La ecuación del transporte neutrónico describe la población de neutrones y las reacciones nucleares dentro de un reactor nuclear. Primero, introducimos esta ecuación y las aproximaciones de la misma. Entonces, estudiamos la ecuación de la difusión neutrónica, la aproximación al transporte más utilizada. Para el caso estacionario, esta aproximación da lugar a un problema diferencial de valores propios. Para resolver la ecuación de la difusión se ha desarrollado un método de elementos finitos h-p. Para mejorar la eficiencia del método se ha implementado un precondicionador del tipo Restricted Additive Schwarz. Una vez hemos obtenido la distribución neutrónica en estado estacionario, usamos esta solución como condición inicial para integrar la ecuación de la difusión. Para probar el comportamiento del método propuesto, hemos simulado numéricamente ejecciones accidentales de barras de control. Sin embargo, cuando una celda tiene parcialmente introducida una barra de control aparece un comportamiento no físico, el efecto rod cusping. Para mitigar este efecto proponemos un esquema de malla móvil, es decir, la malla sigue el movimiento de las barras de control. Los resultados muestran que el efecto rod cusping disminuye con el esquema expuesto. Después, desarrollamos la aproximación de armónicos esféricos simplificados, SPN, para simular el comportamiento del núcleo del reactor el problema en estado estacionario. Esta aproximación extiende los armónicos esféricos en geometrías unidimensionales, PN, a geometrías multidimensionales usando fuertes aproximaciones. Las ecuaciones SPN mejoran la teoría de la difusión pero no convergen cuando N tiende a infinito. Probamos las ventajas y limitaciones de esta aproximación en diversos reactores. Finalmente, estudiamos la homogenización espacial en el contexto de los elementos finitos. La homogenización consiste en cambiar subdominios heterogéneos por homogéneos, de forma que el problema homogeneizado da eficientemente resultados promedios. La Teoría Generalizada de la Equivalencia para la homogenización propone factores de discontinuidad. Así pues, se ha introducido un método de elementos finitos de Galerkin discontinuo donde la condición de discontinuidad se impone de forma débil usando términos de penalización. También, hemos investigado el uso de factores de discontinuidad para la corrección de errores de homogenización cuando se usan la ecuaciones SPN. / The neutron transport equation describes the neutron population and the nuclear reactions inside a nuclear reactor core. First, this equation is introduced and its assumptions are stated. Then, the stationary neutron diffusion equation which is the most useful approximation of this equation, is studied. This approximation leads to a differential eigenvalue problem. To solve the neutron diffusion equation, a h-p finite element method is investigated. To improve the efficiency of the method a Restricted Additive Schwarz preconditioner is implemented. Once the solution for the steady state neutron distribution is obtained, it is used as initial condition for the time integration of the neutron diffusion equation. To test the behaviour of the method, rod ejection accidents are numerically simulated. However, a non-physical behaviour appears when a cell is partially rodded: this is, the rod cusping effect, which is solved by using a moving mesh scheme. In other words, the mesh follows the movement of the control rod. Numerical results show that the rod cusping effect is corrected with this scheme. After that, the simplified spherical harmonics approximation, SPN, is developed to solve the steady state problem. This approximation extends the spherical harmonics approximation, PN, in one dimensional geometries to multidimensional geometries with strong assumptions. It improves the diffusion theory results but does not converge as N tends to infinity. The advantages and limitations of this approximation are tested on several one-, two- and three-dimensional reactors. Finally, the spatial homogenization in the context of the finite element method is studied. Homogenization consists in replacing heterogeneous subdomains by homogeneous ones, in such a way that the homogenized problem provides fast and accurate average results. Discontinuous solutions were proposed in the Generalized Equivalence Theory. Here, a discontinuous Galerkin finite element method where the jump condition for the neutron flux is imposed in a weak sense using interior penalty terms is introduced. Also, the use of discontinuity factors for the correction of the homogenization error when using the SPN equations is investigated. / L'equació del transport neutrònic descriu la població de neutrons i les reaccions nuclears dins del nucli d'un reactor nuclear. Primer, introduïm aquesta equació i les seues principals aproximacions. Aleshores, estudiem l'equació de la difusió neutrònica, l'aproximació al transport neutrònic més utilitzada. Aquesta equació genera un problema diferencial de valors propis. Per a resoldre l'equació de la difusió s'ha desenvolupat un mètode d'elements finits h-p. Per millorar l'eficiencia del mètode s'ha implementat un precondicionador del tipus Restricted Additive Schwarz. Una vegada hem obtingut la distribució neutrònica en estat estacionari, usem aquesta solució com a condició inicial per integrar l'equació de la difusió depenent del temps. Amb la voluntat de provar el comportament del mètode proposat, hem simulat numèricament expusions accidentals de barres de control. Però, quan un node té parcialment introduïda una barra de control apareix un comportament no físic, l'efecte rod cusping. Per mitigar aquest efecte proposem un esquema de malla mòbil, és a dir, la malla segueix el moviment de les barres de control. Els resultats numèrics mostren que l'efecte rod cusping disminueix amb l'esquema exposat. Després, desenvolupem l'aproximació d'harmònics esfèrics simplificats, SPN, per a resoldre el problema en estat estacionari. Aquesta equació estén l'aproximació d'harmònics esfèrics en geometries unidimensionals, PN, a geometries multidimensionals usant fortes aproximacions. Les equacions SPN milloren la teoria de la difusió però no convergeixen quan N tendeix a infinit. Provem els avantatges i limitacions d'aquesta aproximació en diversos reactors. Finalment, estudiem l'homogeneïtzació espacial en el context dels elements finits. L'homogeneïtzació consisteix en canviar subdominis heterogenis per homogenis, de forma que el problema homogeneïtzat dóna eficientment resultats mitjos. La Teoria Generalitzada de l'Equivalència per a l'homogeneïtzació proposa factors de discontinuïtat. Així, s'ha introduït un mètode d'elements finits de Galerkin discontinu on la condició de discontinuïtat per al flux neutrònic s'imposa de forma dèbil usant termes de penalització. També, hem investigat l'ús de factors de discontinuïtat per a la correcció dels errors d'homogeneïtzació quan usen les equacions SPN. / Vidal Ferràndiz, A. (2018). Development of a finite element method for neutron transport equation approximations [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/98522

El principal objetivo de esta tesis es el desarrollo de un Método Modal para resolver dos ecuaciones: la Ecuación de la Difusión de Neutrones y la de las Ordenadas Discretas del Transporte de Neutrones. Además, este método está basado en el Método de Volúmenes Finitos para discretizar las variables espaciales. La solución de estas ecuaciones proporciona el flujo de neutrones, que está relacionado con la potencia que se produce en los reactores nucleares, por lo que es un factor fundamental para los Análisis de Seguridad Nuclear. Por una parte, la utilización del Método Modal está justificada para realizar análisis de inestabilidades en reactores. Por otra parte, el uso del Método de Volúmenes Finitos está justificado por la utilización de este método para resolver las ecuaciones termohidráulicas, que están fuertemente acopladas con la generación de energía en el combustible nuclear. En primer lugar, esta tesis incluye la definición de estas ecuaciones y los principales métodos utilizados para resolverlas. Además, se introducen los principales esquemas y características del Método de Volúmenes Finitos. También se describen los principales métodos numéricos para el Método Modal, que incluye tanto la solución de problemas de autovalores como la solución de Ecuaciones Diferenciales Ordinarias dependientes del tiempo. A continuación, se desarrollan varios algoritmos del Método de Volúmenes Finitos para el Estado Estacionario de la Ecuación de la Difusión de Neutrones. Se consigue desarrollar una formulación multigrupo, que permite resolver el problema de autovalores para cualquier número de grupos de energía, incluyendo términos de upscattering y de fisión en varios grupos de energía. Además, se desarrollan los algoritmos para realizar la computación en paralelo. La solución anterior es la condición inicial para resolver la Ecuación de Difusión de Neutrones dependiente del tiempo. En esta tesis se utiliza un Método Modal, que transforma el Sistema de Ecuaciones Diferenciales Ordinarias en uno de mucho menor tamaño, que se resuelve con el Método de la Matriz Exponencial. Además, se ha desarrollado un método rápido para estimar el flujo adjunto a partir del directo, ya que se necesita en el Método Modal. Por otra parte, se ha desarrollado un algoritmo que resuelve el problema de autovalores de la Ecuación del Transporte de Neutrones. Este algoritmo es para la formulación de Ordenadas Discretas y el Método de Volúmenes Finitos. En concreto, se han aplicado dos tipos de cuadraturas para las Ordenadas Discretas y dos esquemas de interpolación para el Método de Volúmenes Finitos. Finalmente, se han aplicado estos métodos a diferentes tipos de reactores nucleares, incluyendo reactores comerciales. Se han evaluado los valores de la constante de multiplicación y de la potencia, ya que son las variables fundamentales en los Análisis de Seguridad Nuclear. Además, se ha realizado un análisis de sensibilidad de diferentes parámetros como la malla y métodos numéricos. En conclusión, se obtienen excelentes resultados, tanto en precisión como en coste computacional. / The main objective of this thesis is the development of a Modal Method to solve two equations: the Neutron Diffusion Equation and the Discrete Ordinates Neutron Transport Equation. Moreover, this method uses the Finite Volume Method to discretize the spatial variables. The solution of these equations gives the neutron flux, which is related to the power produced in nuclear reactors; thus, the neutron flux is a paramount variable in Nuclear Safety Analyses. On the one hand, the use of Modal Methods is justified because one uses them to perform instability analyses in nuclear reactors. On the other hand, it is worth using the Finite Volume Method because one uses it to solve thermalhydraulic equations, which are strongly coupled with the energy generation in the nuclear fuel. First, this thesis defines the equations mentioned above and the main methods to solve these equations. Furthermore, the thesis describes the major schemes and features of the Finite Volume Method. In addition, the author also introduces the major methods used in the Modal Method, which include the methods used to solve the eigenvalue problem, as well as those used to solve the time dependent Ordinary Differential Equations. Next, the author develops several algorithms of the Finite Volume Method applied to the Steady State Neutron Diffusion Equation. In addition, the thesis includes an improvement of the multigroup formulation, which solves problems involving upscattering and fission terms in several energy groups. Moreover, the author optimizes the algorithms to do calculations with parallel computing. The previous solution is used as initial condition to solve the time dependent Neutron Diffusion Equation. The author uses a Modal Method to do so, which transforms the Ordinary Differential Equations System into a smaller system that is solved by using the Exponential Matrix Method. Furthermore, the author developed a computationally efficient method to estimate the adjoint flux from the forward one, because the Modal Method uses the adjoint flux. Additionally, the thesis also presents an algorithm to solve the eigenvalue problem of the Neutron Transport Equation. This algorithm uses the Discrete Ordinates formulation and the Finite Volume Method. In particular, the author uses two types of quadratures for the Discrete Ordinates and two interpolation schemes for the Finite Volume Method. Finally, the author tested the developed methods in different types of nuclear reactors, including commercial ones. The author checks the accuracy of the values of the crucial variables in Nuclear Safety Analyses, which are the multiplication factor and the power distribution. Furthermore, the thesis includes a sensitivity analysis of several parameters, such as the mesh and numerical methods. In conclusion, excellent results are reported in both accuracy and computational cost. / El principal objectiu d'esta tesi és el desenvolupament d'un Mètode Modal per a resoldre dos equacions: l'Equació de Difusió de Neutrons i la de les Ordenades Discretes del Transport de Neutrons. A més a més, este mètode està basat en el Mètode de Volums Finits per a discretitzar les variables espacials. La solució d'estes equacions proporcionen el flux de neutrons, que està relacionat amb la potència que es produïx en els reactors nuclears; per tant, el flux de neutrons és un factor fonamental en els Anàlisis de Seguretat Nuclear. Per una banda, la utilització del Mètode Modal està justificada per a realitzar anàlisis d'inestabilitats en reactors. Per altra banda, l'ús del Mètode de Volums Finits està justificat per l'ús d'este mètode per a resoldre les equacions termohidràuliques, que estan fortament acoblades amb la generació d'energia en el combustible nuclear. En primer lloc, esta tesi inclou la definició d'estes equacions i els principals mètodes utilitzats per a resoldre-les. A més d'això, s'introduïxen els principals esquemes i característiques del Mètode de Volums Finits. Endemés, es descriuen els principals mètodes numèrics per al Mètode Modal, que inclou tant la solució del problema d'autovalors com la solució d'Equacions Diferencials Ordinàries dependents del temps. A continuació, es desenvolupa diversos algoritmes del Mètode de Volums Finits per a l'Estat Estacionari de l'Equació de Difusió de Neutrons. Es conseguix desenvolupar una formulació multigrup, que permetre resoldre el problema d'autovalors per a qualsevol nombre de grups d'energia, incloent termes d' upscattering i de fissió en diversos grups d'energia. A més a més, es desenvolupen els algoritmes per a realitzar la computació en paral·lel. La solució anterior és la condició inicial per a resoldre l'Equació de Difusió de Neutrons dependent del temps. En esta tesi s'utilitza un Mètode Modal, que transforma el Sistema d'Equacions Diferencials Ordinàries en un problema de menor tamany, que es resol amb el Mètode de la Matriu Exponencial. Endemés, s'ha desenvolupat un mètode ràpid per a estimar el flux adjunt a partir del directe, perquè es necessita en el Mètode Modal. Per altra banda, s'ha desenvolupat un algoritme que resol el problema d'autovalors de l'Equació de Transport de Neutrons. Este algoritme és per a la formulació d'Ordenades Discretes i el Mètode de Volums Finits. En concret, s'han aplicat dos tipos de quadratures per a les Ordenades Discretes i dos esquemes d'interpolació per al Mètode de Volums Finits. Finalment, s'han aplicat estos mètodes a diversos tipos de reactors nuclears, incloent reactors comercials. S'han avaluat els valor de la constat de multiplicació i de la potència, perquè són variables fonamentals en els Anàlisis de Seguretat Nuclear. Endemés, s'ha realitzat un anàlisi de sensibilitat de diversos paràmetres com la malla i mètodes numèrics. En conclusió, es conseguix obtenir excel·lents resultats, tant en precisió com en cost computacional. / Bernal García, Á. (2018). Development of a 3D Modal Neutron Code with the Finite Volume Method for the Diffusion and Discrete Ordinates Transport Equations. Application to Nuclear Safety Analyses [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/112422

<p>Transport properties within the Boltzmann transport equation for metallic multi-layer structures as well as bulk materials, were the prime topic of this work. <i>Ab initio</i> total energy calculations for Hydrogen loaded metallic multi-layers were performed in order to shed some light onto problem of H depleted layers at the interfaces that have been experimentally observed. It was explained in connection with structural relaxation of the interface layers. </p><p>Further on conductivity behavior of Fe/V vs. Mo/V during Hydrogen load was discussed. The difference in, on first sight, rather similar multi-layer structures was explained by the magnitude of Hydrogen induced Vanadium expansion. Problem of variation of conductivity with changed c/a ratio of metals and semiconductors in general was addressed as well. The variations due to change of the Fermi surface of the corresponding materials were observed as well as some intriguing general patterns. The phenomenon could be regarded as piezoresistivity on electronic structure level. For the 3d transition metals variation of conductivity/resistivity through the period was studied.</p><p>A possible explanation for anomalous behavior of Manganese resistivity due to its much greater lattice constant in comparison to its neighbors in the period is presented. Field of disordered alloys and low dimensional magnetism was touched by discussing Mo/Ru formation energy as well as magnetic nano-wires grown on surfaces.</p><p>All total energy calculations as well as band structure calculations were performed by using Density Functional Theory based numerical computations. A short but comprehensive review of most common linear-response electron transport techniques is given.</p>

Transport properties within the Boltzmann transport equation for metallic multi-layer structures as well as bulk materials, were the prime topic of this work. Ab initio total energy calculations for Hydrogen loaded metallic multi-layers were performed in order to shed some light onto problem of H depleted layers at the interfaces that have been experimentally observed. It was explained in connection with structural relaxation of the interface layers. Further on conductivity behavior of Fe/V vs. Mo/V during Hydrogen load was discussed. The difference in, on first sight, rather similar multi-layer structures was explained by the magnitude of Hydrogen induced Vanadium expansion. Problem of variation of conductivity with changed c/a ratio of metals and semiconductors in general was addressed as well. The variations due to change of the Fermi surface of the corresponding materials were observed as well as some intriguing general patterns. The phenomenon could be regarded as piezoresistivity on electronic structure level. For the 3d transition metals variation of conductivity/resistivity through the period was studied. A possible explanation for anomalous behavior of Manganese resistivity due to its much greater lattice constant in comparison to its neighbors in the period is presented. Field of disordered alloys and low dimensional magnetism was touched by discussing Mo/Ru formation energy as well as magnetic nano-wires grown on surfaces. All total energy calculations as well as band structure calculations were performed by using Density Functional Theory based numerical computations. A short but comprehensive review of most common linear-response electron transport techniques is given.

The ultra-short gate (LG < 20 nm) CMOS components (Complementary Metal-Oxide-Semiconductor) face thermal limitations due to significant local heating induced by phonon emission by hot carriers in active regions of reduced size. This phenomenon, called self-heating effect, is identified as one of the most critical for the continuous increase in the integration density of circuits. This is especially crucial in SOI technology (silicon on insulator), where the presence of the buried insulator hinders the dissipation of heat.At the nanoscale, the theoretical study of these heating phenomena, which cannot be led using the macroscopic models (heat diffusion coefficient), requires a detailed microscopic description of heat transfers that are locally non-equilibrium. It is therefore appropriate to model, not only the electron transport and the phonon generation, but also the phonon transport and the phonon-phonon and electron-phonon interactions. The formalism of the Boltzmann transport equation (BTE) is very suitable to study this problem. In fact, it is widely used for years to study the transport of charged particles in semiconductor components. This formalism is much less standard to study the transport of phonons. One of the problems of this work concerns the coupling of the phonon BTE with the electron transport.In this context, wse have developed an algorithm to calculate the transport of phonons by the direct solution of the phonon BTE. This algorithm of phonon transport was coupled with the electron transport simulated by the simulator "MONACO" based on a statistical (Monte Carlo) solution of the BTE. Finally, this new electro-thermal simulator was used to study the self-heating effects in nano-transistors. The main interest of this work is to provide an analysis of electro-thermal transport beyond a macroscopic approach (Fourier formalism for thermal transport and the drift-diffusion approach for electric current, respectively). Indeed, it provides access to the distributions of phonons in the device for each phonon mode. In particular, the simulator provides a better understanding of the hot electron effects at the hot spots and of the electron relaxation in the access.

We investigate charmonium production in the hot medium created by heavy-ion collisions by setting up a framework in which in-medium charmonium properties are constrained by thermal lattice QCD (lQCD) and subsequently implemented into kinetic approaches. A Boltzmann transport equation is employed to describe the time evolution of the charmonium phase space distribution with the loss and gain term accounting for charmonium dissociation and regeneration (from charm quarks), respectively. The momentum dependence of the charmonium dissociation rate is worked out. The dominant process for in-medium charmonium regeneration is found to be a 3-to-2 process. Its corresponding regeneration rates from different input charmquark momentum spectra are evaluated. Experimental data on J/[psi] production at CERN-SPS and BNL-RHIC are compared with our numerical results in terms of both rapidity-dependent inclusive yields and transverse momentum (pt) spectra. Within current uncertainties from (interpreting) lQCD data and from input charm-quark spectra the centrality dependence of J/[psi] production at SPS and RHIC (for both mid-and forward rapidity) is reasonably well reproduced. The J/[psi] pt data are shown to have a discriminating power for in-medium charmonium properties as inferred from different interpretations of lQCD results.

Longshore sediment transport rate was measured during energetic sea breeze activity, on intermediate-to-reflective sandy beaches in Southwestern Australia. Estimates of suspended load were obtained using backscatter sensors, current meters and streamer traps. Total load was determined using fluorescent tracer sand and an impoundment study. The measurementsw ere cross-compareda nd usedt o evaluates everalw idely-used longshore transport equations. The streamer trap measurement revealed an exponential distribution of the suspended sediment flux with vertical mixing decreasing in the onshore direction. A continuous time series of the longshore suspended sediment flux across the surf zone was obtained by combining the streamer trap measurements with data collected using surf zone instruments. Comparison of the suspended longshore flux with the total longshore flux derived from the dispersal of the sand tracer indicated that the relative contribution of the suspendedlo ad to the total load was at least 59 %. The movement of sandt racer on four different beaches demonstrated that nearshore sediments were transported obliquely across the surf zone, challenging our conventional view of dividing nearshore sediment transport into cross-shore and longshore components. Furthermore, tracer was found to move from the outer surf zone to the swash zone and vice versa, indicating a cross-shore sediment exchange. The contribution of the swash zone to the total longshore flux was estimated around 30-40 %. Despite large differences in the temporal and spatial scales of the measurement techniques, the littoral drift rates are comparable, suggesting a northward transport rate of 138,000-200,000 m3 year-1. Longshore sediment transport during sea breezes is mainly the result of a high longshore energy flux exerted by wind waves. This is accurately predicted by the equations of Inman and Bagnold (1963) and CERC (1984). The bimodal wave field, characteristic of Southwestern Australia, renders the Kamphuis (1991b) formula unsuitable in this instance.

L'objectif de ce travail de thèse est le développement d'une approximation polynomiale axiale dans un solveur basé sur la Méthode des Caractéristiques. Le contexte, est celui de la solution stationnaire de l'équation de transport des neutrons pour des systèmes critiques, et l'implémentation pratique a été réalisée dans le solveur "Two/three Dimensional Transport" (TDT), faisant partie du projet APOLLO3®. Un solveur MOC pour des géométries en trois dimensions a été implémenté dans ce code pendant un projet de thèse antécédent, se basant sur une approximation constante par morceaux du flux et des sources des neutrons. Les développements présentés dans la suite représentent la continuation naturelle de ce travail. Les solveurs MOC en trois dimensions sont capables de produire des résultats précis pour des géométries complexes. Bien que précis, le coût computationnel associé à ce type de solveur est très important. Une représentation polynomiale en direction axiale du flux angulaire des neutrons a été utilisée pour réduire ce coût computationnel.Le travail réalisé pendant cette thèse peut être considéré comme divisé en trois parties: transport, accélération et autres. La première partie est constituée par l'implémentation de l'approximation polynomiale choisie dans les équations de transmission et de bilan typiques de la Méthode des Caractéristiques. Cette partie a aussi été caractérisée par le calcul d'une série de coefficients numériques qui se sont révélés nécessaires afin d'obtenir un algorithme stable. Pendant la deuxième partie, on a modifié et implémenté la solution des équations de la méthode d'accélération DPN. Cette méthode était déjà utilisée pour l'accélération et des itérations internes et externes dans TDT pour les solveurs deux et trois dimensionnels avec l'approximation des flux plat, quand ce travail a commencé. L'introduction d'une approximation polynomiale a demandé plusieurs développements numériques regardant la méthode d'accélération. Dans la dernière partie de ce travail on a recherché des solutions pour un mélange de différents problèmes liés aux premières deux parties. En premier lieux, on a eu à faire avec des instabilités numériques associées à une discrétisation spatiale ou angulaire pas suffisamment précise, soit pour la partie transport que pour la partie d'accélération. Ensuite, on a essayé d'utiliser différentes méthodes pour réduire l'empreinte mémoire des coefficients d'accélération. L'approche qu'on a finalement choisie se base sur une régression non-linéaire au sens des moindres carrés de la dépendance en fonction des sections efficaces typique de ces coefficients. L'approche standard consiste dans le stockage d'une série de coefficients pour chaque groupe d'énergie. La méthode de régression permet de remplacer cette information avec une série de coefficients calculés pendant la régression qui sont utilisés pour reconstruire les matrices d'accélération au cours des itérations. Cette procédure ajoute un certain coût computationnel à la méthode, mais nous pensons que la réduction de la mémoire rende ce surcoût acceptable.En conclusion, le travail réalisé a été concentré sur l'application d'une simple approximation polynomiale avec l'objectif de réduire le coût computationnel et l'empreinte mémoire associées à un solveur basée sur la Méthodes des Caractéristiques qui est utilisé pour calculer le flux neutroniques pour des géométries à trois dimensions extrudées. Même si cela ne constitue pas une amélioration radicale des performances, l'approximation d'ordre supérieur qu'on a introduit permet une réduction en termes de mémoire et de temps de calcul d'un facteur compris entre 2 et 5, selon le cas. Nous pensons que ces résultats constitueront une base fertile pour des futures améliorations. / The purpose of this PhD is the implementation of an axial polynomial approximation in a three-dimensional Method Of Characteristics (MOC) based solver. The context of the work is the solution of the steady state Neutron Transport Equation for critical systems, and the practical implementation has been realized in the Two/three Dimensional Transport (TDT) solver, as a part of the APOLLO3® project. A three-dimensional MOC solver for 3D extruded geometries has been implemented in this code during a previous PhD project, relying on a piecewise constant approximation for the neutrons fluxes and sources. The developments presented in the following represent the natural continuation of this work. Three-dimensional neutron transport MOC solvers are able to produce accurate results for complex geometries. However accurate, the computational cost associated to this kind of solvers is very important. An axial polynomial representation of the neutron angular fluxes has been used to lighten this computational burden.The work realized during this PhD can be considered divided in three major parts: transport, acceleration and others. The first part is constituted by the implementation of the chosen polynomial approximation in the transmission and balance equations typical of the Method Of Characteristics. This part was also characterized by the computation of a set of numerical coefficients which revealed to be necessary in order to obtain a stable algorithm. During the second part, we modified and implemented the solution of the equations of the DPN synthetic acceleration. This method was already used for the acceleration of both inners and outers iteration in TDT for the two and three dimensional solvers at the beginning of this work. The introduction of a polynomial approximation required several equations manipulations and associated numerical developments. In the last part of this work we have looked for the solutions of a mixture of different issues associated to the first two parts. Firstly, we had to deal with some numerical instabilities associated to a poor numerical spatial or angular discretization, both for the transport and for the acceleration methods. Secondly, we tried different methods to reduce the memory footprint of the acceleration coefficients. The approach that we have eventually chosen relies on a non-linear least square fitting of the cross sections dependence of such coefficients. The default approach consists in storing one set of coefficients per each energy group. The fit method allows replacing this information with a set of coefficients computed during the regression procedure that are used to re-construct the acceleration matrices on-the-fly. This procedure of course adds some computational cost to the method, but we believe that the reduction in terms of memory makes it worth it.In conclusion, the work realized has focused on applying a simple polynomial approximation in order to reduce the computational cost and memory footprint associated to a Method Of Characteristics solver used to compute the neutron fluxes in three dimensional extruded geometries. Even if this does not a constitute a radical improvement, the high order approximation that we have introduced allows a reduction in terms of memory and computational times of a factor between 2 and 5, depending on the case. We think that these results will constitute a fertile base for further improvements.