of this document focuses on the study of its essential spectrum. This analysis is interesting to get the necessary and sufficient conditions of solution uniqueness of the problem especially when we consider the diffraction of waves by negative materials where classic tools lose their usefulness. After justifying the adequate choice of the functional framework, we first study the case where the characteristics parameters of the medium like the electric permittivity and magnetic permeability are piecewise constant with discontinuity across the boundary of the target. In this context, we give a full answer to the question for smooth and Lipschitz domains. Then, by using a localization technique, we give an extension of those results in the case of piecewise regular parameters for two integrals operators, one which corresponds to the dielectric version of the problem and the other for its magnetic version. We end this thesis by the study of the shape derivative of the dielectric and magnetic operators and we derive a new characterization of the shape derivative of the two diffraction problems solution
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Dorosh, Anastasiia. "Design of Microstrip Microwave Devices with Lumped Elements by Means of Modern CADs." Thesis, Linnéuniversitetet, Institutionen för fysik och elektroteknik (IFE), 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-30365.
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In this report the analysis of microstrip electrodynamic structures on basis of high-temperature superconductors is carried out and a mathematical model of microstrip devices with lumped and distributed nonlinear properties is created. For this purpose nonlinear integral equations method and method of moments are used. In the issue of the work a SHF filter based on the equivalent circuit of elements with lumped parameters is also studied. It is ascertained that the received mathematical model allows to achieve more proper results of modeling on compensation of variation of current-density distribution nearby the edges of conductor break.
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Bertoco, Juliana. "Solução numérica do modelo constitutivo KBKZ-PSM para escoamentos com superfícies livres." Universidade de São Paulo, 2016. http://www.teses.usp.br/teses/disponiveis/55/55134/tde-16012017-162912/.
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Escoamentos viscoelásticos não estacionários com superfícies livres são comuns em muitos processos industriais e diversas técnicas numéricas têm sido empregadas para reproduzir computacionalmente estes processos. A maioria dos modelos empregados utiliza equações diferenciais na definição do tensor de tensões. Porém, para alguns grupos de fluidos complexos, por exemplo, fluidos de Boger, os modelos integrais mostram-se mais capacitados em fornecer uma boa aproximação para os comportamentos não lineares desses fluidos. Este trabalho trata da solução numérica do modelo constitutivo integral KBKZ-PSM para escoamentos transientes bidimensionais com superfícies livres. O método numérico proposto é uma técnica numérica que utiliza diferenças finitas para simular escoamentos com superfícies livres na presença de paredes sólidas. As principais características do método numérico proposto são: solução das equações de conservação de quantidade de movimento e massa utilizando um método semi-implícito; a condição de contorno na superfície livre é acoplada à equação de Poisson, o que garante conservação de massa; a discretização do tempo t é realizada por uma nova técnica numérica; o tensor de Finger é calculado pelo método dos campos de deformação e avançado no tempo pelo método de Euler modificado. Essa nova técnica é verificada em escoamentos cisalhantes e elongacionais. Adicionalmente, uma solução analítica desenvolvida para escoamentos em canais bidimensionais é empregada para verificar e analisar a convergência do método proposto. Com relação a escoamentos com superfícies livres, a convergência é verificada por meio de refinamento de malha nas simulações de um jato incidindo sobre placa rígida e no problema do inchamento do extrudado. Finalmente, o método é aplicado para investigar os problemas jet buckling e inchamento do extrudado de fluidos KBKZ-PSM.Unsteady viscoelastic free surface flows are common in many industrial processes and a variety of numerical techniques have been employed to simulate these flows. The majority of constitutive models employed are based on differential equations to define the extra stress tensor. However, for some complex fluids, for instance, Boger fluids, integral models are more adequate to approximate the nonlinear behaviour of these fluids. This work deals with the numerical solution of the integral constitutive model KBKZ-PSM for two-dimensional unsteady free surface flows. The proposed numerical method is a numerical technique that employs finite differences to simulate moving free surface flows that interact with solid walls. The main features of the method are: numerical solution of the momentum and mass equations by an implicit method; the pressure condition on the free surface is implicitly coupled with the Poisson equation for obtaining the pressure field from mass conservation; a novel scheme for defining the past times t is employed; the Finger tensor is calculated by the deformation fields method and is advanced in time by the modified Euler method. This new technique is verified by solving shear and uniaxial elongational flows. Moreover, an analytic solution for channel flows is obtained that is used in the verification and convergence analysis of the proposed methodology. For free surface flows, the assessment of convergence lies on the mesh refinement on the simulation of a jet impinging on a flat surface and the extrudade swell problem. Finally, the new method is applied to investigate the jet buckling phenomenon and extrudate swell of KBKZ-PSM fluids.
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Gtet, Abdelfatah. "Calcul asymptotique de résonances de plasmon de cavités rectangulaires." Thesis, Université Grenoble Alpes (ComUE), 2017. http://www.theses.fr/2017GREAM096/document.
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La diffraction d'une onde électromagnétique par une structure présentant des échelles d'espace petites devant la longueur d'onde est un phénomène complexe qui décrit à la fois l'interaction entre l'onde et la géométrie de la structure et la matière qui la constitue. Quand la fréquence n'est pas résonnante, l'onde incidente interagit faiblement avec des petites irrégularités de la structure. En langage mathématique, ceci se traduit par le fait que la différence entre les champs électromagnétiques de la structure perturbée et ceux de la structure de référence est de l'ordre de la perturbation. Par contre, quand la fréquence est résonante, le comportement de l'onde est très sensible aux petites déformations singulières de la géométrie de la structure. Cette sensibilité est susceptible d'être détectée dans les mesures du champ lointain, et est la brique de base de plusieurs capteurs et filtres plasmoniques. Dans ce projet de thèse nous nous sommes intéressés aux propriétés optiques de surfaces métalliques comportant des cavités sub-longueur d'onde distribués périodiquement ou non, et de couches métalliques minces. Ces structures possèdent des résonances électromagnétiques proches de l’axe réel, et sont capables de concentrer l’énergie électromagnétique dans des volumes bien inférieurs à la cubique de la longueur d’onde incidente. La compréhension de ce phénomène est un enjeu important pour le développement des spectroscoepies ultra-sensibles, mais aussi dans le domaine des bio-capteurs et de l’opto-électronique. En utilisant des techniques asymptotiques couplées avec des équations intégrales, nous avons déterminé le développement asymptotique des fréquences de résonance de ces structures quand le rapport entre l'échelle de la structuration spatiale et la longueur d'onde tend vers zéro. Les modèles asymptotiques dérivés sont beaucoup plus simples à étudier et à simuler et rendent parfaitement compte des résultats expérimentaux. Ils permettent de prédire les fréquences résonnantes, la quantité d’énergie localisée en fonction de la géométrie des structures et des propriétés des matériaux qui les constituentRough metallic surfaces with subwavelength structurations possess extraordinary diffractive properties: at certain frequencies, one may observe fine localization and very large enhancement of the electromagnetic fields. The discovery of these phenomena has raised considerable interest as potential applications are numerous (optical switches, sensors, devices for microscopy). This behavior results from the combination of very complex interaction between the incident excitation, the geometry and the material properties of the scatterer. The main goal of this thesis is to better understand these phenomena from the mathematical point of view.In mathematical terms, the localization and concentration of the fields is the mark of a resonance phenomenon. In our context, the corresponding resonant field may be surface plasmons, i.e., waves that propagate along the interface of the grating, and that decay exponentially away from it. Another type of resonance is due to possible cavity modes. Thus, the study of these phenomena pertains to eigenvalue problems for the solutions of the Maxwell system, in geometric configurations where in the whole of a dielectric (generally air) and a metal are separated by an infinite rough interface.We are interested in particular micro-structured devices, namely metallic surfaces that contain rectangular grooves with sub-wavelength apertures, and thin plane layers. Configurations of this type can be manufactured quite precisely and have been subject to many experimental works. The simple geometry of these structures allows us to transform the eigenvalue problem for the Maxwell system into a nonlinear eigenvalue problem for an integral operator that depends on a small parameter, which, using tools from analytic perturbation of operators theory, lends itself to a precise asymptotic analysis. Precisely, we showed that the resonances of these structures converge tothe zeros of some explicit dispersion equations when the ratio between the roughness parameter and the wavelength tends to zero. These asymptotic models provide a precise localization of the resonances in the complex plane, and are suited for numerical approximation, shape and material optimization
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Kulkarni, Shashank D. "Development and validation of a Method of Moments approach for modeling planar antenna structures." Worcester, Mass. : Worcester Polytechnic Institute, 2007. http://www.wpi.edu/Pubs/ETD/Available/etd-042007-151741/.
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Dissertation (Ph.D.)--Worcester Polytechnic Institute.Keywords: patch antennas; volume integral equation (VIE); method of moments (MoM); low order basis functions; convergence. Includes bibliographical references (leaves 169-186 ).
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Fenni, Ines. "Efficient domain decomposition methods for electromagnetic modeling of scattering from forest environments." Thesis, Paris 6, 2014. http://www.theses.fr/2014PA066264/document.
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Cette thèse porte sur la modélisation et l’analyse de la propagation électromagnétique dans un milieu forestier dans les bandes VHF et UHF. L’objectif principal est le développement d’un modèle numérique "full-wave" tridimensionnel de diffusion par la forêt permettant de caractériser l’interaction d’une onde électromagnétique avec un milieu forestier. Un tel modèle s’avère, actuellement, un outil indispensable à l’analyse des mesures radar pour l’étude des paramètres caractéristiques de la forêt tels que la biomasse forestière, la hauteur des arbres et leur densité. La complexité numérique de ce modèle a limité son domaine d’application à de petites parcelles de forêt et aux basses fréquences. Pour pouvoir traiter de larges zones forestières tout en montant en fréquence, et s’approcher ainsi des besoins et exigences des utilisateurs potentiels de notre modèle, nous avons intégré à ce modèle une méthode numérique efficace dédiée à l’analyse de larges problèmes électromagnétiques. La méthode en question,connue sous le nom de Characteristic Basis Function Method (CBFM) était récemment développée dans le laboratoire de Communication et Electromagnétisme de l’université PennState dirigé par le Professeur Mittra. Après une optimisation et une adaptation au problème d’intérêt, la CBFM réalise d’excellentes performances et nous permet une diminution considérable du temps de calcul et des besoins en espace mémoire sans pour autant dégrader la qualité des résultats obtenus ou altérer la fidélité du modèle à la réalité du problème électromagnétique traitéA 3-D full-wave model, based on the integral representation of the electric field and dedicatedto the analysis of bi-static scattering mechanisms by a forest in the VHF and UHF bands wasefficiently enhanced. In order to overcome the limitation of a previous 3D model to small simulationsscenes and low frequencies, we have developed, during this research work, a new model using basis functionsadapted to the problem of interest, in the context of the Characteristic Basis Function Method(CBFM) and we investigated the suitability of this direct method for computing the electromagneticfields inside and outside three-dimensional dielectric objects representing the tree trunks and branches.The CBFM has shown great performances, when applied to the forest scattering modeling, both interms of CPU time and memory resources needed. Once properly set, the CBFM-E is so efficient thatit is able to treat in few minutes electromagnetic problems totally intractable with the classical MoM.Consequently, we have developed a powerful 3D forest electromagnetic scattering tool which allows ustoday to compute large forest electromagnetic problems in few minutes without worrying about theaccuracy of the solution. On the other hand, we have demonstrated the efficiency and accuracy of theCBFM-E when applied to 3D dielectric objects in the context of the electric volumetric integral equation,and have consolidated thus its leading position in the computational electromagnetics, especiallyagainst the iterative solvers based numerical methods
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Ha, Duong Tuong. "Equations intégrales pour la résolution numérique de problèmes de diffraction d'ondes acoustiques dans R**(3)." Paris 6, 1987. http://www.theses.fr/1987PA066420.
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Résolution de problème extérieur pour l'équation des ondes. Etude du cas des ondes harmoniques. Méthode de Schenk, Méthode variationnelle de Nedelec, proposition d'un nouveau système d'équations intégrales pour la résolution du problème du mur absorbant. Analyse de diverses fonctions intégrales pouvant être utilisées pour des calculs d'ondes transitoires (emploi de formules de potentiels retardés). Proposition d'un cadre fonctionnel lié aux formules d'énergie des ondes. Formulations variationnelles espace temps et shémas de type Galerkin basés sur ces mêmes formules d'énergie. Analyse des schémas de type collocation utiles pour discrétiser l'équation intégrale de Kirchoff.
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Machane, Rabha. "Contribution de la méthode intégrale aux frontières au suivi d'interfaces." Université Joseph Fourier (Grenoble ; 1971-2015), 1997. http://www.theses.fr/1997GRE10163.
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Ce travail de these est consacre a l'application des methodes integrales aux frontieres a la simulation numerique des ecoulements non-lineaires a frontieres libres. Deux principales parties peuvent etre distinguees. L'une, est consacree au probleme de la progression en temps dans le cadre d'une approximation potentielle et plus precisement l'etablissement d'une procedure de suivi d'interfaces fondee sur des schemas explicites d'ordres eleves issus de developpements en serie de taylor. L'autre, propose une methode generale pour resoudre les equations de navier-stokes fondee sur une formulation entierement integrale. Basee sur la decomposition de helmholtz, notre demarche porte sur l'etablissement de conditions aux limites et de projection associees a l'equation de transport du tourbillon. Cette etude met en evidence les avantages d'une formulation integrale qui ne sont pas seulement theoriques et numeriques. Ils apportent en effet un eclairage sur la comprehension des phenomenes de la genese et la propagation de la vorticite.
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Mumcu, Gokhan. "EM Characterization of Magnetic Photonic / Degenerate Band Edge Crystals and Related Antenna Realizations." Columbus, Ohio : Ohio State University, 2008. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1221860344.
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Johansen, Jonathan Frederick. "Mathematical modelling of primary alkaline batteries." Thesis, Queensland University of Technology, 2007. https://eprints.qut.edu.au/16412/1/Jonathan_Johansen_Thesis.pdf.
Full textAbstract:
Three mathematical models, two of primary alkaline battery cathode discharge, and one of primary alkaline battery discharge, are developed, presented, solved and investigated in this thesis. The primary aim of this work is to improve our understanding of the complex, interrelated and nonlinear processes that occur within primary alkaline batteries during discharge.
We use perturbation techniques and Laplace transforms to analyse and simplify an existing model of primary alkaline battery cathode under galvanostatic discharge. The process highlights key phenomena, and removes those phenomena that have very little effect on discharge from the model. We find that electrolyte variation within Electrolytic Manganese Dioxide (EMD) particles is negligible, but proton diffusion within EMD crystals is important. The simplification process results in a significant reduction in the number of model equations, and greatly decreases the computational overhead of the numerical simulation software. In addition, the model results based on this simplified framework compare well with available experimental data.
The second model of the primary alkaline battery cathode discharge simulates step potential electrochemical spectroscopy discharges, and is used to improve our understanding of the multi-reaction nature of the reduction of EMD. We find that a single-reaction framework is able to simulate multi-reaction behaviour through the use of a nonlinear ion-ion interaction term.
The third model simulates the full primary alkaline battery system, and accounts for the precipitation of zinc oxide within the separator (and other regions), and subsequent internal short circuit through this phase. It was found that an internal short circuit is created at the beginning of discharge, and this self-discharge may be exacerbated by discharging the cell intermittently. We find that using a thicker separator paper is a very effective way of minimising self-discharge behaviour.
The equations describing the three models are solved numerically in MATLABR, using three pieces of numerical simulation software. They provide a flexible and powerful set of primary alkaline battery discharge prediction tools, that leverage the simplified model framework, allowing them to be easily run on a desktop PC.
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Johansen, Jonathan Frederick. "Mathematical modelling of primary alkaline batteries." Queensland University of Technology, 2007. http://eprints.qut.edu.au/16412/.
Full textAbstract:
Three mathematical models, two of primary alkaline battery cathode discharge, and one of primary alkaline battery discharge, are developed, presented, solved and investigated in this thesis. The primary aim of this work is to improve our understanding of the complex, interrelated and nonlinear processes that occur within primary alkaline batteries during discharge. We use perturbation techniques and Laplace transforms to analyse and simplify an existing model of primary alkaline battery cathode under galvanostatic discharge. The process highlights key phenomena, and removes those phenomena that have very little effect on discharge from the model. We find that electrolyte variation within Electrolytic Manganese Dioxide (EMD) particles is negligible, but proton diffusion within EMD crystals is important. The simplification process results in a significant reduction in the number of model equations, and greatly decreases the computational overhead of the numerical simulation software. In addition, the model results based on this simplified framework compare well with available experimental data. The second model of the primary alkaline battery cathode discharge simulates step potential electrochemical spectroscopy discharges, and is used to improve our understanding of the multi-reaction nature of the reduction of EMD. We find that a single-reaction framework is able to simulate multi-reaction behaviour through the use of a nonlinear ion-ion interaction term. The third model simulates the full primary alkaline battery system, and accounts for the precipitation of zinc oxide within the separator (and other regions), and subsequent internal short circuit through this phase. It was found that an internal short circuit is created at the beginning of discharge, and this self-discharge may be exacerbated by discharging the cell intermittently. We find that using a thicker separator paper is a very effective way of minimising self-discharge behaviour. The equations describing the three models are solved numerically in MATLABR, using three pieces of numerical simulation software. They provide a flexible and powerful set of primary alkaline battery discharge prediction tools, that leverage the simplified model framework, allowing them to be easily run on a desktop PC.
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Maitre, Emmanuel. "Sur une classe d'équations à double non linéarité : application à la simulation numérique d'un écoulement visqueux compressible." Phd thesis, Université Joseph Fourier (Grenoble), 1997. http://tel.archives-ouvertes.fr/tel-00004955.
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L'origine de ce travail est l'étude d'un problème industriel sur la mise en forme des thermoplastiques par injection. Nous nous sommes concentrés sur la partie remplissage du moule et sur la détermination de la position du front du polymère. Le travail présenté dans cette thèse comprend donc deux parties: => L'étude mathématique et numérique de l'équation en pression qui régit l'écoulement du polymère fondu. A partir de cet exemple nous avons mis en évidence et étudié une famille nouvelle d'équations à double non linéarité. => La détermination de l'interface polymère-air par des méthodes de suivi de lignes de niveau, l'interface étant décrite comme la ligne de niveau zéro d'une inconnue auxiliaire, que nous devons calculer. Nous avons obtenu l'existence d'une solution à l'équation de transport linéaire avec conditions aux limites à laquelle satisfait cette nouvelle inconnue. Puis nous avons mis au point une méthode numérique pour le calcul de l'interface polymère/air, en résolvant par éléments finis / volumes finis l'équation en pression et l'équation de transport du front. Notre méthode présente l'avantage d'une mise en oeuvre relativement aisée, robuste car elle permet de gérer les changements de topologie du front.
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Noviani, Evi. "Shape optimisation for the wave-making resistance of a submerged body." Thesis, Poitiers, 2018. http://www.theses.fr/2018POIT2298/document.
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Dans cette thèse, nous calculons la forme d’un objet immergé d’aire donnée qui minimise la résistance de vague. Le corps, considéré lisse, avance à vitesse constante sous la surface libre d’un fluide qui est supposé parfait et incompressible. La résistance de vague est la traînée, c’est-à-dire la composante horizontale de la force exercée par le fluide sur l’obstacle. Nous utilisons les équations de Neumann-Kelvin 2D, qui s’obtiennent en linéarisant les équations d’Euler irrotationnelles avec surface libre. Le problème de Neumann-Kelvin est formulé comme une équation intégrale de frontière basée sur une solution fondamentale qui intègre la condition linéarisée à la surface libre. Nous utilisons une méthode de descente de gradient pour trouver un minimiseur local du problème de résistance de vague. Un gradient par rapport à la forme est calculé par la méthode de variation de frontières. Nous utilisons une approche level-set pour calculer la résistance de vague et gérer les déplacements de la frontière de l’obstacle. Nous obtenons une grande variété de formes optimales selon la profondeur de l’objet et sa vitesseIn this thesis, we compute the shape of a fully immersed object with a given area which minimises the wave resistance. The smooth body moves at a constant speed under the free surface of a fluid which is assumed to be inviscid and incompressible. The wave resistance is the drag, i.e. the horizontal component of the force exerted by the fluid on the obstacle. We work with the 2D Neumann-Kelvin equations, which are obtained by linearising the irrotational Euler equations with a free surface. The Neumann-Kelvin problem is formulated as a boundary integral equation based on a fundamental solution which handles the linearised free surface condition. We use a gradient descent method to find a local minimiser of the wave resistance problem. A gradient with respect to the shape is calculated by a boundary variation method. We use a level-set approach to calculate the wave-making resistance and to deal with the displacements of the boundary of the obstacle. We obtain a great variety of optimal shapes depending on the depth of the object and its velocity
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Farquhar, Megan Elizabeth. "Cardiac modelling with fractional calculus: An efficient computational framework for modelling the propagation of electrical impulses in the heart." Thesis, Queensland University of Technology, 2018. https://eprints.qut.edu.au/120682/1/__qut.edu.au_Documents_StaffHome_StaffGroupH%24_halla_Desktop_Megan_Farquhar_Thesis.pdf.
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Heart failure is one of the most common causes of death in the western world. Many heart problems are linked to disturbances in cardiac electrical activity. Further understanding of how electrical impulses propagate through the heart may lead to new diagnosis and treatment options.
Using our novel numerical scheme, we are able to conduct preliminary investigations into the effect of fixed and variable order fractional Laplacian operators for modelling propagation of electrical impulses through the heart. We implement our numerical framework to solve the coupled monodomain, Beeler-Reuter model. Preliminary results confirm the effectiveness of our numerical scheme, and pave the way to exciting areas of future research.
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Watson, Francis Maurice. "Better imaging for landmine detection : an exploration of 3D full-wave inversion for ground-penetrating radar." Thesis, University of Manchester, 2016. https://www.research.manchester.ac.uk/portal/en/theses/better-imaging-for-landmine-detection-an-exploration-of-3d-fullwave-inversion-for-groundpenetrating-radar(720bab5f-03a7-4531-9a56-7121609b3ef0).html.
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Humanitarian clearance of minefields is most often carried out by hand, conventionally using a a metal detector and a probe. Detection is a very slow process, as every piece of detected metal must treated as if it were a landmine and carefully probed and excavated, while many of them are not. The process can be safely sped up by use of Ground-Penetrating Radar (GPR) to image the subsurface, to verify metal detection results and safely ignore any objects which could not possibly be a landmine. In this thesis, we explore the possibility of using Full Wave Inversion (FWI) to improve GPR imaging for landmine detection. Posing the imaging task as FWI means solving the large-scale, non-linear and ill-posed optimisation problem of determining the physical parameters of the subsurface (such as electrical permittivity) which would best reproduce the data. This thesis begins by giving an overview of all the mathematical and implementational aspects of FWI, so as to provide an informative text for both mathematicians (perhaps already familiar with other inverse problems) wanting to contribute to the mine detection problem, as well as a wider engineering audience (perhaps already working on GPR or mine detection) interested in the mathematical study of inverse problems and FWI.We present the first numerical 3D FWI results for GPR, and consider only surface measurements from small-scale arrays as these are suitable for our application. The FWI problem requires an accurate forward model to simulate GPR data, for which we use a hybrid finite-element boundary-integral solver utilising first order curl-conforming N\'d\'{e}lec (edge) elements. We present a novel `line search' type algorithm which prioritises inversion of some target parameters in a region of interest (ROI), with the update outside of the area defined implicitly as a function of the target parameters. This is particularly applicable to the mine detection problem, in which we wish to know more about some detected metallic objects, but are not interested in the surrounding medium. We may need to resolve the surrounding area though, in order to account for the target being obscured and multiple scattering in a highly cluttered subsurface. We focus particularly on spatial sensitivity of the inverse problem, using both a singular value decomposition to analyse the Jacobian matrix, as well as an asymptotic expansion involving polarization tensors describing the perturbation of electric field due to small objects. The latter allows us to extend the current theory of sensitivity in for acoustic FWI, based on the Born approximation, to better understand how polarization plays a role in the 3D electromagnetic inverse problem. Based on this asymptotic approximation, we derive a novel approximation to the diagonals of the Hessian matrix which can be used to pre-condition the GPR FWI problem.
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Chiocchetti, Simone. "High order numerical methods for a unified theory of fluid and solid mechanics." Doctoral thesis, Università degli studi di Trento, 2022. http://hdl.handle.net/11572/346999.
Full textAbstract:
This dissertation is a contribution to the development of a unified model of
continuum mechanics, describing both fluids and elastic solids as a general
continua, with a simple material parameter choice being the distinction
between inviscid or viscous fluid, or elastic solids or visco-elasto-plastic
media. Additional physical effects such as surface tension, rate-dependent
material failure and fatigue can be, and have been, included in the same
formalism.
The model extends a hyperelastic formulation of solid mechanics in
Eulerian coordinates to fluid flows by means of stiff algebraic relaxation
source terms. The governing equations are then solved by means of high
order ADER Discontinuous Galerkin and Finite Volume schemes on fixed
Cartesian meshes and on moving unstructured polygonal meshes with
adaptive connectivity, the latter constructed and moved by means of a in-
house Fortran library for the generation of high quality Delaunay and Voronoi
meshes.
Further, the thesis introduces a new family of exponential-type and semi-
analytical time-integration methods for the stiff source terms governing
friction and pressure relaxation in Baer-Nunziato compressible multiphase
flows, as well as for relaxation in the unified model of continuum mechanics,
associated with viscosity and plasticity, and heat conduction effects.
Theoretical consideration about the model are also given, from the
solution of weak hyperbolicity issues affecting some special cases of the
governing equations, to the computation of accurate eigenvalue estimates, to
the discussion of the geometrical structure of the equations and involution
constraints of curl type, then enforced both via a GLM curl cleaning method,
and by means of special involution-preserving discrete differential operators,
implemented in a semi-implicit framework.
Concerning applications to real-world problems, this thesis includes
simulation ranging from low-Mach viscous two-phase flow, to shockwaves in
compressible viscous flow on unstructured moving grids, to diffuse interface
crack formation in solids.
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Karimou, Gazibo Mohamed. "Etudes mathématiques et numériques des problèmes paraboliques avec des conditions aux limites." Phd thesis, Université de Franche-Comté, 2013. http://tel.archives-ouvertes.fr/tel-00950759.
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Cette thèse est centrée autour de l'étude théorique et de l'analyse numérique des équations paraboliques non linéaires avec divers conditions aux limites. La première partie est consacrée aux équations paraboliques dégénérées mêlant des phénomènes non-linéaires de diffusion et de transport. Nous définissons des notions de solutions entropiques adaptées pour chacune des conditions aux limites (flux nul, Robin, Dirichlet). La difficulté principale dans l'étude de ces problèmes est due au manque de régularité du flux pariétal pour traiter les termes de bords. Ceci pose un problème pour la preuve d'unicité. Pour y remédier, nous tirons profit du fait que ces résultats de régularités sur le bord sont plus faciles à obtenir pour le problème stationnaire et particulièrement en dimension un d'espace. Ainsi par la méthode de comparaison "fort-faible" nous arrivons à déduire l'unicité avec le choix d'une fonction test non symétrique et en utilisant la théorie des semi-groupes non linéaires. L'existence de solution se démontre en deux étapes, combinant la méthode de régularisation parabolique et les approximations de Galerkin. Nous développons ensuite une approche directe en construisant des solutions approchées par un schéma de volumes finis implicite en temps. Dans les deux cas, on combine les estimations dans les espaces fonctionnels bien choisis avec des arguments de compacité faible ou forte et diverses astuces permettant de passer à la limite dans des termes non linéaires. Notamment, nous introduisons une nouvelle notion de solution appelée solution processus intégrale dont l'objectif, dans le cadre de notre étude, est de pallier à la difficulté de prouver la convergence vers une solution entropique d'un schéma volumes finis pour le problème de flux nul au bord. La deuxième partie de cette thèse traite d'un problème à frontière libre décrivant la propagation d'un front de combustion et l'évolution de la température dans un milieu hétérogène. Il s'agit d'un système d'équations couplées constitué de l'équation de la chaleur bidimensionnelle et d'une équation de type Hamilton-Jacobi. L'objectif de cette partie est de construire un schéma numérique pour ce problème en combinant des discrétisations du type éléments finis avec les différences finies. Ceci nous permet notamment de vérifier la convergence de la solution numérique vers une solution onde pour un temps long. Dans un premier temps, nous nous intéressons à l'étude d'un problème unidimensionnel. Très vite, nous nous heurtons à un problème de stabilité du schéma. Cela est dû au problème de prise en compte de la condition de Neumann au bord. Par une technique de changement d'inconnue et d'approximation nous remédions à ce problème. Ensuite, nous adaptons cette technique pour la résolution du problème bidimensionnel. A l'aide d'un changement de variables, nous obtenons un domaine fixe facile pour la discrétisation. La monotonie du schéma obtenu est prouvée sous une hypothèse supplémentaire de propagation monotone qui exige que la frontière libre se déplace dans les directions d'un cône prescrit à l'avance.
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Padhy, Venkat Prasad. "Study of RCS from Aerodynamic Flow using Parallel Volume-Surface Integral Equation." Thesis, 2016. http://etd.iisc.ac.in/handle/2005/3104.
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Estimation of the Radar Cross Section of large inhomogeneous scattering objects such as composite aircrafts, ships and biological bodies at high frequencies has posed large computational challenge. The detection of scattering from wake vortex leading to detection and possible identification of low observable aircrafts also demand the development of computationally efficient and rigorous numerical techniques. Amongst the various methods deployed in Computational Electromagnetics, the Method of Moments predicts the electromagnetic characteristics accurately. Method of Moments is a rigorous method, combined with an array of modeling techniques such as triangular patch, cubical cell and tetrahedral modeling. Method of Moments has become an accurate technique for solving electromagnetic problems from complex shaped homogeneous and inhomogeneous objects. One of the drawbacks of Method of Moments is the fact that it results into a dense matrix, the inversion of which is a computationally complex both in terms of physical memory and compute power. This has been the prime reason for the Method of Moments hitherto remaining as a low frequency method. With recent advances in supercomputing, it is possible to extend the range of Method of Moments for Radar Cross Section computation of aircraft like structures and radiation characteristic of antennas mounted on complex shaped bodies at realistic frequencies of practical interest. This thesis is a contribution in this direction.
The main focus of this thesis is development of parallel Method of Moments solvers, applied to solve real world electromagnetic wave scattering and radiation problems from inhomogeneous objects. While the methods developed in this thesis are applicable to a variety of problems in Computational Electromagnetics as shown by illustrative examples, in specific, it has been applied to compute the Radar Cross Section enhancement due to acoustic disturbances and flow inhomogeneities from the wake vortex of an aircraft, thus exploring the possibility of detecting stealth aircraft. Illustrative examples also include the analysis of antenna mounted on an aircraft.
In this thesis, first the RWG basis functions have been used in Method of Moments procedure, for solving scattering problems from complex conducting structures such as aircraft and antenna(s) mounted on airborne vehicles, of electrically large size of about 45 and 0.76 million unknowns.
Next, the solver using SWG basis functions with tetrahedral and pulse basis functions with cubical modeling have been developed to solve scattering from 3D inhomogeneous bodies. The developed codes are validated by computing the Radar Cross Section of spherical homogeneous and inhomogeneous layered scatterers, lossy dielectric cylinder with region wise inhomogeneity and high contrast dielectric objects.
Aerodynamic flow solver ANSYS FLUENT, based on Finite Volume Method is used to solve inviscid compressible flow problem around the aircraft. The gradients of pressure/density are converted to dielectric constant variation in the wake region by using empirical relation and interpolation techniques. Then the Radar Cross Section is computed from the flow inhomogeneities in the vicinity of a model aircraft and beyond (wake zone) using the developed parallel Volume Surface Integral Equation using Method of Moments and investigated more rigorously. Radar Cross Section enhancement is demonstrated in the presence of the flow inhomogeneities and detectability is discussed. The Bragg scattering that occurs when electromagnetic and acoustic waves interact is also discussed and the results are interpreted in this light. The possibility of using the scattering from wake vortex to detect low visible aircraft is discussed.
This thesis also explores the possibility of observing the Bragg scattering phenomenon from the acoustic disturbances, caused by the wake vortex. The latter sets the direction for use of radars for target identification and beyond target detection.
The codes are parallelized using the ScaLAPACK and BiCG iterative method on shared and distributed memory machines, and tested on variety of High Performance Computing platforms such as Blue Gene/L (22.4TF), Tyrone cluster, CSIR-4PI HP Proliant 3000 BL460c (360TF) and CRAY XC40 machines. The parallelization speedup and efficiency of all the codes has also been shown.
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Padhy, Venkat Prasad. "Study of RCS from Aerodynamic Flow using Parallel Volume-Surface Integral Equation." Thesis, 2016. http://hdl.handle.net/2005/3104.
Full textAbstract:
Estimation of the Radar Cross Section of large inhomogeneous scattering objects such as composite aircrafts, ships and biological bodies at high frequencies has posed large computational challenge. The detection of scattering from wake vortex leading to detection and possible identification of low observable aircrafts also demand the development of computationally efficient and rigorous numerical techniques. Amongst the various methods deployed in Computational Electromagnetics, the Method of Moments predicts the electromagnetic characteristics accurately. Method of Moments is a rigorous method, combined with an array of modeling techniques such as triangular patch, cubical cell and tetrahedral modeling. Method of Moments has become an accurate technique for solving electromagnetic problems from complex shaped homogeneous and inhomogeneous objects. One of the drawbacks of Method of Moments is the fact that it results into a dense matrix, the inversion of which is a computationally complex both in terms of physical memory and compute power. This has been the prime reason for the Method of Moments hitherto remaining as a low frequency method. With recent advances in supercomputing, it is possible to extend the range of Method of Moments for Radar Cross Section computation of aircraft like structures and radiation characteristic of antennas mounted on complex shaped bodies at realistic frequencies of practical interest. This thesis is a contribution in this direction.
The main focus of this thesis is development of parallel Method of Moments solvers, applied to solve real world electromagnetic wave scattering and radiation problems from inhomogeneous objects. While the methods developed in this thesis are applicable to a variety of problems in Computational Electromagnetics as shown by illustrative examples, in specific, it has been applied to compute the Radar Cross Section enhancement due to acoustic disturbances and flow inhomogeneities from the wake vortex of an aircraft, thus exploring the possibility of detecting stealth aircraft. Illustrative examples also include the analysis of antenna mounted on an aircraft.
In this thesis, first the RWG basis functions have been used in Method of Moments procedure, for solving scattering problems from complex conducting structures such as aircraft and antenna(s) mounted on airborne vehicles, of electrically large size of about 45 and 0.76 million unknowns.
Next, the solver using SWG basis functions with tetrahedral and pulse basis functions with cubical modeling have been developed to solve scattering from 3D inhomogeneous bodies. The developed codes are validated by computing the Radar Cross Section of spherical homogeneous and inhomogeneous layered scatterers, lossy dielectric cylinder with region wise inhomogeneity and high contrast dielectric objects.
Aerodynamic flow solver ANSYS FLUENT, based on Finite Volume Method is used to solve inviscid compressible flow problem around the aircraft. The gradients of pressure/density are converted to dielectric constant variation in the wake region by using empirical relation and interpolation techniques. Then the Radar Cross Section is computed from the flow inhomogeneities in the vicinity of a model aircraft and beyond (wake zone) using the developed parallel Volume Surface Integral Equation using Method of Moments and investigated more rigorously. Radar Cross Section enhancement is demonstrated in the presence of the flow inhomogeneities and detectability is discussed. The Bragg scattering that occurs when electromagnetic and acoustic waves interact is also discussed and the results are interpreted in this light. The possibility of using the scattering from wake vortex to detect low visible aircraft is discussed.
This thesis also explores the possibility of observing the Bragg scattering phenomenon from the acoustic disturbances, caused by the wake vortex. The latter sets the direction for use of radars for target identification and beyond target detection.
The codes are parallelized using the ScaLAPACK and BiCG iterative method on shared and distributed memory machines, and tested on variety of High Performance Computing platforms such as Blue Gene/L (22.4TF), Tyrone cluster, CSIR-4PI HP Proliant 3000 BL460c (360TF) and CRAY XC40 machines. The parallelization speedup and efficiency of all the codes has also been shown.
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Muniganti, Harikiran. "Inverse Problems in 3D Full-wave Electromagnetics." Thesis, 2021. https://etd.iisc.ac.in/handle/2005/5807.
Full textAbstract:
An inverse problem in Electromagnetics (EM) refers to the process of reconstructing the physical system by processing the measured data of its electromagnetic properties. Inverse problems are typically ill-posed, and this makes them far more challenging than the typically well-posed forward problem. The solution of such inverse problems finds applications in nondestructive testing and evaluation, biomedical imaging, geophysical exploration etc. This thesis addresses some inverse problems specific to the area of electromagnetics, arising in three different scenarios.
The first problem is 3-D quantitative imaging primarily targeted towards bio-medical applications. The task is to retrieve the dielectric properties, location and the shape of an unknown object from the measured scattered field. The unknown object is modeled by discretization into several voxels, with each voxel having its own dielectric property. As the inverse problem is non-linear, typically an iterative optimization process is adopted, and a forward problem needs to be solved at every iteration. The total time for reconstruction depends on the forward solver time and the number of iterations. In many cases, the number of unknowns to be reconstructed is prohibitively large. Further, the non-convergence or false-convergence of the optimization process presents its own challenge. This thesis proposes two methodologies to solve these challenges. In the first approach a multilevel methodology is proposed where voxels are hierarchically decomposed into smaller voxels based on an appropriate indicator, leading to a non-uniform multilevel voxel structure aimed at reducing the eventual number of unknowns to be solved for, also enabling faster convergence. In the second approach, a two-stage framework is proposed comprising of Machine Learning classification followed by optimization (ML-OPT). The first stage generates an appropriate adaptive grid for the optimization process and provides a suitable initial guess aiding convergence to the global minima. This approach is aimed at detecting breast tumors where the optimization algorithm can aim for higher resolution in the suspected tumor region, while using lower resolution elsewhere.
The second problem is in the domain of high-speed circuits and is focused on synthesis of transmission line physical parameters given the desired electrical parameters like characteristic impedance and propagation constant. A forward solver is used to train Neural network for several different configurations for analysis and an optimization algorithm is used for synthesis.
The third problem is focused on finding the source of radiation in an electronic system e.g. an automotive ECU, given the measured field at the antenna in the radiated emissions setup. The source of radiation can be from common mode current on the cable harness or from the Design Under Test (DUT). A method based on Huygens box is proposed to quantify the radiation from cable and DUT at each frequency. On each cell of the Huygens box the value of electric field computed at the observation point taking the Electric Current (J) and Magnetic Current (M) on that cell as sources and this information on the Huygens box is used to quantify the radiation.
Some part of the presented work is used via technology-transfer at Simyog Technology Pvt. Ltd., an IISc incubated startup, to develop a simulation software called Compliance-scope which allows the hardware designer to predict the EMI/EMC performance of electronics modules from an early design stage.
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"An efficient volume integral equation approach for characterization of lossy dielectric materials." 2004. http://library.cuhk.edu.hk/record=b6073666.
Full textAbstract:
Lui Man Leung."May 2004."
Thesis (Ph.D.)--Chinese University of Hong Kong, 2004.
Includes bibliographical references.
Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web.
Mode of access: World Wide Web.
Abstracts in English and Chinese.
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Qian, Zhiguo. "Augmented surface integral equation method for low-frequency electromagnetic analysis /." 2009. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3363061.
Full textAbstract:
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2009.Source: Dissertation Abstracts International, Volume: 70-06, Section: B, page: 3698. Adviser: Weng Cho Chew. Includes bibliographical references (leaves 105-110) Available on microfilm from Pro Quest Information and Learning.
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Sayed, Sadeed B. "Transient Electromagnetic Analysis of Complex Penetrable Scatterers using Volume Integral Equations." Diss., 2018. http://hdl.handle.net/10754/630075.
Full textAbstract:
Simulation tools capable of analyzing electromagnetic (EM) field/wave interactions on complex penetrable scatterers have applications in various areas of engineering ranging from the design of integrated antennas to the subsurface imaging. EM simulation tools operating in the time domain can be formulated to directly solve the Maxwell equations or the integral equations obtained by enforcing fundamental field relations or boundary conditions. Time domain integral equation (TDIE) solvers offer several benefits over differential equation solvers: They require smaller number discretization elements/sampling points (both in space and time). Despite the advantages, TDIE solvers suffer from increased computational cost, stability issues of the time-marching algorithms, and limited applicability to complex scatterers. This thesis is focused on addressing the last two issues associated with time domain volume integral equation (TD-VIE) solvers, as the issue of increased computational cost has been addressed by recently developed acceleration methods. More specifically, four new closely-related, but different marching on-in-time (MOT) algorithms are formulated and implemented to solve the time domain electric and magnetic field volume integral equations (TD-EFVIE and TD-MFVIE). The first algorithm solves the TD-EFVIE to analyze EM wave interactions on high-contrast dielectric scatterers. The stability of this MOT scheme is ensured by using two-sided approximate prolate spherical wave (APSW) functions to discretize the time dependence of the unknown current density as well as an extrapolation scheme to restore the causality of matrix system resulting from this discretization. The second MOT scheme solves the TDMFVIE to analyze EM wave interactions on dielectric scatterers. The TD-MFVIE is cast in the form of an ordinary differential equation (ODE) and the unknown magnetic field is expanded using spatial basis functions. The time-dependent coefficients of this expansion are found by integrating the resulting ODE system using a linear multistep method. The third method is formulated and implemented to analyze EM wave interactions on scatterers with Kerr nonlinearity. The former scheme integrates in time a coupled of system of the TD-EFVIE and the nonlinear constitutive relation, which is cast in the form of an ODE system, for the expansion coefficients of the electric field and flux using a linear multistep method. The last method described in this thesis is developed to analyze EM wave interactions on ferrite scatterers.
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Heinemeyer, Eric. "Integral Equation Methods for Rough Surface Scattering Problems in three Dimensions." Doctoral thesis, 2008. http://hdl.handle.net/11858/00-1735-0000-000D-F15F-2.
Full text
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NguyenAnh, Tuan, and 阮俊. "Boundary Element Analysis of Three – Dimensional Anisotropic Thermoelasticity by Direct Transformation of the Volume Integral in the Boundary Integral Equation." Thesis, 2017. http://ndltd.ncl.edu.tw/handle/zmu648.
Full text
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Uysal, Ismail Enes. "Time Domain Surface Integral Equation Solvers for Quantum Corrected Electromagnetic Analysis of Plasmonic Nanostructures." Diss., 2016. http://hdl.handle.net/10754/621891.
Full textAbstract:
Plasmonic structures are utilized in many applications ranging from bio-medicine
to solar energy generation and transfer. Numerical schemes capable of solving equations of classical electrodynamics have been the method of choice for characterizing scattering properties of such structures. However, as dimensions of these plasmonic structures reduce to nanometer scale, quantum mechanical effects start to appear. These effects cannot be accurately modeled by available classical numerical methods.
One of these quantum effects is the tunneling, which is observed when two structures
are located within a sub-nanometer distance of each other. At these small distances
electrons “jump" from one structure to another and introduce a path for electric current
to flow. Classical equations of electrodynamics and the schemes used for solving
them do not account for this additional current path. This limitation can be lifted
by introducing an auxiliary tunnel with material properties obtained using quantum
models and applying a classical solver to the structures connected by this auxiliary
tunnel. Early work on this topic focused on quantum models that are generated using
a simple one-dimensional wave function to find the tunneling probability and assume
a simple Drude model for the permittivity of the tunnel. These tunnel models are
then used together with a classical frequency domain solver.
In this thesis, a time domain surface integral equation solver for quantum corrected
analysis of transient plasmonic interactions is proposed. This solver has several
advantages: (i) As opposed to frequency domain solvers, it provides results at a broad band of frequencies with a single simulation. (ii) As opposed to differential
equation solvers, it only discretizes surfaces (reducing number of unknowns), enforces
the radiation condition implicitly (increasing the accuracy), and allows for time step
selection independent of spatial discretization (increasing efficiency). The quantum
model of the tunnel is obtained using density functional theory (DFT) computations,
which account for the atomic structure of materials. Accuracy and applicability of
this (quantum corrected) time domain surface integral equation solver will be shown
by numerical examples.
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Heinemeyer, Eric [Verfasser]. "Integral equation methods for rough surface scattering problems in three dimensions / vorgelegt von Eric Heinemeyer." 2008. http://d-nb.info/990720748/34.
Full text
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Karsilayan, Nur. "Full-wave Surface Integral Equation Method for Electromagnetic-circuit Simulation of Three-dimensional Interconnects in Layered Media." Thesis, 2010. http://hdl.handle.net/1969.1/ETD-TAMU-2010-05-7668.
Full textAbstract:
A new full-wave surface impedance integral equation method is presented for
three-dimensional arbitrary-shaped interconnect parasitic extraction in layered media.
Various new ways of applying voltage and current excitations for electromagnetic-circuit
simulation are introduced. A new algorithm is proposed for matrix formation
of electromagnetic-circuit simulation, low frequency solution and layered media so
that it can be easily integrated to a Rao-Wilton-Glisson based method of moment
code. Two mixed potential integral equation forms of the electric field integral equation
are adapted along with the Michalski-Mosig formulations for layered kernels to
model electromagnetic interactions of interconnects in layered media over a conducting
substrate. The layered kernels are computed directly for controllable accuracy. The proposed methods are validated against existing methods for both electromagnetic and electromagnetic-circuit problems.
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Chen, Rui. "Transient Analysis of Electromagnetic and Acoustic Scattering using Second-kind Surface Integral Equations." Diss., 2021. http://hdl.handle.net/10754/668895.
Full textAbstract:
Time-domain methods are preferred over their frequency-domain counterparts for solving acoustic and electromagnetic scattering problems since they can produce wide- band data from a single simulation. Among the time-domain methods, time-domain surface integral equation solvers have recently found widespread use because they offer several benefits over differential equation solvers.
This dissertation develops several second-kind surface integral equation solvers for analyzing transient acoustic scattering from rigid and penetrable objects and transient electromagnetic scattering from perfect electrically conducting and dielectric objects.
For acoustically rigid, perfect electrically conducting, and dielectric scatterers, fully explicit marching-on-in-time schemes are developed for solving time domain Kirchhoff, magnetic field, and scalar potential integral equations, respectively. The unknown quantity (e.g., velocity potential, electric current, or scalar potential) on the scatterer surface is discretized using a higher-order method in space and Lagrange interpolation in time. The resulting system is cast in the form of an ordinary differen- tial equation and integrated in time using a predictor-corrector scheme to obtain the unknown expansion coefficients. The explicit scheme can use the same time step size as its implicit counterpart without sacrificing from the stability of the solution and is much faster under low-frequency excitation (i.e., for large time step size). In addition, low-frequency behavior of vector potential integral equations for perfect electrically conducting scatterers is also investigated in this dissertation.
For acoustically penetrable scatterers, presence of spurious interior resonance
modes in the solutions of two forms of time domain surface integral equations is investigated. Numerical results demonstrate that the solution of the form that is widely used in the literature is corrupted by the interior resonance modes. But, the amplitude of these modes in the time domain can be suppressed by increasing the accuracy of discretization especially in time. On the other hand, the proposed one in the combined form shows a resonance-free performance verified via numerical experiments.
In addition to providing detailed formulations of these solvers, the dissertation presents numerical examples, which demonstrate the solvers’ accuracy, efficiency, and applicability in real-life scenarios.
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AlQedra, Mohammed A. I. "Surface impedance formulation for electric field integral equation in magneto-quasistatic and full-wave boundary element models of interconnects." 2010. http://hdl.handle.net/1993/4136.
Full textAbstract:
Today’s high-speed interconnects at the chip, package, and board levels of integration can be rigorously modeled with the boundary element method based on the surface discretization of the electric field integral equation (EFIE). The accuracy of such models critically depends on the surface impedance model, which has to accurately map the behavior of the electromagnetic field inside the wire volumes to their surfaces. This thesis proposes a surface impedance model, which casts the accurate but computationally intensive volumetric EFIE formulation to the boundary element framework. This is accomplished via approximating the volumetric current density as a product of the known exponential factor corresponding to the skin-effect behavior of the field inside the wires and the unknown surface current density on the conductor’s boundary. The reduction of the volumetric EFIE to its surface counterpart results in a physically consistent surface impedance model allowing to achieve the volumetric EFIE accuracy within the boundary element formulation.
The method is initially introduced for lossy 2D interconnects and later generalized to 3D interconnects under magneto-quasistatic approximation. Finally, this work is extended to the Rao-Wilton-Glisson (RWG) method of moments (MoM) solution of the full-wave EFIE. The alternative models exhibit various limitations. For example, in the double-plane model the planar interconnect structure is replaced by two infinitely thin metal sheets at its top and bottom surfaces. This model succeeds for several practical scenarios where the conductor width is sufficiently larger than its thickness, or when the operating frequency is sufficiently low for the current distribution across the conductor cross section to be assumed uniform. The alternative”multi-sheet model” represents the interconnect by a number of infinitely thin metal sheets, which uniformly span its cross section such that the spacing between each two consecutive sheets is small compared to skin-depth. The model succeeds in accurately extracting conductor loss, however, it may require a large number of sheets, which makes the number of unknowns in MoM discretization of the same order as the number of unknowns in volumetric models.
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Aatresh, K. "Microgravity Flow Transients in the Context of On-Board Propellant Gauging." Thesis, 2014. http://etd.iisc.ac.in/handle/2005/3105.
Full textAbstract:
It is well known that surface tension of a liquid has a decisive role in flow dynamics and the eventual equilibrium state, especially in confined flows under low gravity conditions and also in free surface flows. One such instance of a combination of these two cases where surface tension plays an important role is in the microgravity environment of a spacecraft propellant tank. In this specific case both propellant acquisition and residual propellant estimation are critical to the mission objectives particularly in the end-of-life phase. While there have been a few studies pertaining to the equilibrium state in given geometric configurations, the transient flow leading to final state from an initial arbitrary distribution of propellant is rarely described. The present study is aimed at analysing the dynamic behaviour of the liquids under reduced gravity through numerical simulation and also addresses the specific case of propellant flow transient in a cone-in-a-sphere type of tank configuration proposed by Lal and Raghunandan which is likely to result in both improved acquisition and life time estimation of spacecraft. While addressing this specific problem, the present work aims to study the transient nature of such surface tension driven flows in a general form as applicable to other similar problems also. Volume of Fluid (VOF) method for multiphase model in ANSYS FLUENT was adapted with suitable changes for generating numerical solutions to this problem.
Simulations were run for three different cone angles of 17o, 21o & 28o with a flat liquid surface for full scale models to measure the rise height and time of rise. Two scaled models of ½ and 1/10th of the original dimensions with the same liquid configuration of the 28o cone angle case were simulated to see if the time scales involved would come down for experimental feasibility. A third simulation of the 1/10th scale model was run with the liquid spread in the tank to imitate the general conditions found in the propellant tank in microgravity. To understand the behaviour of liquids in the microgravity state to changing physical parameters, a set of simulations was run using liquid phases as water and hydrazine with different physical parameters of temperature and surface tension.
The theory put forward by Lal and Raghunandan was found to stand firm. In the case of the cone angle of 28o it was observed that in the final equilibrium state the liquid collected towards the apex of the cone with the larger volume fraction of liquid accumulating inside the cone. An addition of a cylindrical section at the bottom of the cone seems to help although not uniformly for all case. The equilibrium settling times for all the three cone angle cases were in the order of 300 to 600 seconds for simulations on a spherical tank of diameter two metres which was close to the actual tank dimension used on spacecraft. Scaled down simulations of 1/10th and ½ the tank geometry with both flat liquid surfaces and spread out liquid volumes showed that the smaller models had equilibrium settling times which were considerably lower (in the order of tens of seconds) than the full scale models. Although smaller, these time scales are larger than the maximum time scales available in drop tower tests which provide a maximum free fall time of around 9 to 10 seconds. Validation of the proposed configuration by flying an aircraft in a parabolic flight path is a possibility that could be explored for the scaled down models since the zero-g duration for these flights is on an average between 15-20 seconds.
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Aatresh, K. "Microgravity Flow Transients in the Context of On-Board Propellant Gauging." Thesis, 2014. http://hdl.handle.net/2005/3105.
Full textAbstract:
It is well known that surface tension of a liquid has a decisive role in flow dynamics and the eventual equilibrium state, especially in confined flows under low gravity conditions and also in free surface flows. One such instance of a combination of these two cases where surface tension plays an important role is in the microgravity environment of a spacecraft propellant tank. In this specific case both propellant acquisition and residual propellant estimation are critical to the mission objectives particularly in the end-of-life phase. While there have been a few studies pertaining to the equilibrium state in given geometric configurations, the transient flow leading to final state from an initial arbitrary distribution of propellant is rarely described. The present study is aimed at analysing the dynamic behaviour of the liquids under reduced gravity through numerical simulation and also addresses the specific case of propellant flow transient in a cone-in-a-sphere type of tank configuration proposed by Lal and Raghunandan which is likely to result in both improved acquisition and life time estimation of spacecraft. While addressing this specific problem, the present work aims to study the transient nature of such surface tension driven flows in a general form as applicable to other similar problems also. Volume of Fluid (VOF) method for multiphase model in ANSYS FLUENT was adapted with suitable changes for generating numerical solutions to this problem.
Simulations were run for three different cone angles of 17o, 21o & 28o with a flat liquid surface for full scale models to measure the rise height and time of rise. Two scaled models of ½ and 1/10th of the original dimensions with the same liquid configuration of the 28o cone angle case were simulated to see if the time scales involved would come down for experimental feasibility. A third simulation of the 1/10th scale model was run with the liquid spread in the tank to imitate the general conditions found in the propellant tank in microgravity. To understand the behaviour of liquids in the microgravity state to changing physical parameters, a set of simulations was run using liquid phases as water and hydrazine with different physical parameters of temperature and surface tension.
The theory put forward by Lal and Raghunandan was found to stand firm. In the case of the cone angle of 28o it was observed that in the final equilibrium state the liquid collected towards the apex of the cone with the larger volume fraction of liquid accumulating inside the cone. An addition of a cylindrical section at the bottom of the cone seems to help although not uniformly for all case. The equilibrium settling times for all the three cone angle cases were in the order of 300 to 600 seconds for simulations on a spherical tank of diameter two metres which was close to the actual tank dimension used on spacecraft. Scaled down simulations of 1/10th and ½ the tank geometry with both flat liquid surfaces and spread out liquid volumes showed that the smaller models had equilibrium settling times which were considerably lower (in the order of tens of seconds) than the full scale models. Although smaller, these time scales are larger than the maximum time scales available in drop tower tests which provide a maximum free fall time of around 9 to 10 seconds. Validation of the proposed configuration by flying an aircraft in a parabolic flight path is a possibility that could be explored for the scaled down models since the zero-g duration for these flights is on an average between 15-20 seconds.
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VOPÁLENSKÁ, Lenka. "Riemannuv integrál a jeho aplikace." Master's thesis, 2015. http://www.nusl.cz/ntk/nusl-203671.
Full textAbstract:
The main goal of my diploma work on the topic "The Riemann integral and its applications" is to create an overview that describes the individual use of the Riemann integral. The first three chapters deal with the history, the definition of the Riemann integral and with the calculation of integration. There is the overview of the individual use in the fourth chapter (area plane region, length plane curve, volume solid of revolution and area lateral surface solid of revolution) that is accompanied by solved examples, the examples are accompanied by graphical representation for a better idea. In the fifth chapter there is a collection of unsolved examples, for practising of the individual use. The collection is complemented by results for the reader to check the accuracy of calculation.
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Balu, Narayana Srinivasan. "Propagation Prediction Over Random Rough Surface By Zeroth Order Induced Current Density." 2014. https://scholarworks.umass.edu/masters_theses_2/129.
Full textAbstract:
Electromagnetic wave propagation over random sea surfaces is a classical problem of interest for the Navy, and significant research has been done over the years. Here we make use of numerical and analytical methods to predict the propagation of microwaves over random rough surface. The numerical approach involves utilization of the direct solution (using Volterra integral equation of the second kind) to currents induced on a rough surface due to forward propagating waves to compute the scattered field. The mean scattered field is computed using the Monte-Carlo method. Since the exact solution (consisting of an infinite series) to induced current density is computationally intensive, there exists a need to predict the propagation using the closely accurate zeroth order induced current (first term of the series) for time-varying multiple realizations of a random rough surface in a computationally efficient manner. The wind-speed dependent, fully-developed, Piersen-Moskowitz sea spectrum has been considered in order to model a rough sea surface, although other partially-developed roughness spectra may also be utilized. An analytical solution based on the zeroth order current density obtained by deriving the mean scattered field as a function of the range and vertical height by directly using the Parabolic Equation (PE) approximation method and the resulting Green's function has been utilized for a comparative study. The analytical solution takes into account the diffused component of the scattered field.