Dissertations / Theses on the topic 'Numerical Methods for Neutron Transport'
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ALCARO, FABIO. "Quasi-static Methods in Neutron Transport." Doctoral thesis, Politecnico di Torino, 2012. http://hdl.handle.net/11583/2501653.
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The present work represents a little but valuable contribution to the advancement of the research in the field of the neutron kinetics of innovative nuclear reactors. As modern computer frames are becoming more and more performing and because the treatment of innovative nuclear reactor systems requires high accuracy results, the neutron transport theory is currently being adopted for full-core calculations. Embracing such tendency, in the present work the quasi-static approach has been adopted and implemented for the design of computational codes capable of performing reliable transient calculations. The underlying idea has been the development of the kinetic module on top of the transport solver, in such a way that the former can be flexibly plugged into the codes ystem, independently from the transport solver itself. In particular, two computer codes have been developed: the first has been designed coupling the stand-alone DRAGON transport solver to an "ad hoc" reactor kinetic module; the second code has been developed within the ERANOS code system. A Java object-oriented platform developed by CEA-Cadarache constitutes the framework where a kinetic package has been designed, adopting the code's API (Application Programming Interface) for the full integration in the code system. The well known Improved Quasi-static Method (IQM) and the innovative Predictor-Corrector Quasi-static Method (PCQM) have been implemented in both computer codes. In the present work a deep analysis of the two types of quasi-static schemes has been carried out as well as the description and validation of the aforementioned computer codes.
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BARBARINO, ANDREA. "Numerical Methods for Neutron Transport Calculations of Nuclear Reactors." Doctoral thesis, Politecnico di Torino, 2014. http://hdl.handle.net/11583/2561774.
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The objective of this thesis, which in clearly inspired by an industrial framework, is to try and narrow the gap between theoretical neutron modelling and application in the context of nuclear reactor design. This thesis is divided into three main chapters, preceded by a general overview. This structure reflects the three main topics which were chosen for this research project.
The first topic develops the Spectral Element Method (SEM) approach and its use in conjunction with transport approximations. As it is documented in the specialized numerical analysis handbooks and in previous works by the author, the method has an excellent convergence rate which outperforms most classical schemes, but it has also some important drawbacks which sometimes seem to discourage its use for linear transport problems applied to nontrivial benchmarks. In order to elaborate the methodology of the specific problems encountered in reactor physics, three aspects are addressed looking for improvements. The first topic analyzed is related to the convergence order, whose value is less straightforward to define a priori by means of functional analysis than other numerical schemes. The adjective “spectral” refers in fact to the maximum order claimed, exponential with respect to the average size of the mesh. A comprehensive set of convergence tests is carried out applying SEM to a few transport models and with the aid of manufactured solutions, thus isolating the numerical effects from the deviations which are due only to modelling approximations. The hypothesis of grid conformity is also relaxed, replacing the classical Galerkin variational formulation with the Discontinuous Galerkin theory, characterized by a more flexible treatment of the mesh interfaces; this scheme allows local grid refinement and opens the way, in perspective, to mesh adaption. Finally, a simple and sufficiently flexible technique to deform the boundaries of each mesh is introduced and applied, in order to adapt the grid to curved geometries. In this way, the advantages of SEM can be applied to a vast class of common problems like lattice calculations. Moreover, thanks to a change of the basis functions used in SEM, it is possible to obtain elements with three sides (straight or deformed), that are a typical war horse of the Finite Element approach.
The second topic is essentially devoted to the most “industrial” part of the thesis, developed entirely during the stay of the author in the AREVA NP headquarters in Paris. In AREVA, and in all other nuclear engineering enterprises, neutron diffusion is still the preferred neutronic model for full-core studies. Better approximations are reserved for library preparation, fuel studies and code validation, none of these being typically too much time or budget-constrained. Today needs start to require a certain level of improvement also in full-core analyses, trying to fitly model localized dis-homogeneities and reduce the penalizing engineering margins which are taken as provisions. On the other hand, a change in the model does not mean only an effort to write a new code, but has huge follow-ups due to the validation processes required by the authorities. Second-order transport may support the foreseen methodology update because it can be implemented re-using diffusion routines as the computational engine. The AN method, a second-order approximation of the transport equation, has been introduced in some studies, and its effect is discussed. Moreover, some effort has been reserved to the introduction of linear anisotropy in the model.
The last topic deals with ray effects; they are a known issue of the discrete ordinate approach (SN methods) which is responsible for a reduction in the accuracy of the solution, especially in penetration problems with low scattering, like several shielding calculations performed for operator safety concerns. Ray effects are here characterized from a formal point of view in both static and time dependent situations. Then, quantitative indicators are defined to help with the interpretation of the SN results. Based on these studies, some mitigation measures are proposed and their efficacy is discussed.
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Marquez, Damian Jose Ignacio. "Multilevel acceleration of neutron transport calculations." Thesis, Atlanta, Ga. : Georgia Institute of Technology, 2007. http://hdl.handle.net/1853/19731.
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Thesis (M.S.)--Nuclear and Radiological Engineering, Georgia Institute of Technology, 2008.Committee Chair: Stacey, Weston M.; Committee Co-Chair: de Oliveira, Cassiano R.E.; Committee Member: Hertel, Nolan; Committee Member: van Rooijen, Wilfred F.G.
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Blackburn, Megan Satterfield. "Numerical benchmarking of a coarse-mesh transport (COMET) method for medical physics applications." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/29763.
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Thesis (Ph.D)--Mechanical Engineering, Georgia Institute of Technology, 2010.Committee Chair: Farzad Rahnema; Committee Co-Chair: Eric Elder; Committee Member: C.-K. Chris Wang; Committee Member: Rebecca Howell; Committee Member: Sang Cho. Part of the SMARTech Electronic Thesis and Dissertation Collection.
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Byambaakhuu, Tseelmaa. "Development of Advanced Numerical Methods for Solving Neutron Transport Problems: DG-DSA and the Shishkin Mesh for Problems with Sharp Layers." The Ohio State University, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=osu1618855174338701.
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Blake, Jack. "Domain decomposition methods for nuclear reactor modelling with diffusion acceleration." Thesis, University of Bath, 2016. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.698988.
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In this thesis we study methods for solving the neutron transport equation (or linear Boltzmann equation). This is an integro-differential equation that describes the behaviour of neutrons during a nuclear fission reaction. Applications of this equation include modelling behaviour within nuclear reactors and the design of shielding around x-ray facilities in hospitals. Improvements in existing modelling techniques are an important way to address environmental and safety concerns of nuclear reactors, and also the safety of people working with or near radiation. The neutron transport equation typically has seven independent variables, however to facilitate rigorous mathematical analysis we consider the monoenergetic, steady-state equation without fission, and with isotropic interactions and isotropic source. Due to its high dimension, the equation is usually solved iteratively and we begin by considering a fundamental iterative method known as source iteration. We prove that the method converges assuming piecewise smooth material data, a result that is not present in the literature. We also improve upon known bounds on the rate of convergence assuming constant material data. We conclude by numerically verifying this new theory. We move on to consider the use of a specific, well-known diffusion equation to approximate the solution to the neutron transport equation. We provide a thorough presentation of its derivation (along with suitable boundary conditions) using an asymptotic expansion and matching procedure, a method originally presented by Habetler and Matkowsky in 1975. Next we state the method of diffusion synthetic acceleration (DSA) for which the diffusion approximation is instrumental. From there we move on to explore a new method of seeing the link between the diffusion and transport equations through the use of a block operator argument. Finally we consider domain decomposition algorithms for solving the neutron transport equation. Such methods have great potential for parallelisation and for the local application of different solution methods. A motivation for this work was to build an algorithm applying DSA only to regions of the domain where it is required. We give two very different domain decomposed source iteration algorithms, and we prove the convergence of both of these algorithms. This work provides a rigorous mathematical foundation for further development and exploration in this area. We conclude with numerical results to illustrate the new convergence theory, but also solve a physically-motivated problem using hybrid source iteration/ DSA algorithms and see significant reductions in the required computation time.
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ABRATE, NICOLO'. "Methods for safety and stability analysis of nuclear systems." Doctoral thesis, Politecnico di Torino, 2022. http://hdl.handle.net/11583/2971611.
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Di, Chicco Augusto. "Optimization of a calculation scheme through the parametric study of effective nuclear cross sections and application to the estimate of neutronic parameters of the ASTRID fast nuclear reactor." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2018.
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This thesis presents the project for the optimization of the APOLLO3® neutronic calculation scheme applied to the 4th generation fast neutron reactor ASTRID. APOLLO3® is the new multipurpose neutronic platform developed by the CEA. It incorporates many of the previous generation codes used in the French reactor core design supply chain. Like all deterministic codes, APOLLO3® solves the neutron transport equation with a discretization of the variables of interest: multi-group method for the energy, discrete ordinates and spherical harmonics for the angular variable, collision probabilities and characteristics methods for the spatial variable. The resolution of the transport equation handles useful quantities such as the neutron flux and multiplication factor, fission rates and cross sections to understand the physical behaviour of the reactor core. Currently it is not possible to use deterministic codes to simulate an entire reactor with a heterogeneous 3D geometry and a fine energy description, so to simplify the study of complete neutron field at core level, the calculation scheme is divided into two phases: lattice and core calculation. The main purpose of this work is to find an optimal degree of approximations of the calculation scheme for the evaluation of a desired physical effect and of the user constraints. In order to reach this optimum, several studies have been carried out with different levels of approximations. The results have been benchmarked with the ones obtained using the stochastic code TRIPOLI4®, used as a reference and to ensure a good accuracy. Furthermore, several sensitivity studies have been carried out to understand how the different approximations affect the macroscopic cross sections evaluation, because these dependences are not yet fully understood.
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Sheehan, B. P. "Multigrid methods for isotropic neutron transport." Connect to online resource, 2007. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3256437.
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Muddle, John Christopher. "Advanced numerical methods for neutron star interfaces." Thesis, University of Southampton, 2015. https://eprints.soton.ac.uk/375551/.
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Baker, David James. "Characteristic-based methods for modelling neutron transport." Thesis, University of Nottingham, 2012. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.580409.
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In this thesis we study techniques based on the method of characteristics applied to neutron transport problems. These methods have been widely used in the solution of such problems and have been implemented in a number of commercial and re- search codes, such as the CACTUS module of Serco Assurance's WIMS software. Since characteristics-based methods are widely used in the field of nuclear energy, where safety, reliability and predictability are of paramount importance, a rigorous analysis of the convergence properties of these methods is required; this topic represents the main focus of this thesis. We begin by using results from functional analysis to obtain an a priori bound on the error in the L [infinity] norm when employing the method of long characteristics (LC) in space in conjunction with a discrete ordinates (SN) method in angle. Our analysis applies to a source problem in 20 space with vacuum boundary conditions. We show that, with refinement in element diameter h, convergence of the LC method is at least O(h), and under certain assumptions, the SN scheme is also at least first order. These results are confirmed by numerical tests. Next we obtain a similar bound on the L[infinity]-error in the case when a variety of the short characteristic (SC) method, which approximates the neutron flux with an arbitrarily high-order piecewise polynomial approximation, is exploited. We prove that for a qth order polynomial approximation, we can expect at least O(hq) convergence in the SC solution. This result is again validated by numerical results. Finally, the SC method described above is implemented in a code and applied to a variety of standard theoretical benchmark problems as well as a number of realistic models, both from the literature and provided by Serco Assurance. Results from the code show close agreement with those from a variety of independent, external sources.
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Scheben, Fynn. "Iterative methods for criticality computations in neutron transport theory." Thesis, University of Bath, 2011. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.545319.
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This thesis studies the so-called “criticality problem”, an important generalised eigenvalue problem arising in neutron transport theory. The smallest positive real eigenvalue of the problem contains valuable information about the status of the fission chain reaction in the nuclear reactor (i.e. the criticality of the reactor), and thus plays an important role in the design and safety of nuclear power stations. Because of the practical importance, efficient numerical methods to solve the criticality problem are needed, and these are the focus of this thesis. In the theory we consider the time-independent neutron transport equation in the monoenergetic homogeneous case with isotropic scattering and vacuum boundary conditions. This is an unsymmetric integro-differential equation in 5 independent variables, modelling transport, scattering, and fission, where the dependent variable is the neutron angular flux. We show that, before discretisation, the nonsymmetric eigenproblem for the angular flux is equivalent to a related eigenproblem for the scalar flux, involving a symmetric positive definite weakly singular integral operator(in space only). Furthermore, we prove the existence of a simple smallest positive real eigenvalue with a corresponding eigenfunction that is strictly positive in the interior of the reactor. We discuss approaches to discretise the problem and present discretisations that preserve the underlying symmetry in the finite dimensional form. The thesis then describes methods for computing the criticality in nuclear reactors, i.e. the smallest positive real eigenvalue, which are applicable for quite general geometries and physics. In engineering practice the criticality problem is often solved iteratively, using some variant of the inverse power method. Because of the high dimension, matrix representations for the operators are often not available and the inner solves needed for the eigenvalue iteration are implemented by matrix-free inneriterations. This leads to inexact iterative methods for criticality computations, for which there appears to be no rigorous convergence theory. The fact that, under appropriate assumptions, the integro-differential eigenvalue problem possesses an underlying symmetry (in a space of reduced dimension) allows us to perform a systematic convergence analysis for inexact inverse iteration and related methods. In particular, this theory provides rather precise criteria on how accurate the inner solves need to be in order for the whole iterative method to converge. The theory is illustrated with numerical examples on several test problems of physical relevance, using GMRES as the inner solver. We also illustrate the use of Monte Carlo methods for the solution of neutron transport source problems as well as for the criticality problem. Links between the steps in the Monte Carlo process and the underlying mathematics are emphasised and numerical examples are given. Finally, we introduce an iterative scheme (the so-called “method of perturbation”) that is based on computing the difference between the solution of the problem of interest and the known solution of a base problem. This situation is very common in the design stages for nuclear reactors when different materials are tested, or the material properties change due to the burn-up of fissile material. We explore the relation ofthe method of perturbation to some variants of inverse iteration, which allows us to give convergence results for the method of perturbation. The theory shows that the method is guaranteed to converge if the perturbations are not too large and the inner problems are solved with sufficiently small tolerances. This helps to explain the divergence of the method of perturbation in some situations which we give numerical examples of. We also identify situations, and present examples, in which the method of perturbation achieves the same convergence rate as standard shifted inverse iteration. Throughout the thesis further numerical results are provided to support the theory.
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Bennison, Tom. "Adaptive discontinuous Galerkin methods for the neutron transport equation." Thesis, University of Nottingham, 2014. http://eprints.nottingham.ac.uk/28944/.
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In this thesis we study the neutron transport (Boltzmann transport equation) which is used to model the movement of neutrons inside a nuclear reactor. More specifically we consider the mono-energetic, time independent neutron transport equation. The neutron transport equation has predominantly been solved numerically by employing low order discretisation methods, particularly in the case of the angular domain. We proceed by surveying the advantages and disadvantages of common numerical methods developed for the numerical solution of the neutron transport equation before explaining our choice of using a discontinuous Galerkin (DG) discretisation for both the spatial and angular domain. The bulk of the thesis describes an arbitrary order in both angle and space solver for the neutron transport equation. We discuss some implementation issues, including the use of an ordered solver to facilitate the solution of the linear systems resulting from the discretisation. The resulting solver is benchmarked using both source and critical eigenvalue computations. In the pseudo three--dimensional case we employ our solver for the computation of the critical eigenvalue for three industrial benchmark problems. We then employ the Dual Weighted Residual (DWR) approach to adaptivity to derive and implement error indicators for both two--dimensional and pseudo three--dimensional neutron transport source problems. Finally, we present some preliminary results on the use of a DWR indicator for the eigenvalue problem.
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Lanser, Debby. "Numerical methods for atmospheric flow and transport problems." [S.l. : Amsterdam : s.n.] ; Universiteit van Amsterdam [Host], 2002. http://dare.uva.nl/document/64490.
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Mauger, R. L. "Nodal methods for solving the neutron transport equation for reactor analysis." Thesis, Imperial College London, 1988. http://hdl.handle.net/10044/1/47178.
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Weston, Joseph. "Numerical methods for time-resolved quantum nanoelectronics." Thesis, Université Grenoble Alpes (ComUE), 2016. http://www.theses.fr/2016GREAY040/document.
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De récents progrès dans la nanoélectronique quantique ont donné lieu à denouvelles expériences avec des sources cohérentes d'électrons unique. Lorsqu'undispositif électronique quantique est manipulé sur une échelle de temps pluscourte que le temps de vol caractéristique d'un électron à travers ledispositif, toute une gamme de possibilités qui sont conceptuellement nouvellesdeviennent possible. Pour traiter de telles situations physiques, des avancéescorrespondantes sont nécessaires dans les techniques de simulation, pour aiderà comprendre, ainsi qu'à concevoir, la prochaine génération d'expériences dansce domaine.Les techniques les plus avancées pour simuler ce genre de physique nécessitentun temps de calcul qui croît de linéairement avec la taille dusystème, mais de manière quadratique avec la durée simulée.Ceci est particulièrement problématique pour les cas où un électron restedans le dispositif pendant une durée beaucoup plus longue que le temps devol balistique. Dans cette thèse on propose d'améliorer un algorithmeexistant, basé sur des fonctions d'onde, pour traiter le transport quantiquerésolu en temps dont le temps de calcul croît linéairement avec la taille du système ainsique la durée simulée. Par la suite on exploite cet algorithme pour étudierplusieurs systèmes physiques intéressants. En particulier on trouve quel'application d'un train d'impulsions de tension à un interféromètre à électronspeut stabiliser la modification dynamique du schéma d'interférence.On exploite cet effet pour faire de la spectroscopied'états d'Andreev et de Majorana existant dans des structure hybridessupraconducteur-nanofil.Les algorithmes numériques sont implémentés en tant qu'extension du logicielde transport quantique Kwant. Cette implémentation est utilisée pour tousles résultats numériques présentés dans la thèse, ainsi que d'autres projetsde recherche couvrants une grande gamme de physique: effet Hall quantique,isolants topologiques de Floquet, interféromètres de type Fabry-Pérot, etjonctions supraconductricesRecent technical progress in the field of quantum nanoelectronics have lead toexciting new experiments involving coherent single electron sources.When quantum electronic devices are manipulated on time scales shorterthan the characteristic time of flight of electrons through the device, a wholeclass of conceptually new possibilities become available. In order totreat such physical situations, corresponding advances in numerical techniquesand their software implementation are required both as a tool to aidunderstanding, and also to help when designing the next generation ofexperiments in this domain.Recent advances in numerical methods have lead to techniques for which thecomputation times scales linearly with the system volume, but as thesquare of the simulation time desired. This is particularly problematicfor cases where the characteristic dwell time of electrons in the centraldevice is much longer than the ballistic time of flight. Here, we proposean improvement to an existing wavefunction based algorithm fortreating time-resolved quantum transport which scales linearly in both thesystem volume and desired simulation time. We use this technique tostudy a number of interesting physical cases. In particular we find that theapplication of a train of voltage pulses to an electronic interferometercan be used to stabilise the dynamical modification of the interferencethat was recently proposed. We use this to perform spectroscopy on Majoranaand Andreev resonances in hybrid superconductor-nanowire structures.The numerical algorithms are implemented as an extension to the Kwantquantum transport software. This implementation is used for all the numericalresults presented here, in addition to other work, covering a wide varietyof physical applications: quantum Hall effect, Floquet topological insulators,Fabry-Perot interferometers and superconducting junction
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Besselman, Michael J. "Advanced Numerical Methods in General Relativistic Magnetohydrodynamics." BYU ScholarsArchive, 2012. https://scholarsarchive.byu.edu/etd/3394.
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We show our work to refine the process of evolutions in general relativistic magnetohydrodynamics. We investigate several areas in order to improve the overall accuracy of our results. We test several versions of conversion methodologies between different sets of variables. We compare both single equation and two equations solvers to do the conversion. We find no significant improvement for multiple equation conversion solvers when compared to single equation solvers. We also investigate the construction of initial data and the conversion of coordinate systems between initial data code and evolution code. In addition to the conversion work, we have improved some methodologies to ensure data integrity when moving data from the initial data code to the evolution code. Additionally we add into the system of MHD equations a new field to help control the no monopole constraint. We perform a characteristic decomposition of the system of equations in order to derive the associated boundary condition for this new field. Finally, we implement a WENO (weighted non-oscillatory) system. This is done so we can evolve and track shocks that are generated during an evolution of our GRMHD equations.
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Carreño, Sánchez Amanda María. "Integration methods for the time dependent neutron diffusion equation and other approximations of the neutron transport equation." Doctoral thesis, Universitat Politècnica de València, 2020. http://hdl.handle.net/10251/144771.
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[ES] Uno de los objetivos más importantes en el análisis de la seguridad en el campo de la ingeniería nuclear es el cálculo, rápido y preciso, de la evolución de la potencia dentro del núcleo del reactor. La distribución de los neutrones se puede describir a través de la ecuación de transporte de Boltzmann. La solución de esta ecuación no puede obtenerse de manera sencilla para reactores realistas, y es por ello que se tienen que considerar aproximaciones numéricas.
En primer lugar, esta tesis se centra en obtener la solución para varios problemas estáticos asociados con la ecuación de difusión neutrónica: los modos lambda, los modos gamma y los modos alpha. Para la discretización espacial se ha utilizado un método de elementos finitos de alto orden. Diversas características de cada problema espectral se analizan y se comparan en diferentes reactores.
Después, se investigan varios métodos de cálculo para problemas de autovalores y estrategias para calcular los problemas algebraicos obtenidos a partir de la discretización espacial. La mayoría de los trabajos destinados a la resolución de la ecuación de difusión neutrónica están diseñados para la aproximación de dos grupos de energía, sin considerar dispersión de neutrones del grupo térmico al grupo rápido. La principal ventaja de la metodología que se propone es que no depende de la geometría del reactor, del tipo de problema de autovalores ni del número de grupos de energía del problema.
Tras esto, se obtiene la solución de las ecuaciones estacionarias de armónicos esféricos. La implementación de estas ecuaciones tiene dos principales diferencias respecto a la ecuación de difusión neutrónica. Primero, la discretización espacial se realiza a nivel de pin. Por tanto, se estudian diferentes tipos de mallas. Segundo, el número de grupos de energía es, generalmente, mayor que dos. De este modo, se desarrollan estrategias a bloques para optimizar el cálculo de los problemas algebraicos asociados.
Finalmente, se implementa un método modal actualizado para integrar la ecuación de difusión neutrónica dependiente del tiempo. Se presentan y comparan los métodos modales basados en desarrollos en función de los diferentes modos espaciales para varios tipos de transitorios. Además, también se desarrolla un control de paso de tiempo adaptativo, que evita la actualización de los modos de una manera fija y adapta el paso de tiempo en función de varias estimaciones del error.[CAT] Un dels objectius més importants per a l'anàlisi de la seguretat en el camp de l'enginyeria nuclear és el càlcul, ràpid i precís, de l'evolució de la potència dins del nucli d'un reactor. La distribució dels neutrons pot modelar-se mitjançant l'equació del transport de Boltzmann. La solució d'aquesta equació per a un reactor realístic no pot obtenir's de manera senzilla. És per això que han de considerar-se aproximacions numèriques. En primer lloc, la tesi se centra en l'obtenció de la solució per a diversos problemes estàtics associats amb l'equació de difusió neutrònica: els modes lambda, els modes gamma i els modes alpha. Per a la discretització espacial s'ha utilitzat un mètode d'elements finits d'alt ordre. Algunes de les característiques dels problemes espectrals s'analitzaran i es compararan per a diferents reactors. Tanmateix, diversos solucionadors de problemes d'autovalors i estratègies es desenvolupen per a calcular els problemes obtinguts de la discretització espacial. La majoria dels treballs per a resoldre l'equació de difusió neutrònica estan dissenyats per a l'aproximació de dos grups d'energia i sense considerar dispersió de neutrons del grup tèrmic al grup ràpid. El principal avantatge de la metodologia exposada és que no depèn de la geometria del reactor, del tipus de problema d'autovalors ni del nombre de grups d'energia del problema. Seguidament, s'obté la solució de les equacions estacionàries d'harmònics esfèrics. La implementació d'aquestes equacions té dues principals diferències respecte a l'equació de difusió. Primer, la discretització espacial es realitza a nivell de pin a partir de l'estudi de diferents malles. Segon, el nombre de grups d'energia és, generalment, major que dos. D'aquesta forma, es desenvolupen estratègies a blocs per a optimitzar el càlcul dels problemes algebraics associats. Finalment, s'implementa un mètode modal amb actualitzacions dels modes per a integrar l'equació de difusió neutrònica dependent del temps. Es presenten i es comparen els mètodes modals basats en l'expansió dels diferents modes espacials per a diversos tipus de transitoris. A més a més, un control de pas de temps adaptatiu es desenvolupa, evitant l'actualització dels modes d'una manera fixa i adaptant el pas de temps en funció de vàries estimacions de l'error.
[EN] One of the most important targets in nuclear safety analyses is the fast and accurate computation of the power evolution inside of the reactor core. The distribution of neutrons can be described by the neutron transport Boltzmann equation. The solution of this equation for realistic nuclear reactors is not straightforward, and therefore, numerical approximations must be considered. First, the thesis is focused on the attainment of the solution for several steady-state problems associated with neutron diffusion problem: the $\lambda$-modes, the $\gamma$-modes and the $\alpha$-modes problems. A high order finite element method is used for the spatial discretization. Several characteristics of each type of spectral problem are compared and analyzed on different reactors. Thereafter, several eigenvalue solvers and strategies are investigated to compute efficiently the algebraic eigenvalue problems obtained from the discretization. Most works devoted to solve the neutron diffusion equation are made for the approximation of two energy groups and without considering up-scattering. The main property of the proposed methodologies is that they depend on neither the reactor geometry, the type of eigenvalue problem nor the number of energy groups. After that, the solution of the steady-state simplified spherical harmonics equations is obtained. The implementation of these equations has two main differences with respect to the neutron diffusion. First, the spatial discretization is made at level of pin. Thus, different meshes are studied. Second, the number of energy groups is commonly bigger than two. Therefore, block strategies are developed to optimize the computation of the algebraic eigenvalue problems associated. Finally, an updated modal method is implemented to integrate the time-dependent neutron diffusion equation. Modal methods based on the expansion of the different spatial modes are presented and compared in several types of transients. Moreover, an adaptive time-step control is developed that avoids setting the time-step with a fixed value and it is adapted according to several error estimations.
Carreño Sánchez, AM. (2020). Integration methods for the time dependent neutron diffusion equation and other approximations of the neutron transport equation [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/144771
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Käser, Martin Andreas. "Adaptive methods for the numerical simulation of transport processes." [S.l.] : [s.n.], 2003. http://deposit.ddb.de/cgi-bin/dokserv?idn=970272855.
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Nelson, Adam Gregory Ivanov Kostadin N. "Monte Carlo methods for neutron transport on Graphics Processing Units using CUDA." [University Park, Pa.] : Pennsylvania State University, 2009. http://etda.libraries.psu.edu/theses/approved/WorldWideIndex/ETD-4605/index.html.
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Nenna, Luca. "Numerical Methods for Multi-Marginal Optimal Transportation." Thesis, Paris Sciences et Lettres (ComUE), 2016. http://www.theses.fr/2016PSLED017/document.
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Dans cette thèse, notre but est de donner un cadre numérique général pour approcher les solutions des problèmes du transport optimal (TO). L’idée générale est d’introduire une régularisation entropique du problème initial. Le problème régularisé correspond à minimiser une entropie relative par rapport à une mesure de référence donnée. En effet, cela équivaut à trouver la projection d’un couplage par rapport à la divergence de Kullback-Leibler. Cela nous permet d’utiliser l’algorithme de Bregman/Dykstra et de résoudre plusieurs problèmes variationnels liés au TO. Nous nous intéressons particulièrement à la résolution des problèmes du transport optimal multi-marges (TOMM) qui apparaissent dans le cadre de la dynamique des fluides (équations d’Euler incompressible à la Brenier) et de la physique quantique (la théorie de fonctionnelle de la densité ). Dans ces cas, nous montrons que la régularisation entropique joue un rôle plus important que de la simple stabilisation numérique. De plus, nous donnons des résultats concernant l’existence des transports optimaux (par exemple des transports fractals) pour le problème TOMMIn this thesis we aim at giving a general numerical framework to approximate solutions to optimal transport (OT) problems. The general idea is to introduce an entropic regularization of the initialproblems. The regularized problem corresponds to the minimization of a relative entropy with respect a given reference measure. Indeed, this is equivalent to find the projection of the joint coupling with respect the Kullback-Leibler divergence. This allows us to make use the Bregman/Dykstra’s algorithm and solve several variational problems related to OT. We are especially interested in solving multi-marginal optimal transport problems (MMOT) arising in Physics such as in Fluid Dynamics (e.g. incompressible Euler equations à la Brenier) and in Quantum Physics (e.g. Density Functional Theory). In these cases we show that the entropic regularization plays a more important role than a simple numerical stabilization. Moreover, we also give some important results concerning existence and characterization of optimal transport maps (e.g. fractal maps) for MMOT
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Douglass, Steven James. "Consistent energy treatment for radiation transport methods." Diss., Georgia Institute of Technology, 2012. http://hdl.handle.net/1853/47612.
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A condensed multigroup formulation is developed which maintains direct consistency with the continuous energy or fine-group structure, exhibiting the accuracy of the detailed energy spectrum within the coarse-group calculation. Two methods are then developed which seek to invert the condensation process turning the standard one-way condensation (from fine-group to coarse-group) into the first step of a two-way iterative process. The first method is based on the previously published Generalized Energy Condensation, which established a framework for obtaining the fine-group flux by preserving the flux energy spectrum in orthogonal energy expansion functions, but did not maintain a consistent coarse-group formulation. It is demonstrated that with a consistent extension of the GEC, a cross section recondensation scheme can be used to correct for the spectral core environment error. A more practical and efficient new method is also developed, termed the "Subgroup Decomposition (SGD) Method," which eliminates the need for expansion functions altogether, and allows the fine-group flux to be decomposed from a consistent coarse-group flux with minimal additional computation or memory requirements. In addition, a new whole-core BWR benchmark problem is generated based on operating reactor parameters in 2D and 3D, and a set of 1D benchmark problems is developed for a BWR, PWR, and VHTR core.
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Wagner, Carsten. "Transport phenomena in complex turbulent flows : numerical and experimental methods." kostenfrei, 2007. http://e-collection.ethbib.ethz.ch/view/eth:30077.
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Mercier, Olivier. "Numerical methods for set transport and related partial differential equations." Thesis, McGill University, 2013. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=119767.
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In many cases, the simulation of a physical system requires to track the evolution of a set. This set can be a piece of cloth in the wind, the boundary between a body of water and air, or even a fire front burning through a forest. From a numerical point of view, transporting such sets can be difficult, and algorithms to achieve this task more efficiently and with more accuracy are always in demand. In this thesis, we present various methods to track sets in a given vector field. We also apply those techniques to various physical systems where the vector field is coupled to the advected set in a non-linear way.Dans plusieurs situations, la simulation de systèmes physiques requiert de suivre l'évolution d'un ensemble. Cet ensemble peut être un bout de tissu dans le vent, la frontière entre une masse d'eau et l'air, ou même le front d'un feu brûlant à travers une forêt. D'un point de vue numérique, transporter de tels ensembles peut être difficile, et des algorithmes pour accomplir cette tâche plus efficacement et avec plus de précision sont toujours en demande. Dans ce mémoire, nous présentons plusieurs méthodes pour suivre l'évolution d'ensembles dans un champ de vecteur donné. Nous appliquons aussi ces techniques à divers systèmes physiques où le champ vectoriel est couplé de manière non linéaire aux ensembles évolués.
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Murphy, Steven. "Methods for solving discontinuous-Galerkin finite element equations with application to neutron transport." Phd thesis, Toulouse, INPT, 2015. http://oatao.univ-toulouse.fr/14650/1/murphy.pdf.
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We consider high order discontinuous-Galerkin finite element methods for partial differential equations, with a focus on the neutron transport equation. We begin by examining a method for preprocessing block-sparse matrices, of the type that arise from discontinuous-Galerkin methods, prior to factorisation by a multifrontal solver. Numerical experiments on large two and three dimensional matrices show that this pre-processing method achieves a significant reduction in fill-in, when compared to methods that fail to exploit block structures. A discontinuous-Galerkin finite element method for the neutron transport equation is derived that employs high order finite elements in both space and angle. Parallel Krylov subspace based solvers are considered for both source problems and $k_{eff}$-eigenvalue problems. An a-posteriori error estimator is derived and implemented as part of an h-adaptive mesh refinement algorithm for neutron transport $k_{eff}$-eigenvalue problems. This algorithm employs a projection-based error splitting in order to balance the computational requirements between the spatial and angular parts of the computational domain. An hp-adaptive algorithm is presented and results are collected that demonstrate greatly improved efficiency compared to the h-adaptive algorithm, both in terms of reduced computational expense and enhanced accuracy. Computed eigenvalues and effectivities are presented for a variety of challenging industrial benchmarks. Accurate error estimation (with effectivities of 1) is demonstrated for a collection of problems with inhomogeneous, irregularly shaped spatial domains as well as multiple energy groups. Numerical results are presented showing that the hp-refinement algorithm can achieve exponential convergence with respect to the number of degrees of freedom in the finite element space
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Walsh, Jonathan A. (Jonathan Alan). "Computational methods for efficient nuclear data management in Monte Carlo neutron transport simulations." Thesis, Massachusetts Institute of Technology, 2014. http://hdl.handle.net/1721.1/95570.
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Thesis: S.M., Massachusetts Institute of Technology, Department of Nuclear Science and Engineering, 2014.Cataloged from PDF version of thesis.
Includes bibliographical references (pages 127-133).
This thesis presents the development and analysis of computational methods for efficiently accessing and utilizing nuclear data in Monte Carlo neutron transport code simulations. Using the OpenMC code, profiling studies are conducted in order to determine the types of nuclear data that are used in realistic reactor physics simulations, as well as the frequencies with which those data are accessed. The results of the profiling studies are then used to motivate the conceptualization of a nuclear data server algorithm aimed at reducing on-node memory requirements through the use of dedicated server nodes for the storage of infrequently accessed data. A communication model for this algorithm is derived and used to make performance predictions given data access frequencies and assumed system hardware parameters. Additionally, a new, accelerated approach for rejection sampling the free gas resonance elastic scattering kernel that reduces the frequency of zero-temperature elastic scattering cross section data accesses is derived and implemented. Using this new approach, the runtime overhead incurred by an exact treatment of the free gas resonance elastic scattering kernel is reduced by more than 30% relative to a standard sampling procedure used by Monte Carlo codes. Finally, various optimizations of the commonly-used binary energy grid search algorithm are developed and demonstrated. Investigated techniques include placing kinematic constraints on the range of the searchable energy grid, index lookups on unionized material energy grids, and employing energy grid hash tables. The accelerations presented routinely result in overall code speedup by factors of 1.2-1.3 for simulations of practical systems.
by Jonathan A. Walsh.
S.M.
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J, Labossière-Hickman Travis. "Modeling and simulation of The Transient Reactor Test Facility using modern neutron transport methods." Thesis, Massachusetts Institute of Technology, 2019. https://hdl.handle.net/1721.1/123360.
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This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Thesis: S.M., Massachusetts Institute of Technology, Department of Nuclear Science and Engineering, 2019
Cataloged from student-submitted PDF version of thesis.
Includes bibliographical references (pages 111-113).
The Transient Reactor Test Facility (TREAT) has regained the interest of the nuclear engineering community in recent years. While TREAT's design makes it uniquely suited to transient fuel testing, it also makes the reactor very challenging to model and simulate. In this thesis, we build a Monte Carlo model of TREAT's Minimum Critical Mass core to examine the effects of fuel impurities, calculate a reference solution, and analyze a number of multigroup cross section generation approaches. Several method of characteristics (MOC) simulations employing these cross sections are then converged in space and angle, corrected for homogenization, and compared to the Monte Carlo reference solution. The thesis concludes with recommendations for future analysis of TREAT using MOC.
by Travis J. Labossière-Hickman.
S.M.
S.M. Massachusetts Institute of Technology, Department of Nuclear Science and Engineering
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Ford, Wesley. "The Advancement of Stable, Efficient and Parallel Acceleration Methods for the Neutron Transport Equation." Thesis, Université Paris-Saclay (ComUE), 2019. http://www.theses.fr/2019SACLX105/document.
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Dans cet article, nous proposons une nouvelle bibliothèque de techniques non linéaires pour accélérer l’équation de transport en ordonnées discrètes. Deux nouveaux types de méthodes d'accélération non linéaire appelées méthode de rééquilibrage spatialement variable (SVRM) et accélération de matrice de réponse (RMA), respectivement, sont proposées et étudiées. La première méthode, SVRM, est basée sur le calcul de la variation spatiale de premier ordre de l'équation de la balance des neutrons. RMA, est une méthode DP0 qui utilise la connaissance de l'opérateur de transport pour former une relation cohérente. Deux variantes distinctes de RMA, appelées respectivement Explicit-RMA (E-RMA) et Balance (B-RMA), sont dérivées. Les propriétés de convergence des deux méthodes d'accélération sont étudiées pour deux schémas d'itération différents de l'opérateur de transport de la méthode des caractéristiques (MOC) pour une dalle 1D, en utilisant une analyse spectrale et une analyse de Fourier. Sur la base des résultats de la comparaison 1D, seuls les outils RMA et CMFD ont été implémentés dans la bibliothèque. Les performances de RMA sont comparées à celles de CMFD en utilisant les tests 3D C5G7, ZPPR et UH12. Les schémas de résolution parallèles et séquentiels sont considérés. L'analyse des résultats indique que les deux variantes de RMA ont une efficacité et une stabilité améliorées par rapport au CMFD, pour les matériaux à diffusion optique. De plus, le RMA montre une amélioration importante de la stabilité et de l'efficacité lorsque la géométrie est décomposée spatialement. Pour obtenir des performances numériques optimales, une combinaison de RMA et de CMFD est suggérée. Une enquête plus approfondie sur l'utilisation et l'amélioration de la RMA est proposée. De plus, de nombreuses idées pour étendre les fonctionnalités de la bibliothèque sont présentéesIn this paper we propose a new library of non-linear techniques for accelerating the discrete-ordinates transport equation. Two new types of nonlinear acceleration methods called Spatially Variant Rebalancing Method (SVRM) and Response Matrix Acceleration (RMA), respectively, are proposed and investigated. The first method, SVRM, is based on the computation of the zeroth and first order spatial variation of the neutron balance equation. RMA, is a DP0 method that uses knowledge of the transport operator to form a consistent relationship. Two distinct variants of RMA, called Explicit-RMA (E-RMA) and Balance (B-RMA), respectively, are derived. The convergence properties of both acceleration methods are investigated for two different iteration schemes of the method of characteristics (MOC) transport operator for a 1D slab, using spectral and Fourier analysis. Based off the results of the 1D comparison, only RMA and CMFD were implemented in the library. The performance of RMA is compared to CMFD using the C5G7, ZPPR, and UH12 3D benchmarks. Both parallel and sequential solving schemes are considered. Analysis of the results indicates that both variants of RMA have improved effectiveness and stability relative to CMFD, for optically diffusive materials. Moreover, RMA shows great improvement in stability and effectiveness when the geometry is spatially decomposed. To achieve optimal numerical performance, a combination of RMA and CMFD is suggested. Further investigation into the use and improvement of RMA is proposed. As well, many ideas for extending the features of the library are presented
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Simon, Stefan [Verfasser]. "Numerical Methods for Optimal Transport and Elastic Shape Optimization / Stefan Simon." Bonn : Universitäts- und Landesbibliothek Bonn, 2019. http://d-nb.info/1201727898/34.
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Jobic, Yann. "Numerical approach by kinetic methods of transport phenomena in heterogeneous media." Thesis, Aix-Marseille, 2016. http://www.theses.fr/2016AIXM4723/document.
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Les phénomènes de transport en milieux poreux sont étudiés depuis près de deux siècles, cependant les travaux concernant les milieux fortement poreux sont encore relativement peu nombreux. Les modèles couramment utilisés pour les poreux classiques (lits de grains par exemple) sont peu applicables pour les milieux fortement poreux (les mousses par exemple), un certain nombre d’études ont été entreprises pour combler ce manque. Néanmoins, les résultats expérimentaux et numériques caractérisant les pertes de charge dans les mousses sont fortement dispersés. Du fait des progrès de l’imagerie 3D, une tendance émergente est la détermination des paramètres des lois d’écoulement à partir de simulations directes sur des géométries reconstruites. Nous présentons ici l’utilisation d’une nouvelle approche cinétique pour résoudre localement les équations de Navier-Stokes et déterminer les propriétés d’écoulement (perméabilité, dispersion, ...)A novel kinetic scheme satisfying an entropy condition is developed, tested and implemented for the simulation of practical problems. The construction of this new entropic scheme is presented. A classical hyperbolic system is approximated by a discrete velocity vector kinetic scheme (with the simplified BGK collisional operator), but applied to an inviscid compressible gas dynamics system with a small Mach number parameter, according to the approach of Carfora and Natalini (2008). The numerical viscosity is controlled, and tends to the physical viscosity of the Navier-Stokes system. The proposed numerical scheme is analyzed and formulated as an explicit finite volume flux vector splitting (FVS) scheme that is very easy to implement. It is close in spirit to Lattice Boltzmann schemes, but it has the advantage to satisfy a discrete entropy inequality under a CFL condition and a subcharacteristic stability condition involving a cell Reynolds number. The new scheme is proved to be second-order accurate in space. We show the efficiency of the method in terms of accuracy and robustness on a variety of classical benchmark tests. Some physical problems have been studied in order to show the usefulness of both schemes. The LB code was successfully used to determine the longitudinal dispersion of metallic foams, with the use of a novel indicator. The entropic code was used to determine the permeability tensor of various porous media, from the Fontainebleau sandstone (low porosity) to a redwood tree sample (high porosity). These results are pretty accurate. Finally, the entropic framework is applied to the advection-diffusion equation as a passive scalar
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Mosher, Scott William. "A Variational Transport Theory Method for Two-Dimensional Reactor Core Calculations." Diss., Georgia Institute of Technology, 2004. http://hdl.handle.net/1853/5070.
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A Variational Transport Theory Method for
Two-Dimensional Reactor Core Calculations
Scott W. Mosher
110 Pages
Directed by Dr. Farzad Rahnema
It seems very likely that the next generation of reactor analysis methods will be based largely on neutron transport theory, at both the assembly and core levels. Signifi-cant progress has been made in recent years toward the goal of developing a transport method that is applicable to large, heterogeneous coarse-meshes. Unfortunately, the ma-jor obstacle hindering a more widespread application of transport theory to large-scale calculations is still the computational cost.
In this dissertation, a variational heterogeneous coarse-mesh transport method has been extended from one to two-dimensional Cartesian geometry in a practical fashion. A generalization of the angular flux expansion within a coarse-mesh was developed. This allows a far more efficient class of response functions (or basis functions) to be employed within the framework of the original variational principle. New finite element equations were derived that can be used to compute the expansion coefficients for an individual coarse-mesh given the incident fluxes on the boundary. In addition, the non-variational method previously used to converge the expansion coefficients was developed in a new and more thorough manner by considering the implications of the fission source treat-ment imposed by the response expansion.
The new coarse-mesh method was implemented for both one and two-dimensional (2-D) problems in the finite-difference, multigroup, discrete ordinates approximation. An efficient set of response functions was generated using orthogonal boundary conditions constructed from the discrete Legendre polynomials. Several one and two-dimensional heterogeneous light water reactor benchmark problems were studied. Relatively low-order response expansions were used to generate highly accurate results using both the variational and non-variational methods. The expansion order was found to have a far more significant impact on the accuracy of the results than the type of method. The varia-tional techniques provide better accuracy, but at substantially higher computational costs. The non-variational method is extremely robust and was shown to achieve accurate re-sults in the 2-D problems, as long as the expansion order was not very low.
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Willert, Jeffrey Alan. "Hybrid Deterministic/Monte Carlo Methods for Solving the Neutron Transport Equation and k-Eigenvalue Problem." Thesis, North Carolina State University, 2013. http://pqdtopen.proquest.com/#viewpdf?dispub=3575891.
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The goal of this thesis is to build hybrid deterministic/Monte Carlo algorithms for solving the neutron transport equation and associated k-eigenvalue problem. We begin by introducing and deriving the transport equation before discussing a series of deterministic methods for solving the transport equation. To begin we consider moment-based acceleration techniques for both the one and two-dimensional fixed source problems. Once this machinery has been developed, we will apply similar techniques for computing the dominant eigenvalue of the neutron transport equation. We'll motivate the development of hybrid methods by describing the deficiencies of deterministic methods before describing Monte Carlo methods and their advantages. We conclude the thesis with a chapter describing the detailed implementation of hybrid methods for both the fixed-source and k-eigenvalue problem in both one and two space dimensions. We'll use a series of test problems to demonstrate the effectiveness of these algorithms before hinting at some possible areas of future work.
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Bello, Kelani. "Modeling multiphase solid transport velocity in long subsea tiebacks : numerical and experimental methods." Thesis, Robert Gordon University, 2013. http://hdl.handle.net/10059/3138.
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Transportation of unprocessed multiphase reservoir fluids from deep/ultra deep offshore through a long subsea tieback/pipeline is inevitable. This form of transportation is complex and requires accurate knowledge of critical transport velocity, flow pattern changes, phase velocity, pressure drop, particle drag & lift forces, sand/liquid/gas holdup, flow rate requirement and tieback sizing etc at the early design phase and during operation for process optimisation. This research investigated sand transport characteristics in multiphase, water‐oil‐gas‐sand flows in horizontal, inclined and vertical pipes. Two critical factors that influence the solid particle transport in the case of multiphase flow in pipes were identified; these are the transient phenomena of flow patterns and the characteristic drag & lift coefficients ( D C , L C ). Therefore, the equations for velocity profile were developed for key flow patterns such as dispersed bubble flow, stratified flow, slug flow and annular flow using a combination of analytical equations and numerical simulation tool (CFD). The existing correlations for D C & L C were modified with data acquired from multiphase experiment in order to account for different flow patterns. Minimum Transport Velocity (MTV) models for suspension and rolling were developed by combining the numerically developed particle velocity profile models with semi‐empirical models for solid particle transport. The models took into account the critical parameters that influence particle transport in pipe flow such as flow patterns and particle drag & lift coefficients, thus eliminate inaccuracies currently experienced with similar models in public domain. The predictions of the proposed MTV models for suspension and rolling in dispersed bubble, slug flow and annular flow show maximum average error margin of 12% when compared with experimental data. The improved models were validated using previously reported experimental data and were shown to have better predictions when compared with existing models in public domain. These models have the potential to solve the problems of pipe and equipment sizing, the risk of sand deposition and bed formation, elimination of costs of sand unloading, downtime and generally improve sand management strategies.
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Leroy, Thomas. "Reduced models and numerical methods for kinetic equations applied to photon transport." Thesis, Paris 6, 2016. http://www.theses.fr/2016PA066047/document.
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La modélisation d'expériences de fusion par confinement inertiel fait intervenir des équations cinétiques dont la discrétisation peut être très coûteuse. La recherche de modèles simplifiés permet de réduire la taille et donc la complexité de ces systèmes. La justification mathématique de ces modèles simplifiés devient alors un enjeu central. Dans ce travail nous étudions plusieurs modèles réduits pour l'équation du transfert radiatif dans différents contextes, tant du point de vue théorique que du point de vue numérique. En particulier nous étudions l'équation du transfert radiatif relativiste dans le régime de diffusion hors équilibre, et nous montrons la convergence de la solution de cette équation vers la solution d'une équation de drift diffusion, dans laquelle les effets Doppler sont modélisés par un terme de transport en fréquence. Cette équation de transport est discrétisée par une nouvelle classe de schémas "bien équilibrés" (well-balanced), pour lesquels nous montrons que ces nouveaux schémas sont consistants lorsque la vitesse d'onde tends vers zero, par opposition aux schémas de type Greenberg-Leroux. Nous étudions également de nouveaux modèles réduits pour le scattering Compton (collision inélastique photon-électron). Une hiérarchie d'équations cinétiques non linéaires généralisant l'équation de Kompaneets pour des distributions anisotropes sont dérivées et leurs propriétés étudiées. Les modèles aux moments de type P_1 et M_1 sont dérivés à partir de l'une de ces équations, et nous montrons que la prise en compte de l'anisotropie du rayonnement peut modifier le phénomène de condensation de Bose expliqué par Caflisch et Levermore. Ce manuscrit se termine avec les comptes rendus de deux projets. Le premier est une preuve technique de la convergence uniforme du schéma de Gosse-Toscani sur maillages non structurés. Ce schéma est "asymptotic preserving", au sens ou il préserve au niveau discret la limite de diffusion pour l'équation de la chaleur hyperbolique, et cette preuve de convergence uniforme sur maillage non structurés en 2D est originale. Le second concerne la dérivation d'un modèle cinétique pour le Bremsstrahlung électron-ion qui préserve la limite thermiqueThe modeling of inertial confinement experiments involves kinetic equations whose discretization can become very costly. The research of reduced models allows to decrease the size and the complexity of these systems. The mathematical justification of such reduced models becomes an important issue. In this work we study several reduced models for the transfer equation in several contexts, from the theoretical and numerical point of view. In particular we study the relativistic transfer equation in the non-equilibrium diffusion regime, and we prove the convergence of the solution of this equation to the solution of a drift diffusion equation, in which the Doppler effects are modeled by a frequency transport term. This transport equation is discretized by a new class of well-balanced schemes, and we show that these schemes are consistant as the wave velocity tends to zero, by opposition to the Greenberg-Leroux type schemes. We also study several original reduced models for the Compton scattering (inelastic electron-photon collision). A hierarchy of nonlinear kinetic equations generalizing the Kompaneets equation for anisotropic distributions are derived and their properties are studied. The M_1 and P_1 angular moments models are derived from one of these equations, and we show that the anisotropic part of a radiation beam can modify the Bose condensation phenomena observed by caflisch and Levermore. This work ends with the reports of two side projects. The first one is a technical proof of the uniform convergence of the Gosse-Toscani scheme on unstructured meshes. This scheme is asymptotic preserving, since it preserves at the discrete level the diffusion limit of the hyperbolic heat equation, and this proof on unstructured meshes in 2D is original. The second one is devoted to the derivation of a kinetic model for the electron-ion Bremsstrahlung that preserves the thermal limit
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Duerigen, Susan. "Neutron transport in hexagonal reactor cores modeled by trigonal-geometry diffusion and simplified P3 nodal methods." Forschungszentrum Dresden, 2013. http://nbn-resolving.de/urn:nbn:de:bsz:d120-qucosa-124665.
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The superior advantage of a nodal method for reactor cores with hexagonal fuel assemblies discretized as cells consisting of equilateral triangles is its mesh refinement capability. In this thesis, a diffusion and a simplified P3 (or SP3) neutron transport nodal method are developed based on trigonal geometry. Both models are implemented in the reactor dynamics code DYN3D. As yet, no other well-established nodal core analysis code comprises an SP3 transport theory model based on trigonal meshes. The development of two methods based on different neutron transport approximations but using identical underlying spatial trigonal discretization allows a profound comparative analysis of both methods with regard to their mathematical derivations, nodal expansion approaches, solution procedures, and their physical performance.
The developed nodal approaches can be regarded as a hybrid NEM/AFEN form. They are based on the transverse-integration procedure, which renders them computationally efficient, and they use a combination of polynomial and exponential functions to represent the neutron flux moments of the SP3 and diffusion equations, which guarantees high accuracy.
The SP3 equations are derived in within-group form thus being of diffusion type. On this basis, the conventional diffusion solver structure can be retained also for the solution of the SP3 transport problem.
The verification analysis provides proof of the methodological reliability of both trigonal DYN3D models. By means of diverse hexagonal academic benchmark and realistic detailed-geometry full-transport-theory problems, the superiority of the SP3 transport over the diffusion model is demonstrated in cases with pronounced anisotropy effects, which is, e.g., highly relevant to the modeling of fuel assemblies comprising absorber material.
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Tallarek, Ulrich. "Electrokinetic flow and transport in porous media: Experimental methods, numerical analysis, and applications." [S.l. : s.n.], 2004. http://deposit.ddb.de/cgi-bin/dokserv?idn=974460923.
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Olbrant, Edgar [Verfasser]. "Models and numerical methods for time- and energy-dependent particle transport / Edgar Olbrant." Aachen : Hochschulbibliothek der Rheinisch-Westfälischen Technischen Hochschule Aachen, 2012. http://d-nb.info/1023980002/34.
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Watson, Aaron Michael. "The WN adaptive method for numerical solution of particle transport problems." Texas A&M University, 2005. http://hdl.handle.net/1969.1/3133.
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The source and nature, as well as the history of ray-effects, is described. A
benchmark code, using piecewise constant functions in angle and diamond differencing
in space, is derived in order to analyze four sample problems. The results of this
analysis are presented showing the ray effects and how increasing the resolution
(number of angles) eliminates them. The theory of wavelets is introduced and the use of
wavelets in multiresolution analysis is discussed. This multiresolution analysis is
applied to the transport equation, and equations that can be solved to calculate the
coefficients in the wavelet expansion for the angular flux are derived. The use of
thresholding to eliminate wavelet coefficients that are not required to adequately solve a
problem is then discussed. An iterative sweeping algorithm, called the SN-WN method,
is derived to solve the wavelet-based equations. The convergence of the SN-WN method
is discussed. An algorithm for solving the equations is derived, by solving a matrix
within each cell directly for the expansion coefficients. This algorithm is called the CWWN
method. The results of applying the CW-WN method to the benchmark problems are presented. These results show that more research is needed to improve the convergence
of the SN-WN method, and that the CW-WN method is computationally too costly to be
seriously considered.
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Dallan, Eleonora. "Numerical and experimental methods for stream and wetland modelling." Doctoral thesis, Università degli studi di Padova, 2019. http://hdl.handle.net/11577/3422714.
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The general aim of my research was the development of innovative numerical and experimental methods for the study of water bodies, in particular wetlands and streams. The use of constructed wetlands (CWs) for waste water treatment is one technique that has shown potential to remove a variety of contaminants including municipal, agricultural, industrial wastewater and storm water. Also, for terrestrial environments and human activities is of primary importance to ensure quality and health safety of rivers and streams. Water quality degradation is mostly caused by the transport and transformation of solutes (pollutants) in rivers. The study of solute transport in wetlands and in rivers appears scientifically significant within a Doctoral Degree in Industrial Engineering since it is related to anthropogenic impacts mainly of industrial origin on the natural environment and on ecosystem services, in particular on surface water bodies and aquatic ecosystems. For these reasons, the improvements of both numerical and experimental methods used for understanding transport phenomena in transitional environments (rivers and wetlands) has a fundamental role for achieving better knowledge on the pollutants removal processes in such zones and thus better management and design of these water bodies.
In Chapter 1 a short literature review is presented about: (i) hydrodynamics and removal performance modelling in constructed wetland systems, (ii) conservative and smart tracer techniques and (iii) solute transport modelling in rivers. Then the specific aims of my doctorate research are described.
Chapter 2 presents the numerical modelling developed in COMSOL Multiphysics for the study of suspended sediment transport in vegetated wetlands, with different vegetation densities. The removal efficiencies were estimated and compared for the different vegetation densities and grain sizes.
Chapter 3 presents the numerical modelling developed combining Telemac2D and Matlab codes for simulating hydrodynamics and solute transport in wetland with randomly generated bathymetries, but characterized by different statistical parameters determining different configurations of the bed forms. The removal efficiencies were then estimated and compared for the different bathymetries.
Chapter 4 introduces first activities carried out on numerical and experimental methods for streams and executed with a classical approach at the retention processes study. The numerical model STIR was applied at several conservative tracer datasets, measured for the same reaches in different flow rate conditions. Classical retention parameters, such as diffusion coefficient, exchange rate, mean residence time, were calibrated and compared for the different flow rates.
Chapter 5 focuses on the development and application of an innovative numerical tool for the study of reactive and smart tracers. The theoretical basis of STIR-RST software tool is described, in particular about the introduction of parameters representing decay and transformation of the smart tracer and about the chance of choosing if the 2 storage zones are arranged in-series or in-parallel with the main channel. Finally it is shown its application on a smart tracer field test case where Resazurin was used.
Chapter 6 reports the experimental study developed for investigating the mass balance closure of the Resazurin-Resorufin (Raz-Rru) system at the cellular scale. In the designed laboratory experiments, the sorption and photodecay of the tracers were minimized and the use of different microbial communities allowed analysing recovery patterns independent of specific microbial species. For each test, total recovery (Raz + Rru) was monitored in the time for evaluating if tracer mass disappeared during the experiments for uptake by cells.
A summary of main results and conclusions obtained in this 3-years research is given in Chapter 7.
For an easier search of the bibliographic sources used in the text, references are given separately for each chapter and included at the end of the related chapter.
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Herrera, Paulo Andres Ricci. "Particle and streamline numerical methods for conservative and reactive transport simulations in porous media." Thesis, University of British Columbia, 2009. http://hdl.handle.net/2429/15967.
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Reactive transport modeling has become an important tool to study and understand the transport and fate of solutes in the subsurface. However, the accurate simulation of reactive transport represents a formidable challenge because of the characteristics of flow, transport and chemical reactions that govern the migration of solutes in geological formations.
In particular, solute transport in natural porous media is advection-controlled and dispersion is higher in the direction of flow than in the transverse direction. Both characteristics create difficulties for traditional numerical schemes that result in numerical dispersion and/or spurious oscillations. While these errors can often be tolerated in conservative transport simulations, they can be amplified in presence of chemical reactions resulting in much larger errors or unstable solutions.
In this thesis, new Lagrangian based methods to simulate conservative and reactive transport in porous media are investigated. First, the derivation of a new meshless approximation based on smoothed particle hydrodynamics (SPH) to simulate conservative multidimensional solute transport, including advection and anisotropic dispersion, is presented. Second, a hybrid scheme that combines some of the advantages of streamline-based simulations and meshless methods and that allows simulating longitudinal and transverse dispersion without requiring a background grid is also derived. The numerical properties of both methods are analyzed analytical and numerically. Furthermore, both formulations are compared with existing numerical techniques in a set of two- and three-dimensional benchmark problems.
It is demonstrated that the proposed schemes provide accurate and efficient solutions of physical transport processes in heterogeneous porous media and overcome most of the issues in existing numerical formulations. The new methods have the potential to remove or minimize numerical dispersion and grid orientation effects and, in the case of the hybrid streamline method, also eliminate spurious oscillations even in presence of large longitudinal to transverse dispersivity ratios.
Therefore, the results presented in this thesis confirm that the Lagrangian formulations of solute transport investigated here are viable and compelling alternatives to simulate reactive transport versus more standard numerical techniques.
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Bouloutas, Efthimios T. "Improved numerical methods for modeling flow and transport processes in partially saturated porous media." Thesis, Massachusetts Institute of Technology, 1989. http://hdl.handle.net/1721.1/14355.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Civil Engineering, 1989.M.I.T. copy lacks leaf 258.
Includes bibliographical references (leaves 264-275).
by Efthimios T. Bouloutas.
Ph.D.
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Pasdunkorale, Arachchige Jayantha. "Accurate finite volume methods for the numerical simulation of transport in highly anistropic media." Thesis, Queensland University of Technology, 2003.
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Yasseri, Saam. "Generalized spatial homogenization method in transport theory and high order diffusion theory energy recondensation methods." Diss., Georgia Institute of Technology, 2013. http://hdl.handle.net/1853/51727.
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In this dissertation, three different methods for solving the Boltzmann neutron transport equation (and its low-order approximations) are developed in general geometry and implemented in 1D slab geometry. The first method is for solving the fine-group diffusion equation by estimating the in-scattering and fission source terms with consistent coarse-group diffusion solutions iteratively. This is achieved by extending the subgroup decomposition method initially developed in neutron transport theory to diffusion theory. Additionally, a new stabilizing scheme for on-the-fly cross section re-condensation based on local fixed source calculations is developed in the subgroup decomposition framework. The method is derived in general geometry and tested in 1D benchmark problems characteristic of Boiling Water Reactors (BWR) and Gas Cooled Reactor (GCR). It is shown that the method reproduces the standard fine-group results with 3-4 times faster computational speed in the BWR test problem and 1.5 to 6 times faster computational speed in the GCR core. The second method is a hybrid diffusion transport method for accelerating multi-group eigenvalue transport problems. This method extends the subgroup decomposition method to efficiently couple a coarse-group high-order diffusion method with a set of fixed-source transport decomposition sweeps to obtain the fine-group transport solution. The advantages of this new high-order diffusion theory are its consistent transport closure, straight forward implementation and numerical stability. The method is analyzed for 1D BWR and High Temperature Test Reactor (HTTR) benchmark problems. It is shown that the method reproduces the fine-group transport solution with high accuracy while increasing the computationally efficiency up to 16 times in the BWR core and up to 3.3 times in the HTTR core compared to direct fine-group transport calculations. The third method is a new spatial homogenization method in transport theory that reproduces the heterogeneous solution by using conventional flux weighted homogenized cross sections. By introducing an additional source term via an “auxiliary cross section” the resulting homogeneous transport equation becomes consistent with the heterogeneous equation, enabling easy implementation into existing solution methods/codes. This new method utilizes on-the-fly re-homogenization, performed at the assembly level, to correct for core environment effects on the homogenized cross sections. The method is derived in general geometry and continuous energy, and implemented and tested in fine-group 1D slab geometries typical of BWR and GCR cores. The test problems include two single assembly and 4 core configurations. It is believed that the coupling of the two new methods, namely the hybrid method for treating the energy variable and the new spatial homogenization method in transport theory set the stage, as future work, for the development of a robust and practical method for highly efficient and accurate whole core transport calculations.
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Oliveira, Anabela Pacheco de Pacheco de Oliveira Anabela De Oliveira Anabela Pacheco. "A comparison of Eulerian-Lagrangian methods for the solution of the transport equation /." Full text open access at:, 1994. http://content.ohsu.edu/u?/etd,208.
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Teaca, Bogdan. "Numerical simulations of transport processes in magnetohydrodynamic turbulence." Doctoral thesis, Universite Libre de Bruxelles, 2010. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/210082.
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Le couplage important entre les différentes échelles d’un écoulement est une des caractéristiques prin-cipales des turbulences. Cela est exprimé mathématiquement par les termes non linéaires présents dans les équations d’équilibre de l’écoulement, dominants en dynamique turbulente. En magnétohy-drodynamique (MHD), la force de Lorentz influe sur l’équation de conservation de l’impulsion et le nombre de termes non linéaires passe à quatre au lieu d’un seul pour un fluide non conducteur.L’objectif principal de cette thèse est d’analyser le transport d’énergie inter-échelles en utilisant une simulation numérique directe d’un écoulement turbulent MHD. Les propriétés de localité du transport de l’énergie entre les échelles pour un écoulement anisotropique ou isotropique, généré par la présence d’un champ magnétique constant, sont renforcées. Un objectif secondaire est d’établir un cadre de travail pour l’étude du transport de particules test chargées dans un champ électromagnétique turbu-lent, i.e. généré par le mouvement d’un fluide conducteur, qui possède des structures à plusieurs ordres de grandeur. La structure de la thèse est présentée ci-dessous.
Dans la première partie, composée des deux premiers chapitres, l’auteur présente les notions de turbu-lences, aussi bien hydrodynamiques que MHD. Ces deux chapitres sont des synthèses.
La deuxième partie est la principale source de nouveaux résultats. Le chapitre 3 présente les méthodes numériques pour la résolution des équations, les méthodes pseudo-spectrales. Un nouveau type de force est introduit, imposant un niveau de dissipation pour tous les invariants. Dans le chapitre 4, il est effectué une analyse du transfert d'énergie entre ordres de grandeur pour les turbulences MHD. Pour explorer ces transferts d'énergie, le domaine spectral est décomposé en une série de coques de même nombre d'onde. Le transfert moyen d'énergie entre ces coques est analysé. Les transferts d'énergie s'avèrent être surtout locaux en ordre de grandeur, alors qu'une contribution non locale existe due à la force. En présence d'un champ magnétique, l'écoulement développe une direction préférentielle, une anisotropie, où une idée nouvelle de décomposition de l'espace spectral en structures annulaires est présentée. Utilisant cette décomposition annulaire on trouve que le transfert entre anneaux est local, surtout dans les anneaux de direction perpendiculaire au champ magnétique. Pour les turbulences isotropiques, dans le chapitre 5, la localité des flux d'énergie est explorée par le biais de fonctions de localité. Dans le cas de la turbulence MHD, nous avons un comportement non local plus prononcé.
La dernière partie, les chapitres 6 et 7, présente le formalisme de suivi des trajectoires de particules chargées évoluant dans un champ électromagnétique turbulent. L'influence de la méthode d'interpola-tion du solveur de particules est étudiée avant la présentation des concepts liés au transport de particu-les et aux régimes de diffusion. L'adiabatisme du mouvement des particules chargées est discuté et le transport de particules chargées dans un champ magnétique turbulent est montré en exemple.
Doctorat en sciences, Spécialisation physique
info:eu-repo/semantics/nonPublished
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Morato, Rafet Sergio. "Contributions to solve the Multi-group Neutron Transport equation with different Angular Approaches." Doctoral thesis, Universitat Politècnica de València, 2021. http://hdl.handle.net/10251/159271.
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[ES] La forma más exacta de conocer el desplazamiento de los neutrones a través de un medio material se consigue resolviendo la Ecuación del Transporte Neutrónico. Tres diferentes aproximaciones de esta ecuación se han investigado en esta tesis: Ecuación del transporte neutrónico resuelta por el método de Ordenadas Discretas, Ecuación de la Difusión y Ecuación de Armónicos Esféricos Simplificados.
Para resolver estás ecuaciones se estudian diferentes esquemas del Método de Diferencias Finitas. La solución a estas ecuaciones describe la población de neutrones y las reacciones ocasionadas dentro de un reactor nuclear. A su vez, estas variables están relacionadas con el flujo y la potencia, parámetros fundamentales para el Análisis de Seguridad Nuclear.
La tesis introduce la definición de las ecuaciones mencionadas y en particular se detallan para el estado estacionario. Se plantea el Método Modal como solución a los problemas de autovalores definidos por dichas ecuaciones.
Primero se desarrollan varios algoritmos para la resolución del estado estacionario de la Ecuación del Transporte de Neutrones con el Método de Ordenadas Discretas para la discretización angular y el Método de Diferencias Finitas para la discretización espacial. Se ha implementado una formulación capaz de resolver el problema de autovalores para cualquier número de grupos energéticos con
upscattering y anisotropía. Varias cuadraturas utilizadas por este método en su resolución angular han sido estudiadas e implementadas para cualquier orden de aproximación de Ordenadas Discretas. Además, otra formulación se desarrolla para la solución del problema fuente de la ecuación del transporte neutrónico.
A continuación, se lleva a cabo un algoritmo que permite resolver la Ecuación de la Difusión de Neutrones con dos variantes del método de diferencias Finitas, una centrada en celda y otra en vértice o nodo. Se utiliza también el Método Modal calculando cualquier número de autovalores para varios grupos de energía y con upscattering.
También se implementan los dos esquemas del Método de Diferencias Finitas anteriormente mencionados en el desarrollo de diferentes algoritmos para resolver las Ecuaciones de Armónicos Esféricos Simplificados. Además, se ha realizado un análisis de diferentes aproximaciones de las condiciones de contorno.
Finalmente, se han realizado cálculos de la constante de multiplicación, los modos subcríticos, el flujo neutrónico y la potencia para diferentes tipos de reactores nucleares. Estas variables resultan esenciales en Análisis de Seguridad Nuclear. Además, se han realizado diferentes estudios de sensibilidad de parámetros como tamaño de malla, orden utilizado en cuadraturas o tipo de cuadraturas.[CA] La forma més exacta de conèixer el desplaçament dels neutrons a través d'un mitjà material s'aconsegueix resolent l'Equació del Transport Neutrònic. Tres diferents aproximacions d'esta equació s'han investigat en aquesta tesi: Equació del Transport Neutrònic resolta pel mètode d'Ordenades Discretes, Equació de la Difusió i Equació d'Ármonics Esfèrics Simplificats. Per a resoldre estes equacions s'estudien diferents esquemes del Mètode de Diferències Finites. La solució a estes equacions descriu la població de neutrons i les reaccions ocasionades dins d'un reactor nuclear. Al seu torn, estes variables estan relacionades amb el flux i la potència, paràmetres fonamentals per a l'Anàlisi de Seguretat Nuclear. La tesi introduïx la definició de les equacions mencionades i en particular es detallen per a l'estat estacionari. Es planteja el Mètode Modal com a solució als problemes d'autovalors definits per les dites equacions. Primer es desenvolupen diversos algoritmes per a la resolució de l'estat estacionari de l'Equació del Transport de Neutrons amb el Mètode d'Ordenades Discretes per a la discretiztació angular i el Mètode de Diferències Finites per a la discretització espacial. S'ha implementat una formulació capaç de resoldre el problema d'autovalors per a qualsevol nombre de grups energètics amb upscattering i anisotropia. Diverses quadratures utilitzades per este mètode en la seua resolució angular han sigut estudiades i implementades per a qualsevol orde d'aproximació d'Ordenades Discretes. A més, una altra formulació es desenvolupa per a la solució del problema font de l'Equació del Transport Neutrònic. A continuació, es du a terme un algoritme que permet resoldre l'Equació de la Difusió de Neutrons amb dos variants del mètode de Diferències Finites, una centrada en cel·la i una altra en vèrtex o node. S'utilitza també el Mètode Modal calculant qualsevol nombre d'autovalors per a diversos grups d'energia i amb upscattering. També s'implementen els dos esquemes del Mètode de Diferències Finites anteriorment mencionats en el desenvolupament de diferents algoritmes per a resoldre les Equacions d'Harmònics Esfèrics Simplificats. A més, s'ha realitzat una anàlisi de diferents aproximacions de les condicions de contorn. Finalment, s'han realitzat càlculs de la constant de multiplicació, els modes subcrítics, el flux neutrònic i la potència per a diferents tipus de reactors nuclears. Estes variables resulten essencials en Anàlisi de Seguretat Nuclear. A més, s'han realitzat diferents estudis de sensibilitat de paràmetres com la grandària de malla, orde utilitzat en quadratures o tipus de quadratures.
[EN] The most accurate way to know the movement of the neutrons through matter is achieved by solving the Neutron Transport Equation. Three different approaches to solve this equation have been investigated in this thesis: Discrete Ordinates Neutron Transport Equation, Neutron Diffusion Equation and Simplified Spherical Harmonics Equations. In order to solve the equations, different schemes of the Finite Differences Method were studied. The solution of these equations describes the population of neutrons and the occurred reactions inside a nuclear system. These variables are related with the flux and power, fundamental parameters for the Nuclear Safety Analysis. The thesis introduces the definition of the mentioned equations. In particular, they are detailed for the steady state case. The Modal Method is proposed as a solution to the eigenvalue problems determined by the equations. First, several algorithms for the solution of the steady state of the Neutron Transport Equation with the Discrete Ordinates Method for the angular discretization and Finite Difference Method for spatial discretization are developed. A formulation able to solve eigenvalue problems for any number of energy groups, with scattering and anisotropy has been developed. Several quadratures used by this method for the angular discretization have been studied and implemented for any order of approach of the discrete ordinates. Furthermore, an adapted formulation has been developed as a solution of the source problem for the Neutron Transport Equation. Next, an algorithm is carried out that allows to solve the Neutron Diffusion Equation with two variants of the Finite Difference Method, one with cell centered scheme and another edge entered. The Modal method is also used for calculating any number of eigenvalues for several energy groups and upscattering. Both Finite Difference schemes mentioned before are also implemented to solve the Simplified Spherical Harmonics Equations. Moreover, an analysis of different approaches of the boundary conditions is performed. Finally, calculations of the multiplication factor, subcritical modes, neutron flux and the power for different nuclear reactors were carried out. These variables result essential in Nuclear Safety Analysis. In addition, several sensitivity studies of parameters like mesh size, quadrature order or quadrature type were performed.
Me gustaría dar las gracias al Ministerio de Economía, Industria y Competitividad y a la Agencia Estatal de Investigación de España por la concesión de mi contrato predoctoral de formación de personal investigador con referencia BES-2016-076782. La ayuda económica proporcionada por este contrato fue esencial para el desarrollo de esta tesis, así como para el financiamiento de una estancia.
Morato Rafet, S. (2020). Contributions to solve the Multi-group Neutron Transport equation with different Angular Approaches [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/159271
TESIS
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Owens, Alex. "Discontinuous isogeometric analysis methods for the first order form of the neutron transport equation with discrete ordinate angular discretisation." Thesis, Imperial College London, 2017. http://hdl.handle.net/10044/1/52924.
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This thesis presents the development of a variety of discontinuous isogeometric discretisations of the discrete ordinates equations for neutron transport in two spatial dimensions. Three discretisations are presented of increasing sophistication, and their convergence properties analysed for a wide selection of test cases. The first discretisation uses a conforming mesh approach, which is analogous to many existing discontinuous Galerkin finite element methods for the discrete ordinates equations. This simplifies the analysis of the differences between isogeometric and finite element methods in terms of the numerical upwinding and sweep ordering. The second discretisation extends this approach by introducing hanging-nodes into the mesh. This overcomes the limitation of the tensor-product refinement structure inherent to isogeometric analysis based on non-uniform rational B-splines with a conforming mesh. Adaptive mesh refinement based on element subdivision is also introduced at this point, driven by a selection of heuristic error indicators. In the final discretisation, each energy group has its own associated mesh. The interpolation of functions between meshes is greatly simplified by deriving the mesh in each energy group from a common initial coarsest mesh. To take full advantage of the flexibility of this discretisation, dual weighted residual error metrics are derived for the multigroup discrete ordinates equations for both fixed source and eigenvalue problems. In a representative deep penetration shielding problem, this method is demonstrated to achieve the same level of accuracy in a detector response as uniform, conforming mesh refinement using approximately an order of magnitude less computational effort.
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Fan, Jianhua. "Numerical study of particle transport and deposition in porous media." Thesis, Rennes, INSA, 2018. http://www.theses.fr/2018ISAR0003/document.
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L'objectif de ce travail de recherche est d'étudier numériquement le transport et le dépôt de particules dans des milieux poreux à l'échelle des pores.Premièrement, un couplage entre la méthode de Boltzmann sur réseau (LBM) et la méthode des éléments discrets (DEM) est réalisé et utilisé pour simuler l'écoulement d'un fluide chargé en particules. La LBM est utilisée pour décrire l'écoulement du fluide autour des fibres tandis que la DEM est utilisée pour traiter la dynamique des particules. Ce couplage est bidirectionnel dans le sens où le mouvement des particules affecte le flux de fluide et réciproquement. Ce modèle nous a permis de prédire l'efficacité de capture et la chute de pression à l'étape initiale du processus de filtration. Le facteur de qualité est également calculé pour déterminer la qualité de filtration.Ensuite, on se focalise sur l'étude de l'efficacité de la capture de fibres de formes de section transversale différentes (circulaire, losange et carrée). Les résultats issus de nos simulations du processus de filtration de la fibre circulaire concordent bien avec les corrélations empiriques. L'impaction des particules sur la face avant de la fibre de forme carrée est plus importante que dans les cas de fibre de formes circulaire et losange. Cependant, en raison d'une chute de pression plus faible, la fibre de section losange présente une meilleure qualité de filtration. Ensuite, les variations du facteur de qualité dues à l'angle d'orientation et au rapport d'aspect des fibres ont été étudiées numériquement pour la forme rectangulaire. Pour chaque cas, on a déterminé la valeur optimale de la zone au vent pour laquelle le facteur de qualité est maximal. La comparaison des valeurs du facteur de qualité obtenues pour les différentes formes de fibre monte une meilleure performance pour la fibre de section carrée orientée avec un angle de π/4.Enfin, l'influence de l'arrangement des fibres sur la qualité de la filtration est analysée en considérant la configuration en quinconce pour les différentes formes. Les simulations conduites pour différentes tailles de particules et différentes valeurs de la densité (particule/air) montent que la fibre de section losange est plus performante en termes de facteur de qualité pour les particules de grande taille et pour les valeurs de densité élevée. La présente étude fournit des pistes pour optimiser le processus de filtration et prédire la qualité de filtrationThe objective of the present research was to numerically investigate the transport and deposition of particles in porous media at the pore scale. Firstly, a developed coupled lattice Boltzmann method (LBM) and discrete element method (DEM) is used to simulate the fluid-particle flow. LBM is employed to describe the fluid flow around fibers whereas DEM is used to deal with the particle dynamics. The corresponding method is two-way coupling in the sense that particle motion affects the fluid flow and reciprocally. It allowed us to predict the capture efficiency and pressure drop at the initial stage of filtration process. The quality factor is also calculated for determining the filtration performance. Secondly, we focus on the study the capture efficiency of single fiber with circular, diamond and square cross-section, respectively. The results of LBM-DEM for filtration process of single circular fiber agree well with the empirical correlation. The impaction of particles on the front side of square-shaped fiber is more favorable than those on circular and diamond cases. However, diamond fiber exhibits a good filtration performance. Then the variations of quality factor due to the different orientation angle and aspect ratio of rectangular fiber were studied using LBM-DEM. For each case, we have found the optimal value of the windward area to which corresponds a maximum value of the quality factor. The comparison of the performance of the different forms of fibers shows that the largest quality factor is obtained for square fiber oriented with angle π/4.Finally, the influence of the arrangement of fiber on filtration performance is analyzed by considering the staggered configuration. Simulations conducted for several particle size and density show that the diamond with staggered array performs better for large particles and high particle-to-fluid density ratio in terms of quality factor. The present study provide an insight to optimize the filtration process and predict filtration performance
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Schramm, Marcelo. "An algorithm for multi-group two-dimensional neutron diffusion kinetics in nuclear reactor cores." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2016. http://hdl.handle.net/10183/142510.
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O objetivo desta tese é introduzir uma nova metodologia para a cinética bidimensional multi- grupo de difusão de nêutrons em reatores nucleares. A metodologia apresentada usa uma aproximação polinomial em um domínio homogêneo retangular com condições de contornos não homogêneas. Como ela consiste em uma série de Taylor truncada, sua estimativa de erro varia de acordo com o tamanho do retângulo. Os coeficientes são obtidos principalmente pelas suas relações com o termo independente, que _e determinado pela equação diferencial. Estas relações são obtidas apenas pelas condições de contorno, e é demonstrado serem linearmente independentes. Um esquema numérico é feito para assegurar uma rápida convergência. Estes procedimentos feitos para um retângulo homogêneo são feitos para construir soluções para problemas de autovalor e dependentes do tempo de geometria ortogonal global com parâmetros seccionalmente constantes pelo método iterativo SOR. O autovalor dominante e sua autofunção são obtidos pelo método da potência no problema de autovalor. A solução para casos dependentes do tempo usam o método de Euler modificado na variável tempo. Quatro casos-teste clássicos são considerados para ilustração.The objective of this thesis is to introduce a new methodology for two{dimensional multi{ group neutron diffusion kinetics in a reactor core. The presented methodology uses a polyno- mial approximation in a rectangular homogeneous domain with non{homogeneous boundary conditions. As it consists on a truncated Taylor series, its error estimates varies with the size of the rectangle. The coefficients are obtained mainly by their relations with the independent term, which is determined by the differential equation. These relations are obtained by the boundary conditions only, and these relations are proven linear independent. A numerical scheme is made to assure faster convergence. The procedures done for one homogeneous rectangle are used to construct the solution of global orthogonal geometry with step{wise constant parameters steady state and time dependent problems by the iterative SOR algo- rithm. The dominant eigenvalue and its eigenfunction are obtained by the power method in the eigenvalue problem. The solution for the time dependent cases uses the modi ed Euler method in the time variable. Four classic test cases are considered for illustration.
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Hou, Jingming [Verfasser]. "Robust Numerical Methods for Shallow Water Flows and Advective Transport Simulation on Unstructured Grids / Jingming Hou." Aachen : Shaker, 2013. http://d-nb.info/1051573904/34.
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