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Votapka, Lane William. "Numerical and Computational Solutions for Biochemical Kinetics, Druggability, and Simulation." Thesis, University of California, San Diego, 2016. http://pqdtopen.proquest.com/#viewpdf?dispub=10062341.
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<p> Computational tools provide the automation and power that enable detailed modeling and analysis of many biomolecular phenomena of interest. Open source programs and automated tools empower researchers and provide opportunities for improvement to existing software. In the past few years, I have developed several open-source scientific software packages for the purposes of automating difficult or menial tasks pertaining to computational biophysics. These software packages involve the analysis of molecular dynamics simulations, Brownian dynamics simulations, electrostatics, pocket volume measurement, solvent fragment mapping, binding site characterization, milestoning theory, and allosteric network communications. In addition to allowing my research group and me to approach biomedical challenges that would otherwise be intractable, I hope and intend that these tools will be useful to the computational and theoretical biophysics research community.</p>
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Gaines, Jessica Gabrielle. "Topics in the numerical simulation of pathwise solutions to stochastic differential equations." Thesis, University of Edinburgh, 1995. http://hdl.handle.net/1842/13867.
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This work contains several developments in the area of numerical solution of pathwise solutions to stochastic differential equations (SDE's). In the first chapter we define and motivate pathwise solutions and give a brief survey of numerical methods for approximating them. The main key to enlarging the scope of numerical methods for SDE's is a good representation of Brownian paths. A binary tree structure is an essential tool in Chapter Two, which presents a general method for solution of SDE's using variable time steps. In the case of a general SDE, improvement of the order of convergence compared with standard methods, demands generation of the Lévy area integrals. Chapter Three presents a method of random generation of the Lévy area for a Brownian path in <I>IR</I><SUP>2</SUP>. The method is based on Marsaglia's rectangle-wedge-tail method for fast generation of normally distributed deviates. Since the solution of an SDE generally depends on an infinite sequence of iterated integrals of the driving noise, it makes sense to examine these integrals and the algebraic relations between them. In Chapter Four, it is shown how known facts about shuffle algebras can be used to get a better understanding of stochastic iterated integrals of Ito and Stratonovich type and obtain practical algebraic bases for these two sets. We use the algebra to calculate moments of stochastic integrals, needed when calculating moments of error during numerical solutions of SDE's. The work on the generation of area integrals, described in Chapter Three, gives rise to general questions about the generation of random deviates, some of which are addressed in the last two chapters. In Chapter Five, we present a polynomial-time algorithm for finding the partition, into rectangles or triangles, of certain types of region in <I>IR</I><SUP>2</SUP>, that has the lowest entropy.
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Bhalala, Ashesh 1964. "Numerical solution algorithms in the DLANET program." Thesis, The University of Arizona, 1989. http://hdl.handle.net/10150/276957.
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Several methods to solve a system of linear equations with real and complex coefficients exist. The most popular methods are Gauss-Jordan, L-U Decomposition, Gauss-Seidel, and Matrix Reduction. These methods are utilized to optimize run-time of the DLANET circuit analysis program. As concluded by this study, the Matrix Reduction method which is presently utilized in the DLANET program, results in run-times which are faster than the other solution methods studied in this paper for lower order systems. Similarly, the L-U Decomposition and Gauss-Jordan methods result in faster run-times than the other techniques for higher order systems. Finally, the Gauss-Seidel Iterative method, when incorporated into the DLANET program, has proven to be much slower than the other solution methods considered in this paper.
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Etekpo, Kossi. "Numerical solution for subsurface reservoir simulation." Master's thesis, University of Cape Town, 2017. http://hdl.handle.net/11427/25007.
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Transport problems in porous media constitute an important field of scientific research in modern world, due to their broad applications in area such as petroleum engineering, water resources, pollutants transport and green- house gases sequestration to just mention few. The mathematical models that describe such problems have been developed and form one of the main classes of partial differential equations (PDEs) that scientists encounter in the real-world modeling. Nevertheless, in most of the cases, the exact solutions in the classical sense of those models are not available. The study of numerical approximation of PDEs is therefore an active research area and there is an extensive literature on numerical methods for PDEs. In this work, we review some numerical techniques, more precisely we present finite volume method with two-point flux approximation and mixed finite volume method for spatial discretization of elliptic and parabolic PDEs modeling transport flow in porous media. We then present some standard explicit and implicit methods, Rosenbrock schemes and exponential time stepping schemes for temporal discretization. We finally run some numerical simulations of advection-diffusion-reaction problems in a heterogeneous and an anisotropic porous media.
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Pinilla, Camilo Ernesto. "Numerical simulation of shear instability in shallow shear flows." Thesis, McGill University, 2008. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=115697.
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The instabilities of shallow shear flows are analyzed to study exchanges processes across shear flows in inland and coastal waters, coastal and ocean currents, and winds across the thermal-and-moisture fronts. These shear flows observed in nature are driven by gravity and governed by the shallow water equations (SWE). A highly accurate, and robust, computational scheme has been developed to solve these SWE. Time integration of the SWE was carried out using the fourth-order Runge-Kutta scheme. A third-order upwind bias finite difference approximation known as QUICK (Quadratic Upstream Interpolation of Convective Kinematics) was employed for the spatial discretization. The numerical oscillations were controlled using flux limiters for Total Variation Diminishing (TVD). Direct numerical simulations (DNS) were conducted for the base flow with the TANH velocity profile, and the base flow in the form of a jet with the SECH velocity profile. The depth across the base flows was selected for the' balance of the driving forces. In the rotating flow simulation, the Coriolis force in the lateral direction was perfectly in balance with the pressure gradient across the shear flow during the simulation. The development of instabilities in the shear flows was considered for a range of convective Froude number, friction number, and Rossby number. The DNS of the SWE has produced linear results that are consistent with classical stability analyses based on the normal mode approach, and new results that had not been determined by the classical method. The formation of eddies, and the generation of shocklets subsequent to the linear instabilities were computed as part of the DNS. Without modelling the small scales, the simulation was able to produce the correct turbulent spreading rate in agreement with the experimental observations. The simulations have identified radiation damping, in addition to friction damping, as a primary factor of influence on the instability of the shear flows admissible to waves. A convective Froude number correlated the energy lost due to radiation damping. The friction number determined the energy lost due to friction. A significant fraction of available energy produced by the shear flow is lost due the radiation of waves at high convective Froude number. This radiation of gravity waves in shallow gravity-stratified shear flow, and its dependence on the convective Froude number, is shown to be analogous to the Mach-number effect in compressible flow. Furthermore, and most significantly, is the discovery from the simulation the crucial role of the radiation damping in the development of shear flows in the rotating earth. Rings and eddies were produced by the rotating-flow simulations in a range of Rossby numbers, as they were observed in the Gulf Stream of the Atlantic, Jet Stream in the atmosphere, and various fronts across currents in coastal waters.
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Tan, Don Bing Dong. "Is the precision of computed solutions more closely related with componentwise condition number than normwise condition number?" HKBU Institutional Repository, 2015. https://repository.hkbu.edu.hk/etd_oa/153.
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We have a conjecture that “the precision of computed solutions for systems of linear equations is more closely related with componentwise condition number c(A) than normwise condition number κ(A). We conducted simulation experiments to verify this conjecture. A statistical tool, Hotelling-Williams T-Test is employed to check if difference between correlations is significant. Simulation results suggest that our conjecture is true for most of the well-known methods and matrix sizes. Keywords: condition numbers, simulation, correlation coefficients, Hotelling-Williams T-Test
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Figueroa, Leonardo E. "Deterministic simulation of multi-beaded models of dilute polymer solutions." Thesis, University of Oxford, 2011. http://ora.ox.ac.uk/objects/uuid:4c3414ba-415a-4109-8e98-6c4fa24f9cdc.
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We study the convergence of a nonlinear approximation method introduced in the engineering literature for the numerical solution of a high-dimensional Fokker--Planck equation featuring in Navier--Stokes--Fokker--Planck systems that arise in kinetic models of dilute polymers. To do so, we build on the analysis carried out recently by Le~Bris, Leli\`evre and Maday (Const. Approx. 30: 621--651, 2009) in the case of Poisson's equation on a rectangular domain in $\mathbb{R}^2$, subject to a homogeneous Dirichlet boundary condition, where they exploited the connection of the approximation method with the greedy algorithms from nonlinear approximation theory explored, for example, by DeVore and Temlyakov (Adv. Comput. Math. 5:173--187, 1996). We extend the convergence analysis of the pure greedy and orthogonal greedy algorithms considered by Le~Bris, Leli\`evre and Maday to the technically more complicated situation of the elliptic Fokker--Planck equation, where the role of the Laplace operator is played out by a high-dimensional Ornstein--Uhlenbeck operator with unbounded drift, of the kind that appears in Fokker--Planck equations that arise in bead-spring chain type kinetic polymer models with finitely extensible nonlinear elastic potentials, posed on a high-dimensional Cartesian product configuration space $\mathsf{D} = D_1 \times \dotsm \times D_N$ contained in $\mathbb{R}^{N d}$, where each set $D_i$, $i=1, \dotsc, N$, is a bounded open ball in $\mathbb{R}^d$, $d = 2, 3$. We exploit detailed information on the spectral properties and elliptic regularity of the Ornstein--Uhlenbeck operator to give conditions on the true solution of the Fokker--Planck equation which guarantee certain rates of convergence of the greedy algorithms. We extend the analysis to discretized versions of the greedy algorithms.
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Petrova, Nadezda. "Turbulence-chemistry interaction models for numerical simulation of aeronautical propulsion systems." Palaiseau, Ecole polytechnique, 2015. https://tel.archives-ouvertes.fr/tel-01138235/document.
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La modélisation de l'interaction turbulence-chimie est un point clé dans la simulation numérique des écoulements réactifs turbulents. Cette thèse est consacrée à l'adaptation et l'intégration de différents modèles de combustion turbulente dans le code d'écoulements diphasiques réactifs pour l'énergétique (CEDRE) de l'ONERA. La première partie de la thèse est dédiée à l'étude des équations quasi-linéaires hyperboliques stochastiques aux dérivées partielles (SPDEs) qui sont statistiquement équivalentes à une équation de transport pour la fonction de densité de probabilité (PDF) jointe vitesse-scalaires. Il est démontré que pour préserver l'équivalence entre les SPDEs et l'équation de transport pour la PDF jointe vitesse-scalaires, les solutions multivaluées des SPDEs doivent être prises en compte. Une nouvelle méthode stochastique pour résoudre les SPDEs, récemment proposée par O. Soulard [EmakoLetizia2014], est étudiée et validée sur des cas-tests unidimensionnels. Il est montré que cette méthode permet de trouver les solutions multivaluées des SPDEs au sens statistique. La résolution numérique des SPDEs étant particulièrement coûteuse, une seconde voie a été explorée au cours de cette thèse. Il s'agit, dans la deuxième partie de ce mémoire, de la mise en oeuvre du modèle "flammelettes tabulées pour la chimie" (FTC) et du modèle "réacteur partiellement mélangé étendu" (EPaSR). Avec le code CEDRE, l'approche FTC est mise à jour en supposant une distribution de type beta-PDF. L'adaptation LES/EPaSR [SabelnikovFureby2013] pour le RANS et son intégration dans CEDRE ont été réalisées. Les modèles EPaSR et "FTC avec beta-PDF présumée" ont été validés par rapport aux données expérimentales [MagreMoreau1988] sur une configuration de flamme stabilisée par une marche descendante. Il est montré que le calcul RANS/EPaSR donne un meilleur accord avec l'expérience que les autres approches évaluées<br>Modeling the turbulence-chemistry interaction is a key point in the numerical simulation of the combustion in the air- breathing engines. The present work is devoted to adaptation and integration of several different turbulent combustion models into the ONERA industrial code CFD package for diphasic reactive ows (CEDRE). The first part of the thesis is focused on the quasi-linear hyperbolic stochastic partial differential equations (SPDEs) which are statistically equivalent to a transport equation for the joint velocity-scalars probability density function (PDF). It is shown that in order to preserve the equivalence between the SPDEs and the transport equation for the joint velocity-scalars PDF, multivalued solutions of the SPDEs should be taken into account. A new stochastic method to solve the SPDEs, recently proposed by O. Soulard [Emako-Letizia2014], is considered and validated on one-dimensional test-cases. It is shown that this method is able to recover the multivalued solutions of the SPDEs in the statistical sense. The numerical solution of the SPDEs is time consuming, therefore the second part of the thesis is concerned with a flamelet tabulated chemistry (FTC) and an extended partially stirred reactor (EPaSR) models. In the framework of CEDRE CFD software the FTC approach is updated, presuming that the distribution is given by a beta-PDF. The adaptation of the LES/EPaSR model [SabelnikovFureby2013] to the RANS and its integration into CEDRE are done. The EPaSR and the FTC with the presumed beta-PDF are validated against experimental data [MagreMoreau1988] on a configuration of a backward-facing step combustor. It is shown that the RANS/EPaSR calculation yields the best agreement with the experiment compared to other considered approaches
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Hu, Guanghui. "Numerical simulations of the steady Euler equations on unstructured grids." HKBU Institutional Repository, 2009. http://repository.hkbu.edu.hk/etd_ra/1106.
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Coussement, Axel. "Direct numerical simulation and reduced chemical schemes for combustion of perfect and real gases." Doctoral thesis, Universite Libre de Bruxelles, 2012. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/209765.
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La première partie de cette thèse traite du développement du code de simulation numérique directe YWC, principalement du développement des conditions aux limites. En effet, une forte contribution scientifique a été apportée aux conditions aux limites appelées "Three dimensional Navier-Stokes characteristic boundary condtions" (3D-NSCBC). Premièrement, la formulation de ces conditions aux arêtes et coins a été complétée, ensuite une extension de la formulation a été proposée pour supprimer les déformations observées en sortie dans le cas d'écoulements non-perpendiculaires à la frontière. <p>De plus, ces conditions ont été étendues au cas des gaz réels et une nouvelle définition du facteur de relaxation pour la pression a été proposée. Ce nouveau facteur de relaxation permet de supprimer les déformations observées en sortie pour des écoulements transcritiques. <p>Les résultats obtenus avec le code YWC ont ensuite été utilisés dans la seconde partie de la thèse pour développer une nouvelle méthode de tabulation basée sur l'analyse en composantes principales. Par rapport aux méthodes existante telles que FPI ou SLFM, la technique proposée, permet une identification automatique des variables à transporter et n'est, de plus, pas lié à un régime de combustion spécifique. Cette technique a permis d'effectuer des calculs d'interaction flamme-vortex en ne transportant que 5 espèces à la place des 9 requises pour le calcul en chimie détaillée complète, sans pour autant perdre en précision. <p>Finalement, dans le but de réduire encore le nombre d'espèces transportées, les techniques T-BAKED et HT-BAKED PCA ont été introduites. En utilisant une pondération des points sous-représentés, ces deux techniques permettent d'augmenter la précision de l'analyse par composantes principales dans le cadre des phénomènes de combustion.<p><br>Doctorat en Sciences de l'ingénieur<br>info:eu-repo/semantics/nonPublished
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Qiao, Zhonghua. "Numerical solution for nonlinear Poisson-Boltzmann equations and numerical simulations for spike dynamics." HKBU Institutional Repository, 2006. http://repository.hkbu.edu.hk/etd_ra/727.
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Fischer, Bernd. "Modélisation d'interfaces par simulations numériques : des polymères en solutions à la troposphère." Thesis, Besançon, 2012. http://indexation.univ-fcomte.fr/nuxeo/site/esupversions/e7097b7d-070a-46b8-8034-1b1d5d455974.
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Ce travail a pour objectif de montrer la capacité des simulations numériques à modéliser les phénomènes aux interfaces solides et liquides. Dans le travail sur les interfaces solides, la méthode GCMC a été utilisée pour simuler l'isotherme d'adsorption de !'acétaldéhyde sur la glace dans les conditions de la haute troposphère, puis l'adsorption de composés organiques bi-fonctionnalisés sur la glace a été caractérisée par dynamique moléculaire avec pour objectif d'interpréter des résl1ltats expérimentaux de la littérature. Une partie de ce travail a été consacrée à la circulation du diagramme de phase (p,T) d'aérosols organiques (acide oxalique et malonique) clans les conditions troposphériques afin d'étudier la capacité de ces aérosols à jouer le rôle de noyaux de condensation pour les particules de glace. Le travail sur les interfaces liquides a concerné tout d'abord l'adsorption compétitive de polymères et de smfactants à la surface de l'eau. Il s'appuie sur une description très précise, par simulation, de la structure et de la dynamique de la surface des systèmes considérés. La deuxième partie des travaux sur les interfaces liquides s'est intéressée à la caractérisation du transfert d'ions à travers une interface liquide/liquide par le biais du calcul des variations de l'énergie libre du système au cours du transfc1i. Afin d'obtenir une description très rigoureuse des détails des processus mis enjeu, une méthode spécifique a été développée dans cette thèse pour calculer le profil d'énergie libre en tenant compte directement du caractère très dynamique de l'interface<br>This work aims to demonstrate the ability of numerical simulations to mode] solid · and liquid interfaces. In the work on the solid interfaces, the GCMC method was used to sin:rnlatc the ads011Jtion isotherrn of acetaldehyde on ice under the conditions of the ·upper tropospherc and the molecular dynamics method was usecl to characterize the adsorption of difünctionalized organic compounds on ice, aiming at interpreting experimental results. Part of this work was devotcd to the simulation of the phase diagrarn (p, T) of organic aerosols (oxalic acid and malonic) in tropospberic conditions to study the ability of aerosols to act as condensation nuclei for icc particlcs. The work: on liquid interfaces concerned firstly the competitive adsorption of polymcrs and surfactants at the water surface. It is based on a very precise desc1iption, by mnncrical simulation, of the structure émd dynamics cif the surface of the considered systems. The second pari of the work on liquid interfaces bas focused on the characterization of ion transfer across a liquid/liquid interface through the calculations of the free energy variations of the system during the transfo·. To obtain a rigorous desc1iptio11 of the details of the corresponding processes, a specific method was developed in this thesis to calculate the free energy profile while taking into account tbe dynamics of the interface
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Xiong, Yong-Liang. "Numerical Investigation on Drag Reduction and Two-Dimensional Turbulence in Diluted Polymer Solutions." Thesis, Bordeaux 1, 2010. http://www.theses.fr/2010BOR14141/document.
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Les polymères jouent un rôle important sur la réduction de la traînée et la modification de la structure des écoulements. Nous avons utilisé le modèle Oldroyd-B pour étudier l’effet de la viscoélasticité de solutions de polymères dilués sur des écoulements en deux dimensions autour d’obstacles dans un canal. Les obstacles sont pris en compte par la méthode de pénalisation volumique et des condition aux limites artificielles sans réflexion sont imposées à la sortie du canal. La discrétisation est effectuée par des schémas performants en différences finies et la résolution par une méthode multigrille. Les simulations numériques sont effectuées pour une large gamme de nombres de Reynolds et de nombres de Weissenberg. Les caractéristiques détaillées des écoulements viscoélastiques sont analysées et comparées entre elles et celles de l’écoulement du fluide sans polymère. En particulier les jeux de paramètres conduisant à une augmentation ou à une baisse de la traînée. Enfin les effets du polymère sur des écoulements turbulents sont aussi analysés<br>Polymer plays an important role on the drag reduction and modification of the structure of flow. In this thesis, Oldroyd B model is employed to study the effectof viscoelasticity for polymer solutions diluted by two-dimensional direct numerical simulation. The obstacles are taken into account by penalization method. The artificial boundary condition is imposed without any reflection on the channel outlet. Flow pasta cylinder is investigated in detailed by present numerical methods. The numerical codes are valid for predicting the drag force and capturing the important character of viscoelastic flow by comparing with experimental and other numerical results. The drag map of the cylinder is obtained at a wide range of Reynolds number and Weissenberg number space. The detailed characteristics of viscoelastic flow are reported in the thesis. The effects of polymer on two-dimensional turbulent flow are also discussed by grid turbulent flow
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Bächle, Simone. "Numerical solution of differential-algebraic systems arising in circuit simulation." [S.l.] : [s.n.], 2007. http://opus.kobv.de/tuberlin/volltexte/2007/1524.
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Nheili, Rafife. "How to improve the numerical reproducibility of hydrodynamics simulations : analysis and solutions for one open-source HPC software." Thesis, Perpignan, 2016. http://www.theses.fr/2016PERP0045/document.
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La non-reproductibilité numérique apparait dans divers domaines d'application de la simulation HPC. En effet, les différentes distributions d'un calcul parallèle peuvent mener à des résultats numériques différents, à cause des particularités de l'arithmétique flottante. Le besoin de reproductibilité numérique est motivé pour le débogage, le test et la validation des codes de calcul scientifique. Nous nous intéressons aux simulations par éléments finis en hydrodynamique implémentées dans le logiciel openTelemac qui est largement utilisé pour des applications industrielles et scientifiques. Nous identifions et analysons les sources de cette non-reproductibilité. Nous définissons et implementons comment récupérer la reproductibilité numérique de deux modules d'openTelemac. Nous mesurons que le sur-coût en terme de temps de calcul de la version reproductible est tout à fait raisonnable en pratique<br>HPC simulations in various scientific domains suffer from failures of numerical reproducibility because of floating-point arithmetic peculiarities. Different distributions of a parallel computation may yield different numerical results. Numerical reproducibility is a requested feature to facilitate the debug, the validation and the test of industrial or large software. In this thesis, we focus on the openTelemac software that implements finite element simulation for industrial and scientific hydrodynamics. We identify and analyze the sources of this reproducibility failure. We define and implement how to recover numerical reproducibility in two openTelemac modules. We also measure that the running time extra-cost of the reproducible version is reasonable enough in practice
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Yannios, Nicholas, and mikewood@deakin edu au. "Computational aspects of the numerical solution of SDEs." Deakin University. School of Computing and Mathematics, 2001. http://tux.lib.deakin.edu.au./adt-VDU/public/adt-VDU20060817.123449.
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In the last 30 to 40 years, many researchers have combined to build the knowledge base of theory and solution techniques that can be applied to the case of differential equations which include the effects of noise. This class of ``noisy'' differential equations is now known as stochastic differential equations (SDEs).
Markov diffusion processes are included within the field of SDEs through the drift and diffusion components of the Itô form of an SDE. When these drift and diffusion components are moderately smooth functions, then the processes' transition probability densities satisfy the Fokker-Planck-Kolmogorov (FPK) equation -- an ordinary partial differential equation (PDE). Thus there is a mathematical inter-relationship that allows solutions of SDEs to be determined from the solution of a noise free differential equation which has been extensively studied since the 1920s.
The main numerical solution technique employed to solve the FPK equation is the classical Finite Element Method (FEM). The FEM is of particular importance to engineers when used to solve FPK systems that describe noisy oscillators. The FEM is a powerful tool but is limited in that it is cumbersome when applied to multidimensional systems and can lead to large and complex matrix systems with their inherent solution and storage problems.
I show in this thesis that the stochastic Taylor series (TS) based time discretisation approach to the solution of SDEs is an efficient and accurate technique that provides transition and steady state solutions to the associated FPK equation.
The TS approach to the solution of SDEs has certain advantages over the classical techniques. These advantages include their ability to effectively tackle stiff systems, their simplicity of derivation and their ease of implementation and re-use. Unlike the FEM approach, which is difficult to apply in even only two dimensions, the simplicity of the TS approach is independant of the dimension of the system under investigation. Their main disadvantage, that of requiring a large number of simulations and the associated CPU requirements, is countered by their underlying structure which makes them perfectly suited for use on the now prevalent parallel or distributed processing systems.
In summary, l will compare the TS solution of SDEs to the solution of the associated FPK equations using the classical FEM technique. One, two and three dimensional FPK systems that describe noisy oscillators have been chosen for the analysis. As higher dimensional FPK systems are rarely mentioned in the literature, the TS approach will be extended to essentially infinite dimensional systems through the solution of stochastic PDEs.
In making these comparisons, the advantages of modern computing tools such as computer algebra systems and simulation software, when used as an adjunct to the solution of SDEs or their associated FPK equations, are demonstrated.
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Sumon, Sarwan Kumar. "Innovative and effective transport solutions for masonry arch bridges, safety barriers and road humps through testing and numerical simulation." Thesis, University of Ulster, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.446253.
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Applebaum, Michael Paul. "Unstructured technology for high speed flow simulations." Diss., Virginia Tech, 1994. http://hdl.handle.net/10919/40057.
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Accurate and efficient numerical algorithms for solving the three dimensional Navier Stokes equations with a generalized thermodynamic and chemistry model and a one equation turbulence model on structured and unstructured mesh topologies are presented. In the thermo-chemical modeling, particular attention is paid to the modeling of the chemical source terms, modeling of equilibrium thermodynamics, and the modeling of the non-equilibrium vibrational energy source terms. In this work, nonequilibrium thermo-chemical models are applied in the unstructured environment for the first time.
A three-dimensional, second-order accurate k-exact reconstruction algorithm for the inviscid and viscous fluxes is presented. Several new methods for determining the stencil required for the inviscid and viscous k-exact reconstruction are discussed. A new simplified method for the computation of the viscous fluxes is also presented.
Implementation of the one equation Spalart and Allmaras turbulence model is discussed. In particular, an new integral formulation is developed for this model which allows flux splitting to be applied to the resulting convective flux.
Solutions for several test cases are presented to verify the solution algorithms discussed. For the thermo-chemical modeling, inviscid solutions to the three dimensional Aeroassist Flight Experiment vehicle and viscous solutions for the axi-symmetric Ram-II C are presented and compared to experimental data and/or published results. For the hypersonic AFE and Ram-II C solutions, focus is placed on the effects of the chemistry model in flows where ionization and dissociation are dominant characteristics of the flow field. Laminar and turbulent solutions over a flat plate are presented and compared to exact solutions and experimental data. Three dimensional higher order solutions using the k-exact reconstruction technique are presented for an analytic forebody.<br>Ph. D.
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Bujok, Karolina Edyta. "Numerical solutions to a class of stochastic partial differential equations arising in finance." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:d2e76713-607b-4f26-977a-ac4df56d54f2.
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We propose two alternative approaches to evaluate numerically credit basket derivatives in a N-name structural model where the number of entities, N, is large, and where the names are independent and identically distributed random variables conditional on common random factors. In the first framework, we treat a N-name model as a set of N Bernoulli random variables indicating a default or a survival. We show that certain expected functionals of the proportion L<sub>N</sub> of variables in a given state converge at rate 1/N as N [right arrow - infinity]. Based on these results, we propose a multi-level simulation algorithm using a family of sequences with increasing length, to obtain estimators for these expected functionals with a mean-square error of epsilon <sup>2</sup> and computational complexity of order epsilon<sup>−2</sup>, independent of N. In particular, this optimal complexity order also holds for the infinite-dimensional limit. Numerical examples are presented for tranche spreads of basket credit derivatives. In the second framework, we extend the approximation of Bush et al. [13] to a structural jump-diffusion model with discretely monitored defaults. Under this approach, a N-name model is represented as a system of particles with an absorbing boundary that is active in a discrete time set, and the loss of a portfolio is given as the function of empirical measure of the system. We show that, for the infinite system, the empirical measure has a density with respect to the Lebesgue measure that satisfies a stochastic partial differential equation. Then, we develop an algorithm to efficiently estimate CDO index and tranche spreads consistent with underlying credit default swaps, using a finite difference simulation for the resulting SPDE. We verify the validity of this approximation numerically by comparison with results obtained by direct Monte Carlo simulation of the basket constituents. A calibration exercise assesses the flexibility of the model and its extensions to match CDO spreads from precrisis and crisis periods.
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Polikarpov, Alexey. "Numerical simulation of rarefied gas flows based on the kinetic approach." Thesis, Aix-Marseille 1, 2011. http://www.theses.fr/2011AIX10088.
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Ce travail de thèse porte sur le développement de la méthode des vitesses discrètes pour la résolution numérique de équations cinétiques modèles, BGK, S modèle et ES modèle, qui représentent les différentes approximations de l’équation de Boltzmann<br>This work is devoted to the development of the numerical resolution of the kinetic model equations such as BGK, S-model, ES-model by the discrete velocity method. The different approximations of the Boltzmann equation are presented
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Garg, Dhiraj Kumar. "Numerical modeling and simulation of polymerization reactions in coiled flow inverters." Thesis, Strasbourg, 2014. http://www.theses.fr/2014STRAE002/document.
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L’objectif de ce travail fut d’améliorer la modélisation et la simulation de la polymérisation radicalaire dans des réacteurs continus et discontinus. Une solution analytique explicite généralisée (AS) fut obtenue dans le cas de la polymérisation en masse/solution, homogène et isotherme menée dans un réacteur fermé de volume variable. Les différentes étapes considérées furent l'initiation, la propagation, le transfert au monomère, au solvant, à un agent de transfert de chaîne, la terminaison par combinaison et dismutation. Différents modèles rendant compte des effets de gel, de vitrification et de cage ont également été considérés. AS a été validée avec succès par comparaison avec des solutions numériques et des données expérimentales de la littérature. Par ailleurs, AS a été étendue à des conditions pour lesquelles elle ne fut pas originellement développée comme par exemple des conditions non isothermes. La polyvalence et la flexibilité de AS sur l’ensemble de l’échelle de conversion du monomère furent ainsi démontrées. Ensuite, pour élargir encore plus son champ d'application, AS fut utilisée dans des simulations numériques (CFD). Une nouvelle transformation très simple a été proposée afin d’adimensionnaliser les constantes cinétiques en terme de concentration. Cela a permis de rentrer dans les simulations les données chimiques sous leur forme originale en mole et de faciliter ainsi le codage et le débogage du code de calcul. Cette transformation a ensuite été utilisée pour évaluer trois géométries tubulaires de microréacteur, un réacteur tubulaire droit (STR), à géométrie hélicoïdale (CTR) et à inversion de flux (CFIR), dans des conditions d'alimentation différentes (fluides d’entrée non ou parfaitement mélangés) et à de très faibles nombres de Reynolds (<1). La modélisation a été réalisée avec des paramètres constants ou variables des propriétés physiques du fluide sous écoulement (densité, viscosité et conductivité thermique) ainsi qu’en variant de manière discrète les coefficients de diffusion. Leurs effets sur les résultats de simulation ont été observés et comparés avec les données expérimentales publiées pour 4 monomères différents et furent en très bon accord. Les résultats pour le cas d’un mélange parfait furent indépendants de la géométrie des microréacteurs. Le CFIR semble être le réacteur le plus prometteur puisque, dans les conditions de microréaction étudiées, il a permis le meilleur contrôle des caractéristiques du polymère synthétisé<br>This thesis aimed at improving the modeling and simulation of free radical polymerization (FRP) in batch as well as in flow reactors. A generalized explicit analytical solution (AS) was obtained in case of variable volume, bulk/solution polymerization, homogeneous and isothermal batch reactor. The reaction steps included initiation, propagation, transfer to monomer, transfer to solvent, transfer to chain transfer agent (CTA), termination by combination and disproportionation. Different models of gel, glass and cage effects were also implemented explicitly. AS was validated against numerical solutions as well as published experimental data and was found in good agreement. Furthermore, its applicability was extended to conditions for which AS was not derived, i.e. non-isothermal conditions. The versatility and flexibility of AS over the complete range of monomer conversion were thus demonstrated. Then, to broaden its applications range even more, AS was used in CFD simulations. A new and simple transformation was proposed to make kinetic rate coefficients dimensionless in terms of concentration. This enabled chemical data to be fed in molar form to CFD modeling. It also enabled easy coding and debugging by keeping the original form of generation terms intact. The results were found to be improved after validation against experimental data. This transformation was then used for evaluating three tubula microreactor geometries, namely straight tube reactor (STR), coiled tube reactor (CTR) and coil flow inverter reactor (CFIR), under different feed conditions (unmixed or perfectly mixed) at very low Reynolds numbers (<1). The modeling for FRP was performed with constant or variable fluid physical parameters (density, viscosity and thermal conductivity) along with discrete variation of diffusion coefficients. Their effects on simulation results were observed and compared with published experimental data for 4 different monomers and were found to match perfectly. Results for mixed feed condition were found to be independent of microreactor geometry. CFIR seems to be the most promising reactor design under microreaction investigated conditions as it allowed the best control over polymer characteristics
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Kazakov, Mikhaïl. "A Methodology of semi-automated software integration : an approach based on logical inference. Application to numerical simulation solutions of Open CASCADE." INSA de Rouen, 2004. http://www.theses.fr/2004ISAM0001.
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Application integration is a process of bringing of data or functionality from one program together with that from another application programs that were not initially created to work together. Recently, the integration of numerical simulation solvers gained the importance. Integration within this domain has high complexity due to the presence of non-standard application interfaces that exchange complex, diverse and often ambiguous data. Nowadays, the integration is done mostly manually. Difficulties of the manual process force to increase the level of automation of the integration process. The author of this dissertation created a methodology and its software implementation for semi-automated (i. E. Partially automated) application integration. Application interfaces are usually represented by their syntactical definitions, but they miss the high-level semantics of applicative domains - human understanding on what the software does. The author proposes to use formal specifications (ontologies) expressed in Description Logics in order to specify software interfaces and define their high-level semantics. The author proposes a three-tier informational model for structuring ontologies and the integration process. This model distinguishes among computation-indeoendent domain knowledge (domain ontology), platform-independent interface specifications (interface ontology) and platform-specific technological integration information (technological ontology). A mediation ontology is defined to fuse the specifications. A reasoning procedure over these ontologies searches for semantic links among syntactic definitions of application interfaces. Connectors among applications are generated using the information about semantic links. Integrated applications communicate later via the connectors. The author designed a meta-model based data manipulation approach that facilitates and supports the software implementation of the integration process.
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Jones, Robert Linzey III. "Simulation and numerical solution of stochastic Petri nets with discrete and continuous timing." W&M ScholarWorks, 2002. https://scholarworks.wm.edu/etd/1539623410.
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We introduce a novel stochastic Petri net formalism where discrete and continuous phase-type firing delays can appear in the same model. By capturing deterministic and generally random behavior in discrete or continuous time, as appropriate, the formalism affords higher modeling fidelity and efficiencies to use in practice. We formally specify the underlying stochastic process as a general state space Markov chain and show that it is regenerative, thus amenable to renewal theory techniques to obtain steady-state solutions. We present two steady-state analysis methods depending on the class of problem: one using exact numerical techniques, the other using simulation. Although regenerative structures that ease steady-state analysis exist in general, a noteworthy problem class arises when discrete-time transitions are synchronized. In this case, the underlying process is semi-regenerative and we can employ Markov renewal theory to formulate exact and efficient numerical solutions for the stationary distribution. We propose a solution method that shows promise in terms of time and space efficiency. Also noteworthy are the computational tradeoffs when analyzing the "embedded" versus the "subordinate" Markov chains that are hidden within the original process. In the absence of simplifying assumptions, we propose an efficient regenerative simulation method that identifies hidden regenerative structures within continuous state spaces. The new formalism and solution methods are demonstrated with two applications.
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Steinbrecher, Andreas. "Numerical solution of quasi-linear differential-Algebraic equations and industrial simulation of multibody systems." [S.l.] : [s.n.], 2006. http://deposit.ddb.de/cgi-bin/dokserv?idn=980015936.
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Kurianski, Kristin Marie-Dettmers. "Estimates for solutions to the Dysthe equation and numerical simulations of walking droplets in harmonic potentials." Thesis, Massachusetts Institute of Technology, 2019. https://hdl.handle.net/1721.1/122173.
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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2019<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (pages 119-124).<br>In this thesis, we study wave-type phenomena both from a numerical point of view and a theoretical one. We first present the results of a numerical investigation of droplets walking in a harmonic potential on a vibrating fluid bath. The droplet's trajectory is described by an integro-differential equation, which is simulated numerically in various parameter regimes. We produce a regime diagram that summarizes the dependence of the walker's behavior on the system parameters for a droplet of fixed size. At relatively low vibrational forcing, a number of periodic and quasiperiodic trajectories emerge. In the limit of large vibrational forcing, the walker's trajectory becomes chaotic, but the resulting trajectories can be decomposed into portions of unstable quasiperiodic states. We then recast the integro-differential equation as a coupled system of ordinary differential equations in time. This method is used to simulate droplet lattices in various configurations and in the presence of a harmonic potential, creating structures reminiscent of Wigner molecules. The development of this approach is presented in detail along with its future applications. We then switch focus to a fluid system described by a modified nonlinear Schrödinger equation. The surface of an incompressible, inviscid, irrotational fluid of infinite depth can be described in two dimensions by the Dysthe equation. Recently, this equation has been used to model extraordinarily large waves occurring on the ocean's surface called rogue waves. In this thesis, we prove dispersive estimates and Strichartz estimates for the Dysthe equation. We then prove a Kato-type smoothing effect in which we are able to bound uniformly in space the L² norm in time of a fractional derivative of the linear solution by the L² norm in space of the initial data. This section of the thesis lays the groundwork for further developments in proving well-posedness via a contraction argument.<br>Financial support from National Science Foundation and the MIT School of Science<br>by Kristin Marie-Dettmers Kurianski.<br>Ph. D.<br>Ph.D. Massachusetts Institute of Technology, Department of Mathematics
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Haidar, Ali. "Numerical simulation of nonlinear shallow-water interactions between surface waves and a floating structure." Electronic Thesis or Diss., Université de Montpellier (2022-....), 2022. https://ged.scdi-montpellier.fr/florabium/jsp/nnt.jsp?nnt=2022UMONS093.
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Dans cette Thèse de Doctorat, nous nous intéressons à deux problématiques: (i) le développement de stratégies de stabilisation pour des méthodes de type discontinuous Galerkin (DG) appliquées à des écoulements shallow-water fortement non-linéaires, (ii) le développement d'une stratégie de modélisation et de simulation numérique des interactions non-linéaires entre les vagues et un objet flottant en surface, partiellement immergé. Les outils développés dans le cadre du premier axe de travail sont mis à profit et valorisés au cours de la deuxième partie.Les méthodes de discrétisation de type DG d'ordre élevé présentent en général des problèmes de robustesse en présence de singularités de la solution. Ces singularités peuvent être de plusieurs natures: discontinuité de la solution, discontinuité du gradient ou encore violation de la positivité de la hauteur d'eau pour des écoulements à surface libre. Nous introduisons dans la première partie de ce manuscript deux approches de type Finite-Volume Subcells permettant d'apporter une réponse à ces problèmes de robustesse. La première approche repose sur une correction a priori du schéma DG associée à un limiteur TVB et un limiteur de positivité. La seconde approche s'appuie quant à elle sur une correction a posteriori permettant d'identifier avec une meilleure précision les cellules incriminée, ainsi que sur les propriétés de robustesse inhérentes au schéma Volumes-Finis limite d'ordre un. Cette seconde approche permet d'assurer la robustesse du schéma DG initial en présence de discontinuité, ainsi que la positivité de la hauteur d'eau, tout en préservant une excellente qualité d'approximation, bénéficiant d'une résolution de l'ordre de la sous-maille. De façon préliminaire, cette seconde approche est également étendue au cas de la dimension deux d'espace horizontal. De nombreux cas-test permettent de valider cette approche.Dans la seconde partie, nous introduisons une nouvelle stratégie numérique conçue pour la modélisation et la simulation des interactions non linéaires entre les vagues en eau peu profonde et un objet flottant partiellement immergé. Au niveau continu, l'écoulement situé dans le domaine extérieur est globalement modélisé par les équations hyperboliques non-linéaires de Saint-Venant, tandis que la description de l'écoulement sous l'objet se réduit à une équation différentielle ordinaire non linéaire. Le couplage entre l'écoulement et l'objet est formulé comme un problème au bord, associé au calcul de l'évolution temporelle de la position des points d'interface air-eau-objet. Au niveau discret, la formulation proposée s'appuie sur une approximation DG d'ordre arbitraire, stabilisée à l'aide de la méthode de correction locale des sous-cellules (a posteriori) introduite dans la première partie. L'évolution temporelle de l'interface air-eau-objet est calculée à partir d'une description Arbitrary Lagrangian-Eulerian (ALE) et d'une transformation appropriée entre la configuration initiale et celle dépendant du temps. Pour n'importe quel ordre d'approximation polynomiale, l'algorithme résultant est capable de: (1) préserver la loi de conservation géométrique discrète (DGCL), (2) garantir la préservation de la positivité de la hauteur d'eau au niveau des sous-cellules, (3) préserver la classe des états stationnaires au repos (well-balancing), éventuellement en présence d'un objet partiellement immergé.Plusieurs validations numériques sont présentées, montrant le caractère opératoire de cette approche, et mettant en évidence que le modèle numérique proposé: (1) permet effectivement de modéliser les différents types d'interactions vague / objet flottants, (2) calcul efficacement l' évolution temporelle des points de contact air-eau-objet et redéfinit en conséquence le nouveau maillage grâce à la méthode ALE, (3) gère avec précision et robustesse les possibles singularités de l'écoulement, (4) préserve la haute résolution des schémas DG au niveau des sous-cellules<br>In this Ph.D., we investigate two main research problems: (i) the design of stabilization patches for higher-order discontinuous-Galerkin (DG) methods applied to highly nonlinear free-surface shallow-water flows, (ii) the construction of a new numerical approximation strategy for the simulation of nonlinear interactions between waves in a free-surface shallow flow and a partly immersed floating object. The stabilization methods developed in the first research line are used in the second part of this work.High-order discontinuous-Galerkin (DG) methods generally suffer from a lack of nonlinear stability in the presence of singularities in the solution. Such singularities may be of various kinds, involving discontinuities, rapidly varying gradients or the occurence of dry areas in the particular case of free-surface flows. In the first part of this work, we introduce two new stabilization methods based on the use of Finite-Volume Subcells in order to alleviate these robustness issues. The first method relies on an a priori limitation of the DG scheme, together with the use of a TVB slope-limiter and a PL. The second one is built upon an a posteriori correction strategy, allowing to surgically detect the incriminated local subcells, together with the robustness properties of the corresponding lowest-order Finite-Volume scheme. This last strategy allows to ensure the nonlinear stability of the DG scheme in the vicinity of discontinuities, as well as the positivity of the discrete water-height, while preserving the subcell resolution of the initial scheme. This second strategy is also preliminary investigated in the two dimensional horizontal case. An extensive set of test-cases assess the validity of this approach.In the second part, we introduce a new numerical strategy designed for the modeling and simulation of nonlinear interactions between surface waves in shallow-water and a partially immersed surface piercing object. At the continuous level, the flow located in the textit{exterior} domain is globally modeled with the nonlinear hyperbolic shallow-water equations, while the description of the flow beneath the object reduces to a nonlinear ordinary differential equation. The coupling between the flow and the object is formulated as a free-boundary problem, associated with the computation of the time evolution of the spatial locations of the air-water-body interface. At the discrete level, the proposed formulation relies on an arbitrary-order discontinuous Galerkin approximation, which is stabilized with the a posteriori Local Subcell Correction method through low-order finite volume scheme introduced in the first part. The time evolution of the air-water-body interface is computed from an Arbitrary-Lagrangian-Eulerian (ALE) description and a suitable smooth mapping between the original frame and the current configuration. For any order of polynomial approximation, the resulting algorithm is shown to: (1) preserves the Discrete Geometric Conservation Law, (2) ensures the preservation of the water-height positivity at the subcell level, (3) preserves the class of motionless steady states (well-balancing), possibly with the occurrence of a partially immersed object.Several numerical computations and test-cases are presented, highlighting that the proposed numerical model(1) effectively allows to model all types of wave / object interactions, (2) efficiently provides the time-evolution of the air-water-body contact points and accordingly redefine the new mesh-grid thanks to ALE method (3) accurately handles strong flow singularities without any robustness issues, (4) retains the highly accurate subcell resolution of discontinuous Galerkin schemes
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Atwi, Ali. "Theoretical and numerical calculations for the dynamics of colloidal suspensions of molecular particles in flowing solution inside mesopores." Phd thesis, Université du Maine, 2012. http://tel.archives-ouvertes.fr/tel-00718615.
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The purpose of this thesis is to develop a comprehensive model analysis in a three-dimensional spatial frame for the dynamics of molecular particles in dilute colloidal suspensions in solutions flowing inside pores of variable width, subject to hydrodynamic forces, Brownian motion and diffusive collisions at the rough pore boundaries, by using numerical simulations. The approach by simulations is necessary because it is extremely complex to use analytical tools at present to deal with the problem of diffusive collisions of the particles at the solid pore boundaries. The algorithms which we have developed and the corresponding simulations are sufficiently general and refined to be directly applied to the study of the dynamics of a wide variety of polymer and biological particles in dilute solutions under diverse physical and applicable hydrodynamic conditions inside pores. Moreover, the mechanisms leading to the adhesion of particles of nano sizes under what would be non-equilibrium conditions, due to the conflicting influence of the mechanical diffusive collisions and the attractive Hamaker forces at the boundaries, are of major interest. We have hence investigated a theoretical model to calculate the restitution coefficient from basic physical principles. The objective is to quantify the energy balance during the process of a diffusive collision of a nano particle under the influence of the repulsive forces on one hand, and the attractive Hamaker forces acting on the nano particle on the other. This is done by developing a model, based on the JKR and Hertz theories, to account for the energy losses during collisions, and for the energy gains due to the Hamaker interactions. Adhesion becomes an outcome if the energy balance permits this. Our theoretical model is developed by proposing a special analytic approach based on the Hamaker potential. We derive from the theoretical analysis a characteristic nonlinear equation for the restitution coefficient, and analyze its properties which determine under given physical conditions the outcome for adhesion or not.
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Wang, Bao. "Numerical Simulation of Detonation Initiation by the Space-Time Conservation Element and Solution Element Method." The Ohio State University, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=osu1293461692.
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Martins, Ramon Silva. "Numerical simulation of turbulent viscoelastic fluid flows : flow classification and preservation of positive-definiteness of the conformation tensor." Thesis, Lille 1, 2016. http://www.theses.fr/2016LIL10127/document.
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Le but de ce travail est de fournir une amélioration de la connaissance sur le phénomène de la réduction de la traînée induite par polymère en considérant certains aspects de sa simulation numérique et les changements qui se produisent dans la cinématique de l’écoulement. Dans un premier temps, les transformations du type racine carrée et kernel racine-k pour le tenseur de conformation du modèle FENE-P ont été implémentées afin d’assurer la positivité du tenseur de conformation. Cependant, ces approches divergent en raison du caractère non-borné du tenseur de conformation. Cette contrainte n’a pas été respectée, même avec l’inclusion de diffusion artificielle. L’effet d’amortissement de la diffusion artificielle a permis d’assurer la stabilité numérique, mais il aboutit à une réduction de la traînée relative de 22% à 42% plus faible que prévue par les approches standards. Dans un second temps, les modes hyperboliques, paraboliques et elliptiques des écoulements turbulents viscoélastiques ont été évalués en utilisant de différents critères de classification d’écoulements. Certains avantages concernant les critères objectifs ont été discutés. On a observé que les domaines hyperboliques contribuent de manière significative à la cinématique de l’écoulement. Enfin, on a observé une tendance des domaines elliptiques et hyperboliques à devenir paraboliques et que cette tendance augmente avec l’élasticité<br>The purpose of this work is to provide an enhancement of the knowledge about the polymer-induced drag reduction phenomenon by considering some aspects of its numerical simulation and the changes that occur in the flow kinematics. In the first part, the square root and kernel root-k formulations for the conformation tensor in the FENE-P model were implemented and showed to preserve the positiveness of the conformation tensor. However, they led to numerical divergence due to the loss of boundedness of the conformation tensor. This constraint was violated even with the inclusion of artificial diffusion. The damping effect of artificial diffusion helped to ensure numerical stability, but led to relative drag reduction from 22% to 42% lower than expected from traditional methods. In the second part, the hyperbolic, parabolic and elliptic modes of turbulent viscoelastic flows were evaluated by means of different flow classification criteria. Some advantages of considering objective criteria were discussed. It was shown that the hyperbolic domains significantly contribute to the flow kinematics. Finally, a tendency of both elliptic and hyperbolic domains to become parabolic was observed and found to increase with the elasticity
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Cai, Jiayi. "Turbulence modeling using machine learning driven by direct numerical simulations." Electronic Thesis or Diss., université Paris-Saclay, 2024. http://www.theses.fr/2024UPAST171.
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En simulation numérique de la turbulence, les modèles RANS (Reynolds-Averaged Navier-Stokes) permettent de résoudre les grandeurs moyennes des écoulements pour un coût de calcul très inférieur à la résolution "exacte" par simulation numérique directe (DNS). Ils exigent cependant un effort de modélisation considérable. L'une des problématiques habituellement rencontrées est celle de la modélisation du tenseur de Reynolds (RST), qui apparaît lors de l'application aux équations de Navier-Stokes d'un opérateur de moyenne statistique. Le modèle le plus couramment utilisé pour ce tenseur est l'hypothèse linéaire de Boussinesq, mais il souffre de nombreux défauts. Diverses généralisations ont été proposées dans la littérature, bien qu'elles manquent également d'universalité. Alors que ces fermetures complexes sont souvent basées sur des considérations semi-empiriques, il est désormais possible, grâce à l'accroissement des ressources informatiques, d'établir des modèles de fermeture neuronaux basés à la fois sur la physique et sur les données et notamment les données DNS. Ces dernières années, plusieurs modèles d'apprentissage automatique ont été développés dans ce domaine et ont montré des résultats prometteurs. Un modèle particulièrement pertinent pour cette thèse est celui des réseaux de neurones à base tensorielle (TBNN), s'appuyant sur des réseaux de neurones profonds qui vise à prédire le tenseur d'anisotropie (une version adimensionnée du RST). L'avantage principal de ce modèle est qu'il garantit l'invariance galiléenne et rotationnelle, en incorporant le modèle physique, le Modèle Généralisé de Viscosité Turbulente (GEVM), dans l'architecture du réseau neuronal. En prenant en compte les forces et les limites des études TBNN existantes, l'objectif principal de cette thèse est de développer et valider un TBNN augmenté (aTBNN) pour deux types d'écoulements confinés : l'écoulement de canal plan (PCF) et l'écoulement de canal carré (SDF). Ce travail est divisé en deux phases : la phase a priori et la phase a posteriori. La phase a priori se concentre sur la configuration, l'entraînement et l'évaluation de l'aTBNN. Dans cette phase, des entrées supplémentaires du réseau, une base tensorielle optimisée et des stratégies d'apprentissage avancées sont utilisées pour obtenir des prédictions équilibrées et physiquement correctes du tenseur d'anisotropie. Ensuite, l'aTBNN entraîné est intégré dans le code maison TrioCFD afin d'évaluer ses performances dans la prédiction de l'écoulement, en particulier le champ de vitesse. La validation a posteriori est particulièrement importante car plusieurs études ont montré que, même avec des entrées RST haute-fidélité, les solveurs RANS peuvent produire des prédictions de champ de vitesse insatisfaisantes. Pour répondre à cela, divers modèles de propagation de données haute-fidélité et modèles neuronaux sont implémentés et comparés aux modèles RANS de référence dans TrioCFD. Deux stratégies de couplage, la substitution itérative et la substitution figée, sont testées pour intégrer l'aTBNN avec les modèles RANS de référence, en combinaison avec des réseaux neuronaux supplémentaires pour corriger l'énergie cinétique turbulente et le taux de dissipation. Pour le cas du PCF, les simulations a priori et a posteriori montrent des résultats prometteurs, les modèles neuronaux dépassant les modèles RANS classiques dans plusieurs cas et montrant une forte concordance avec les données DNS. En revanche, le cas SDF présente de plus grands défis en raison de la complexité physique des écoulements secondaires et du manque de données d'entraînement couvrant différents régimes turbulents. En particulier, la méthode de couplage itératif s'est révélée instable dans ce scénario. Cependant, la méthode de substitution figée a montré un potentiel pour obtenir des résultats cohérents, et mérite une investigation plus approfondie pour exploiter pleinement ses capacités<br>In the field of computational fluid dynamics, the Reynolds-Averaged Navier-Stokes (RANS) models allow the resolution of mean flow quantities at a much lower computational cost than the "exact" resolution provided by Direct Numerical Simulation (DNS). However, these models require significant modeling efforts. One major challenge is the modeling of the Reynolds Stress Tensor (RST), which emerges when applying a statistical averaging operator to the Navier-Stokes equations. The most commonly used model for this tensor is the linear Boussinesq hypothesis, but it suffers from some well-known limitations. Numerous generalizations have been proposed in the literature, though they also lack universality. While these complex closures are often based on semi-empirical considerations, advances in computational power now make it possible to establish physics-informed and DNS data-driven neural network-based closure models. In recent years, various machine-learning frameworks have been developed in this domain, showing promising results. Of particular relevance to this thesis is the Tensor Basis Neural Network (TBNN) framework, based on deep neural networks which aims to predict the anisotropy tensor (a scaled version of the RST). A key advantage of this framework is its incorporation of Galilean and rotational invariances, achieved by embedding the General Eddy Viscosity Model into the neural network architecture. Building upon the TBNN framework, this work aims to develop and validate an augmented Tensor Basis Neural Network (aTBNN) for two canonical wall-bounded flows: Plane Channel Flow (PCF) and Square Duct Flow (SDF). The research is divided into two phases: a priori and a posteriori phases. The a priori phase focuses on configuring, training, and evaluating the aTBNN. In this phase, additional input features, an optimized tensor basis, and advanced training strategies are employed to produce balanced and physically accurate predictions of the anisotropy tensor. Following this, the trained aTBNN is integrated into the in-house CFD code TrioCFD to assess its performance in predicting realistic flow behavior, such as velocity profiles. The a posteriori validation is particularly important, as previous studies have shown that even with high-fidelity RST inputs, RANS solvers can produce unsatisfactory velocity field predictions. To address this, various high-fidelity data propagation models and neural network models are implemented and compared with baseline RANS models in TrioCFD. Two coupling strategies, iterative and frozen substitution, are tested to integrate the aTBNN with baseline RANS models, along with extra neural networks for turbulent kinetic energy and dissipation rate corrections. For the PCF case, both a priori and a posteriori results from the proposed framework demonstrate promising outcomes, outperforming classical RANS models in certain cases and showing strong agreement with the DNS data. The SDF case presents more challenges due to the physical complexity of secondary flows and the limited availability of training data across different turbulence regimes. The iterative coupling method, in particular, proved to be unstable in this case. However, the frozen substitution method has shown potential for achieving accurate results, which requires further investigation
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Gryngarten, Leandro Damian. "Multi-phase flows using discontinuous Galerkin methods." Diss., Georgia Institute of Technology, 2012. http://hdl.handle.net/1853/45824.
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This thesis is concerned with the development of numerical techniques to simulate compressible multi-phase flows, in particular a high-accuracy numerical approach with mesh adaptivity. The Discontinuous Galerkin (DG) method was chosen as the framework for this work for being characterized for its high-order of accuracy -thus low numerical diffusion- and being compatible with mesh adaptivity due to its locality. A DG solver named DiGGIT (Discontinuous Galerkin at the Georgia Institute of Technology) has been developed and several aspects of the method have been studied. The Local Discontinuous Galerkin (LDG) method -an extension of DG for equations with high-order derivatives- was extended to solve multiphase flows using Diffused Interface Methods (DIM). This multi-phase model includes the convection of the volume fraction, which is treated as a Hamilton-Jacobi equation. This is the first study, to the author's knowledge, in which the volume fraction of a DIM is solved using the DG and the LDG methods. The formulation is independent of the Equation of State (EOS) and it can differ for each phase. This allows for a more accurate representation of the different fluids by using cubic EOSs, like the Peng-Robinson and the van der Waals models. Surface tension is modeled with a new numerical technique appropriate for LDG. Spurious oscillations due to surface tension are common to all the capturing schemes, and this new approach presents oscillations comparable in magnitude to the most common schemes. The moment limiter (ML) was generalized for non-uniform grids with hanging nodes that result from adaptive mesh refinement (AMR). The effect of characteristic, primitive, or conservative decomposition in the limiting stage was studied. The characteristic option cannot be used with the ML in multi-dimensions. In general, primitive variable decomposition is a better option than with conservative variables, particularly for multiphase flows, since the former type of decomposition reduces the numerical oscillations at material discontinuities. An additional limiting technique was introduced for DIM to preserve positivity while minimizing the numerical diffusion, which is especially important at the interface. The accuracy-preserving total variation diminishing (AP-TVD) marker for ``troubled-cell' detection, which uses an averaged-derivative basis, was modified to use the Legendre polynomial basis. Given that the latest basis is generally used for DG, the new approach avoids transforming to the averaged-derivative basis, what results in a more efficient technique.
Furthermore, a new error estimator was proposed to determine where to refine or coarsen the grid. This estimator was compared against other estimator used in the literature and it showed an improved performance. In order to provide equal order of accuracy in time as in space, the commonly used 3rd-order TVD Runge-Kutta (RK) scheme in the DG method was replaced in some cases by the Spectral Deferred Correction (SDC) technique. High orders in time were shown to only be required when the error in time is significant. For instance, convection-dominated compressible flows require for stability a time step much smaller than is required for accuracy, so in such cases 3rd-order TVD RK resulted to be more efficient than SDC with higher orders.
All these new capabilities were included in DiGGIT and have provided a generalized approach capable of solving sub- and super-critical flows at sub- and super-sonic speeds, using a high-order scheme in space and time, and with AMR.
Canonical test cases are presented to verify and validate the formulation in one, two, and three dimensions. Finally, the solver is applied to practical applications. Shock-bubble interaction is studied and the effect of the different thermodynamic closures is assessed. Interaction between single-drops and a wall is simulated. Sticking and the onset of splashing are observed. In addition, the solver is used to simulate turbulent flows, where the high-order of accuracy clearly shows its benefits. Finally, the methodology is challenged with the simulation of a liquid jet in cross flow.
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Zhou, Lin. "Simulations of emissivity in passive microwave remote sensing with 3-dimensional numerical solutions of Maxwell equations and fast algorithm /." Thesis, Connect to this title online; UW restricted, 2003. http://hdl.handle.net/1773/5986.
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Arregui, Iñigo. "Une technique eulérienne pour la simulation des coques minces en grands déplacements." Châtenay-Malabry, Ecole centrale de Paris, 1994. http://www.theses.fr/1994ECAP0332.
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Nous présentons dans cette thèse une formulation eulérienne pour l'étude des coques minces en grands deplacements. Le modèle de coque utilisé est l'un de ceux proposés par W. T. Koiter, et sur lequel Ph. Destuynder et M. Salaun avaient développé une formulation variationnelle mixte et une technique d'approximation de la géométrie de la surface moyenne. Dans la formulation eulérienne, à chaque itération, nous faisons l'hypothèse de petits déplacements entre deux configurations successives, ce qui nous permet de linéariser les équations. Pour tenir compte des non-linéarités géométriques, certaines grandeurs doivent être transportées entre les différentes configurations. Dans certains cas, la courbe d'équilibre de la coque présente un (voire deux) point limite, et donc des zones d'instabilité. Afin de bien les approcher, une technique originale de pilotage a été mise au point, compte tenu du système à résoudre. Par ailleurs, puisque la géométrie de la coque est approchée, nous avons aussi développé une technique d'approximation de la surface moyenne, afin de pouvoir raffiner le maillage, si on le souhaite, et pouvoir recommencer les calculs à l'itération suivante. Tous ces outils ont été intégrés dans un code de calcul, que nous avons validé avec plusieurs exemples classiques.
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Shao, Haibing. "Modelling reactive transport processes in porous media." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2010. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-61738.
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Reactive transport modelling has wide applications in geosciences. In the field of hydrogeology, it has been utilised to simulate the biogeochemical processes that disperse and degrade contaminants in the aquifer. For geotechnical applications, such as geological CO2 sequestration, the reaction of CO2 with the ambient saline aquifer determines the final success of storage. In a radioactive waste repository, scientists rely on reactive transport models to predict the mobilisation of hazardous radionuclides within space and time.
In this work, the multi-component mass transport code OpenGeoSys, was coupled with two geochemical solvers, the Gibbs Energy Minimization Selektor (GEM) and the Biogeochemical Reaction Network Simulator (BRNS). Both coupled codes were verified against analytical solutions and simulation results from other numerical models. Moreover, the coupling interface was developed for parallel simulation. Test runs showed that the speed-up of reaction part had a very good linearity with number of nodes in the mesh. However, for three dimensional problems with complex geochemical reactions, the model performance was dominated by solving transport equations of mobile chemical components.
OpenGeoSys-BRNS was applied to a two dimensional groundwater remediation problem. Its calculated concentration profiles fitted very well with analytical solutions and numerical results from TBC. The model revealed that natural attenuation of groundwater contaminants is mainly controlled by the mixing of carbon source and electron donor. OpenGeoSys-GEM was employed to investigate the retardation mechanism of radionuclides in the near field of a nuclear waste repository. Radium profiles in an idealised bentonite column was modelled with varying clay/water ratios. When clay content is limited, Ba-Sr-Ra sulfate solid solutions have a very strong retardation effect on the aqueous radium. Nevertheless, when clay mineral is abundant, cation exchange sites also attract Sr and Ba, thus dominates the transport of Ra.
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Delestre, Olivier. "Simulation du ruissellement d'eau de pluie sur des surfaces agricoles." Phd thesis, Université d'Orléans, 2010. http://tel.archives-ouvertes.fr/tel-00587197.
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L'objectif de ce travail est le développement d'un modèle et d'une méthode numérique adaptés à la simulation du ruissellement d'eau de pluie sur des surfaces agricoles. Pour cela, nous utilisons un système d'équations aux dérivées partielles pour les eaux peu profondes : le système de Saint Venant. La pluie et l'infiltration y sont pris en compte par l'ajout de termes source et le couplage avec un modèle d'infiltration. Le système étant hyperbolique et conservatif nous choisissons d'utiliser un schéma aux volumes finis avec reconstruction hydrostatique. Avec cette reconstruction nous obtenons un schéma permettant de traiter les équilibres stationnaires et les interfaces sec/mouillé dues aux événements pluvieux. Tout d'abord, nous effectuons une comparaison systématique de différents flux numériques, de différentes reconstructions d'ordre deux (MUSCL et ENO modifiées) et de différentes méthodes de traitement des frottements sur des solutions analytiques unidimensionnelles. Ces comparaisons nous permettent de choisir une méthode numérique adaptée à la simulation du ruissellement qui en outre capture les phénomènes de type roll-waves. Ensuite nous nous intéressons au traitement de la pluie et de l'infiltration à l'aide du modèle de Green-Ampt. Cette méthode généralisée en dimension deux est validée sur des résultats expérimentaux obtenus à l'INRA d'Orléans et à l'IRD. La méthode numérique choisie et validée a été implémentée dans FullSWOF_2D un logiciel libre écrit en C++ pour la simulation de ruissellement d'eau de pluie sur des surfaces agricoles.
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Morrison, Graeme A. "Thermally driven hydromagnetic dynamos." Thesis, University of Glasgow, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.312706.
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Nikolkina, Irina. "Modélisation des écoulements de gravité et des ondes longues : application à l'évaluation des risques de catastrophes naturelles dans les Antilles françaises." Thesis, Antilles-Guyane, 2011. http://www.theses.fr/2011AGUY0435/document.
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La thèse est consacrée à la recherche des catastrophes marines (tsunamis, ondes de tempête) dans les Antilles françaises, en utilisant des modèles analytiques et numériques de mécanique des fluides. L'accent est mis sur le développement de modèles de mouvement de glissements de terrain et des vagues causées par ces glissements. Le modèle le plus simple du glissement de terrain «solide block» est utilisé pour évaluer les caractéristiques des flux pyroclastiques du volcan Soufrière-Hills (Montserrat). Un modèle plus complexe de modélisation de glissement de terrain (modèle de Savage-Hutter) a été étudié analytiquement, donnant ainsi une nouvelle famille de solutions exactes décrivant le mouvement de l'écoulement par gravité non linéaire dans une vallée ou dans un canyon sous-marin. Le modèle comprend des ondes simples (Riemann waves),le cas d'un barrage qui cède (dam-break problem), des solutions auto-similaires dans la M-fonne et « chapeaux paraboliques ». Grâce à la théorie linéaire de l'eau peu profonde nous avons étudié le processus de génération de tsunamis par des glissements de terrain de volume variable, se déplaçant à une vitesse variable dans un bassin de profondeur variable. Dans le cas d'un fond marin particulier (cas sans "réflexion"), les phénomènes de résonnance ont été étudiés dans un bassin à profondeur variable. Nous avons utilisé des méthodes numériques pour la résolution non-linéaire des équations des eaux peu profondes afin d'analyser des catastrophes marines réelles (les ondes de tempête causées par le cyclone Lili en 2002, le tsunami volcanique de 2003 à Montserrat) et probables (un tsunami prés des côtes de la Martinique). Des données sur les catastrophes<br>The dissertation is devoted to research in the field of marine natural hazards (tsunamis, storm surges) in the French West Indies, using analytical and numerical models of fluid mechanics. Emphasis is placed on the development of models of landslide motion and generated tsunami waves. The simple "solid block" model is used to evaluate the characteristics of pyroclastic flow Soufriere Hills volcano (Montserrat). The "fluid model" of a landslide (so called Savage-Hutter model) is studied analytically; within this model a new family of exact solutions that describe the motion of nonlinear gravity flow in a valley or underwater canyon is found: nonlinear Riemann wave, dan break problem, self-similar solutions (M - wave and parabolic cap). In the framework of the linear shallow water theory the process of generation of tsunami waves by landslides of variable volume moving with variable velocity above the basin of variable depth is studied. For the specific bottom profile ("reflectionless" one) the resonant phenomena is investigated in the basin of variable depth. Numerical methods are used to analyze marine hazards: historical (storm surges, caused by Cyclone LILI in 2002; volcanic tsunami 2003 on Montserrat) and possible events (possible tsunami of the coast of Martinique). Various data on marine natural disasters are obtained during field surveys (volcanic tsunami in 2003, stonn surges caused by Hurricane Dean in 2007). Designed catalogs of tsunamis and storm surges are created based on results of numerical modeling and field studies; some statistical analysis is perfomed
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Hooshyar, Soroush [Verfasser], Natalie [Akademischer Betreuer] Germann, Natalie [Gutachter] Germann, and Nikolaus A. [Gutachter] Adams. "Modeling of semidilute entangled polymer solutions and numerical simulation of industrially relevant benchmark flows to study shear banding / Soroush Hooshyar ; Gutachter: Natalie Germann, Nikolaus A. Adams ; Betreuer: Natalie Germann." München : Universitätsbibliothek der TU München, 2020. http://d-nb.info/1207074950/34.
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Bilyeu, David Lawrence. "Numerical Simulation of Chemical Reactions Inside a Shock-Tube by the Space-Time Conservation Element and Solution Element Method." The Ohio State University, 2008. http://rave.ohiolink.edu/etdc/view?acc_num=osu1213363652.
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Ayasoufi, Anahita. "Numerical Simulation of Heat Conduction with Melting and/or Freezing by Space-Time Conservation Element and Solution Element Method." See Full Text at OhioLINK ETD Center (Requires Adobe Acrobat Reader for viewing), 2004. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=toledo1103147485.
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Dissertation (Ph.D.)--University of Toledo, 2004.<br>Typescript. "A dissertation [submitted] as partial fulfillment of the requirements of the Doctor of Philosophy degree in Engineering." Bibliography: leaves 194-211.
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Rice, Matthew Jason. "High Resolution Simulation of Laminar and Transitional Flows in a Mixing Vessel." Diss., Virginia Tech, 2011. http://hdl.handle.net/10919/27716.
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The present work seeks to fully investigate, describe and characterize the distinct flow regimes existing within a mixing vessel at various rotational speeds. This investigation is computational in nature and simulates the flow within a baffled tank containing a Rushton turbine of the standard configuration. For a Re based on impeller diameter and blade rotational speed (Re â ¡ Ï ND2/μ) the following flow regimes were identified and investigated in detail: Reverse/reciprocating flows at very low Re (<10); stalled flows at low Re (â 10); laminar pumping flow for higher Re and transitional pumping flow (10 squared < Re <10 to the 4th).
For the three Re numbers 1, 10 and 28, it was found that for the higher Re number (28), the flow exhibited the familiar outward pumping action associated with radial impellers under turbulent flow conditions. However, as the Re number decreases, the net radial flow during one impeller revolution was reduced and for the lowest Re number a reciprocating motion with negligible net pumping was observed. In order to elucidate the physical mechanism responsible for the observed flow pattern at low Re, the forces acting on a fluid element in the radial direction were analyzed. Based on this analysis, a simplified quasi-analytic model of the flow was developed that gives a satisfactory qualitative, as well as quantitative representation of the flow at very low Re.
Investigation of the transitional flow regime (Re â 3000) includes a compilation and characterization of ensemble and turbulent quantities such as the Reynolds stress components, dissipation length η and time scales Ï , as well a detailed investigation of the near-impeller flow and trailing vortex. Calculation and compilation of all terms in the turbulent kinetic energy transport equation was performed (including generation and the illusive turbulent pressure work). Specifically, the most important transport mechanism was turbulent convection/diffusion from the impeller disk-plane/trailing vortex region. Mean flow transport of turbulent kinetic energy was primarily towards the impeller disk-plane and radially outward from the trailing vortex region. The turbulent pressure work was found to partially counteract turbulent convection. Turbulent dissipation followed by turbulent viscous work were found to be the least important mechanism responsible for turbulent transport with both terms being maximized within the vortex region and at the disk-plane down-stream from the vortices.<br>Ph. D.
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Philip-Alliez, Camille. "Etude numérique et expérimentale de l'écoulement nasal chez les enfants présentant une obstruction nasale." Thesis, Aix-Marseille 1, 2011. http://www.theses.fr/2011AIX10140/document.
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Une des données essentielles que recherche le clinicien ORL lors de son diagnostic concerne la fonctionnalité des fosses nasales. Dans certains cas, cette fonction n’est approchée que de manière partielle par les diverses méthodes de mesures mises à sa disposition. La prévalence des obstructions nasales chroniques dans la population générale1 (30% de la population) souligne l’intérêt que les orthodontistes doivent porter aux pathologies respiratoires. L’acquisition d’un outil de diagnostic fiable de l’obstruction nasale permettra d’effectuer un traitement plus précoce afin de guider au mieux la croissance crânio-faciale. La RAA ne peut pas être actuellement utilisée comme unique examen diagnostique, car sa corrélation avec les évaluations subjectives peut rester faible. L’objectif de ce travail est de fournir un modèle d’aide au diagnostic de l’obstruction nasale pour tous les patients. Dans les cas où la RAA ne permet pas un diagnostic certain de l’obstruction nasale, la simulation numérique permettrait, après avoir identifié les situations anatomiques particulières, d’obtenir une approche fonctionnelle objective en confirmant ou non le diagnostic de la RAA. La méthode utilisée pour ce travail de thèse consiste en une résolution complète des équations de Navier-Stokes dans des géométries reconstruites en 3D, c’est-à-dire ayant bénéficié d’un traitement numérique pour extraire les contours puis créer les maillages surfaciques et volumiques. Le développement d'outils de mesure objectifs est un enjeu capital pour déterminer les stratégies thérapeutiques optimales et pour évaluer les résultats des traitements. La modélisation par ordinateur de la dynamique des flux aériens au sein des fosses nasales à partir de reconstructions tomodensitométriques tridimensionnelles peut présenter des applications cliniques. Une de ses applications permettrait à l’ORL de visualiser l’écoulement post-opératoire virtuellement<br>One of the essential data sought by the clinician in his diagnosis on the functionality of the nasal cavity. In some cases, this function is only partially approached by various measurement methods at its disposal. The prevalence of chronic nasal obstruction in the population (30% of the population) underlines the interest to orthodontists must wear respiratory disorders. The acquisition of a reliable diagnostic tool of nasal obstruction will allow for earlier treatment to guide the best craniofacial growth. The RAA can not be currently used as single diagnostic test, because its correlation with subjective assessments can remain low. The objective of this work is to provide a model for the diagnosis of nasal obstruction for all patients. In cases where the RAA does not allow a definite diagnosis of nasal obstruction, numerical simulations allow, after identifying the particular anatomical situations, to obtain a functional objective or not confirming the diagnosis of rheumatic fever. The methodology for this thesis consists of a complete resolution of the Navier-Stokes equations in geometries reconstructed in 3D, that is to say who received a digital processing to extract the contours and surface meshes and create volume. The development of objective measurement tools is a key issue in determining optimal treatment strategies and to evaluate treatment outcomes. Computer modeling of the dynamics of air flow within the nasal cavity from three-dimensional CT reconstructions may have clinical applications. One of its applications allow to visualize the flow postoperative virtually
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Arenas, Tawil Abraham José. "Mathematical modelling of virus RSV: qualitative properties, numerical solutions and validation for the case of the region of Valencia." Doctoral thesis, Universitat Politècnica de València, 2010. http://hdl.handle.net/10251/8316.
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El objetivo de esta memoria se centra en primer lugar en la modelización del comportamiento de enfermedades estacionales mediante sistemas de ecuaciones diferenciales y en el estudio de las propiedades dinámicas tales como positividad, periocidad, estabilidad de las soluciones analíticas y la construcción de esquemas numéricos para las aproximaciones de las soluciones numéricas de sistemas de ecuaciones diferenciales de primer orden no lineales, los cuales modelan el comportamiento de enfermedades infecciosas estacionales tales como la transmisión del virus Respiratory Syncytial Virus (RSV).
Se generalizan dos modelos matemáticos de enfermedades estacionales y se demuestran que tiene soluciones periódicas usando un Teorema de Coincidencia de Jean Mawhin. Para corroborar los resultados analíticos, se desarrollan esquemas numéricos usando las técnicas de diferencias finitas no estándar desarrolladas por Ronald Michens y el método de la transformada diferencial, los cuales permiten reproducir el comportamiento dinámico de las soluciones analíticas, tales como positividad y periocidad.
Finalmente, las simulaciones numéricas se realizan usando los esquemas implementados y parámetros deducidos de datos clínicos
De La Región de Valencia de personas infectadas con el virus RSV. Se confrontan con las que arrojan los métodos de Euler, Runge Kutta y la rutina de ODE45 de Matlab, verificándose mejores aproximaciones para tamaños de paso mayor a los que usan normalmente estos esquemas tradicionales.<br>Arenas Tawil, AJ. (2009). Mathematical modelling of virus RSV: qualitative properties, numerical solutions and validation for the case of the region of Valencia [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/8316<br>Palancia
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Therme, Nicolas. "Schémas numériques pour la simulation de l'explosion." Thesis, Aix-Marseille, 2015. http://www.theses.fr/2015AIXM4775/document.
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Dans les installations nucléaires, les explosions, qu’elles soient d’origine interne ou externe, peuvent entrainer la rupture du confinement et le rejet de matières radioactives dans l’environnement. Il est donc fondamental, dans un cadre de sûreté de modéliser ce phénomène. L’objectif de cette thèse est de contribuer à l’élaboration de schémas numériques performants pour résoudre ces modèles complexes. Les travaux présentés s’articule autour de deux axes majeurs : le développement de schémas volumes finis consistants pour les équations d’Euler compressible qui modélise les ondes de choc et celui de schémas performants pour la propagation d’interfaces comme le front de flamme lors d'une déflagration. La discrétisation spatiale est de type mailles décalées pour tous les schémas développés. Les schémas pour les équations d'Euler se basent sur une formulation en énergie interne qui permet de préserver sa positivité ainsi que celle de la masse volumique. Un bilan d'énergie cinétique discret peut être obtenu et permet de retrouver un bilan d'énergie totale par l'ajout d'un terme de correction dans le bilan d'énergie interne. Le schéma ainsi construit est consistant au sens de Lax avec les solutions faibles entropiques des équations continues. On utilise les propriétés des équations de type Hamilton-Jacobi pour construire une classe de schémas volumes finis performants sur une large variété de maillages modélisant la propagation du front de flamme. Ces schémas garantissent un principe du maximum et possèdent des propriétés importantes de monotonie et consistance qui permettent d'obtenir un résultat de convergence<br>In nuclear facilities, internal or external explosions can cause confinement breaches and radioactive materials release in the environment. Hence, modeling such phenomena is crucial for safety matters. The purpose of this thesis is to contribute to the creation of efficient numerical schemes to solve these complex models. The work presented here focuses on two major aspects: first, the development of consistent schemes for the Euler equations which model the blast waves, then the buildup of reliable schemes for the front propagation, like the flame front during the deflagration phenomenon. Staggered discretization is used in space for all the schemes. It is based on the internal energy formulation of the Euler system, which insures its positivity and the positivity of the density. A discrete kinetic energy balance is derived from the scheme and a source term is added in the discrete internal energy balance equation to preserve the exact total energy balance. High order, MUSCL-like interpolators are used in the discrete momentum operators. The resulting scheme is consistent (in the sense of Lax) with the weak entropic solutions of the continuous problem. We use the properties of Hamilton-Jacobi equations to build a class of finite volume schemes compatible with a large number of meshes to model the flame front propagation. These schemes satisfy a maximum principle and have important consistency and monotonicity properties. These latters allows to derive a convergence result for the schemes based on Cartesian grids
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Maunoury, Matthieu. "Méthode de visualisation adaptée aux simulations d'ordre élevé : application à la compression-reconstruction de champs rayonnés pour des ondes harmoniques." Thesis, Toulouse 3, 2019. http://www.theses.fr/2019TOU30021.
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Bien que les méthodes d'ordre élevé permettent de réaliser des simulations très précises et peu coûteuses, il y a un manque d'outils pour analyser et exploiter les résultats obtenus par ces nouveaux schémas. L'objectif de cette thèse est de mettre en place un cadre et des algorithmes efficaces pour visualiser des solutions calculées par des méthodes d'ordre élevé. Notre approche est basée sur la construction d'une approximation affine optimisée de la solution numérique qui peut être post-traitée dans un logiciel de visualisation standard. Un maillage de représentation est créé via un indicateur d'erreurs a posteriori qui contrôle l'erreur de visualisation entre la solution numérique et sa représentation ponctuellement. Une stratégie est établie afin d'assurer que les (dis)continuités soient bien rendues. Un travail particulier est développé pour traiter les éléments d'ordre élevé (éléments courbes) et utilise notamment des indicateurs d'erreurs a posteriori spécifiques. Des exemples numériques montrent le potentiel de la méthode de visualisation. Dans une seconde partie, nous nous intéressons au calcul et à la reconstruction de champs rayonnés pour des problèmes d'ondes en régime harmonique. Nous proposons une méthodologie pour générer une reconstruction précise de champs rayonnés tout en limitant le nombre d'informations nécessaires (i.e. en compressant les données). Pour ce faire, nous nous appuyons sur des fonctions de base composées de polynômes d'ordre élevé et d'ondes planes, ainsi que sur un développement du noyau de la formule intégrale servant au rayonnement. La méthode de visualisation permet alors de représenter fidèlement (décompression) les cartographies obtenues<br>While high order methods allow to perform very accurate simulations with low costs, there is a lack of tools to analyze and exploit results obtained by these new schemes. The objective of this thesis is to design a framework and efficient algorithms to visualize solutions computed by high order methods. Our approach is based on the construction of an optimized affine approximation of the numerical solution which can be handled by any standard visualization software. A representation mesh is created via an a posteriori estimate which control visualization error between the numerical solution and its representation, and is performed pointwise. A strategy is established to ensure that (dis)continuities are well-rendered. A special work is done to treat high order elements (curved elements) and in particular use specific a posteriori estimates. Several numerical examples demonstrate the potential of the visualization method. In a second part, we examine the computation and reconstruction of radiated fields for wave problems in harmonic regime. We propose a methodology to generate an accurate reconstruction of radiated fields while limiting the information needed (i.e. compressing the data). For this purpose, we rely on basis functions composed of high order polynomials and plane waves, as well as a development of the kernel used for the integral representation. The visualization method allows to faithfully represent (decompression process) the cartographies obtained
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He, Hao. "Numerical simulations of unsteady flows in a pulse detonation engine by the conservation element and solution element method." Columbus, Ohio : Ohio State University, 2006. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1141850240.
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Heryudono, Alfa R. H. "Adaptive radial basis function methods for the numerical solution of partial differential equations, with application to the simulation of the human tear film." Access to citation, abstract and download form provided by ProQuest Information and Learning Company; downloadable PDF file, 178 p, 2008. http://proquest.umi.com/pqdweb?did=1601513551&sid=5&Fmt=2&clientId=8331&RQT=309&VName=PQD.
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Chen, Yung-Yu. "A Multi-Physics Software Framework on Hybrid Parallel Computing for High-Fidelity Solutions of Conservation Laws." The Ohio State University, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=osu1313000975.
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Prados, Emmanuel. "Application of the theory of the viscosity solutions to the Shape From Shading problem." Phd thesis, Université de Nice Sophia-Antipolis, 2004. http://tel.archives-ouvertes.fr/tel-00007916.
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Le problème du « Shape From Shading » est aujourd'hui considéré comme un problème mal posé et difficile à résoudre. Afin de bien comprendre les difficultés de ce problème et d'apporter des solutions fiables et pertinentes, nous proposons une approche rigoureuse basée sur la notion de solution de viscosité.<br />Après avoir considéré et exploité au maximum les équations (aux dérivées partielles) obtenues à partir de la modélisation classique du problème du « Shape From Shading », nous proposons et étudions de nouvelles équations provenant de modélisations plus réalistes que celles qui avaient été traitées classiquement dans la littérature. Cette démarche nous permet alors de démontrer qu'avec de telles nouvelles modélisations, le problème du « Shape From Shading » est généralement un problème complètement bien posé. En d'autres termes, nous prouvons que la version classique du problème du « Shape from Shading » est devenu mal posée à cause d'une trop grande simplification de la modélisation.<br />Dans ce travail, nous proposons aussi une extension de la notion de solutions de viscosité singulières développée récemment par Camilli et Siconolfi. Cette extension nous permet de proposer une nouvelle caractérisation des solutions de viscosité discontinues. Ce nouveau cadre théorique nous permet aussi d'unifier les différents résultats théoriques proposés dans le domaine du « Shape From Shading ».
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Vieira, Jardel 1991. "Um estudo computacional de equações pseudo-parabólicas para mecânica dos fluidos e fenômenos de transporte em meios porosos." [s.n.], 2015. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307021.
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Orientador: Eduardo Cardoso de Abreu<br>Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica<br>Made available in DSpace on 2018-08-27T06:42:03Z (GMT). No. of bitstreams: 1
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Previous issue date: 2015<br>Resumo: O foco desta dissertação de mestrado consiste em um estudo computacional de equações pseudo-parabólicas em mecânica dos fluidos e fenômenos de transporte de fluidos em meios porosos. Serão considerados problemas de valor de contorno e inicial associados a duas classes de modelos de equações de evolução pseudo-parabólicas: um modelo de advecção-difusão com termo pseudo-parabólico que exibe um certo caráter dispersivo e um outro modelo pseudo-parabólico "puro", i.e., sem a presença do termo de advecção. O primeiro modelo se relaciona com a modelagem física do fluxo de duas fases incompressíveis em dinâmica de fluidos em meios porosos, onde são considerados modelos de pressão capilar dinâmica, ou seja, em que os efeitos dinâmicos são também incluídos na diferença de pressão entre as fases fluidas. Uma discussão sobre a relevância física em aplicações e da importância matemática do sistema governante de equações para pressão capilar dinâmica em fenômenos de transporte de fluidos em meios porosos é também feita de modo a indicar algum suporte à escolha dos métodos estudados para aproximação numérica dos modelos consideradores. Além disso, um conjunto de experimentos numéricos é apresentado e discutido para avaliar a qualidade das soluções obtidas do estudo proposto, bem como para justificar variações dos métodos numéricos estudados. Especificamente, para o modelo pseudo-parabólico puro, os resultados são comparados com soluções analíticas para o caso linear. Para o modelo pseudo-parabólico com o termo de advecção, é avaliado se os resultados dos métodos numéricos empregados concordam qualitativamente com resultados da literatura<br>Abstract: The focus of this work consists of a computational study of pseudo-parabolic equations in fluid mechanics and transport phenomena in porous media. For concreteness, we consider initial-boundary value problems related to two classes of systems of evolution pseudo-parabolic equations: a advection-diffusion model, which in turn the pseudo-parabolic term exhibits a certain dispersive character, and a second of "purely" pseudo-parabolic nature, i.e., without the presence of advection term. The first model relates to the modeling of incompressible two-phase flow in porous media, which in turn takes into account the nonlinear dynamic capillary pressure effects, where the dynamic effects are also included into the pressure difference between the fluid phases. Further, a discussion of the physical and mathematical relevance of the governing system of equations for dynamic capillary pressure in porous media fluid transport phenomena is also made in order to drive the choice of the numerical approximations for the differential models under investigation. Moreover, a set of numerical experiments are presented and discussed to address the quality of the obtained solutions proposed study, as well as to justify variations of the numerical methods studied. Specifically, to the purely pseudo-parabolic model, the results are compared along with analytical solutions with respect to a linear case. On the other hand, to the nonlinear pseudo-parabolic model with advection term, it is performed numerical experiments in order to account the correct qualitative behavior of the computed solutions against the available results discussed in the recent literature<br>Mestrado<br>Matematica Aplicada<br>Mestre em Matemática Aplicada