Dans le contexte de la physique des réacteurs, l’analyse du comportement non stationnaire de la population neutronique avec contre-réactions dans le combustible et dans le modérateur se rend indispensable afin de caractériser les transitoires opérationnels et accidentels dans les systèmes nucléaires et d’en améliorer par conséquent la sûreté. Pour ces configurations non stationnaires, le développement de méthodes Monte-Carlo qui prennent en compte la dépendance en temps du système neutronique, mais aussi le couplage avec les autres physiques, comme la thermohydraulique et la thermomécanique, a pour but de servir de référence aux calculs déterministes.Ce travail de thèse a consisté à mettre en place une chaîne de calcul pour la simulation couplée neutronique Monte-Carlo, avec le code TRIPOLI-4, en conditions non stationnaires et avec prise en compte des contre-réactions thermohydrauliques.Nous avons d'abord considéré les méthodes cinétiques dans TRIPOLI-4, c'est-à-dire avec prise en compte du temps mais sans prise en compte des contre-réactions, en incluant une évaluation des méthodes existantes ainsi que le développement de nouvelles méthodes. Ensuite, nous avons développé un schéma de couplage entre TRIPOLI-4 et le code de thermohydraulique sous-canal SUBCHANFLOW. Enfin, nous avons réalisé une analyse préliminaire de la propagation des incertitudes au sein du calcul couplé sur un modèle simplifié. En effet, les fluctuations statistiques sont inhérentes à notre schéma de par la nature stochastique de TRIPOLI-4. De plus, les équations de la thermohydraulique étant non-linéaires, la propagation des incertitudes au long du calcul doit être étudiée afin de caractériser la convergence du résultat. / One of the main issues for the study of a reactor behaviour is to model the propagation of the neutrons, described by the Boltzmann transport equation, in the presence of multi-physics phenomena, such as the coupling between neutron transport, thermal-hydraulics and thermomecanics. Thanks to the growing computer power, it is now feasible to apply Monte Carlo methods to the solution of non-stationary transport problems in reactor physics, which play an instrumental role in producing reference numerical solutions for the analysis of transients occurring during normal and accidental behaviour.The goal of this Ph. D. thesis is to develop, verify and test a coupling scheme between the Monte Carlo code TRIPOLI-4 and thermal-hydraulics, so as to provide a reference tool for the simulation of reactivity-induced transients in PWRs.We have first tested the kinetic capabilities of TRIPOLI-4 (i.e., time dependent without thermal-hydraulics feedback), evaluating the different existing methods and implementing new techniques. Then, we have developed a multi-physics interface for TRIPOLI-4, and more specifically a coupling scheme between TRIPOLI-4 and the thermal-hydraulics sub-channel code SUBCHANFLOW. Finally, we have performed a preliminary analysis of the stability of the coupling scheme. Indeed, due to the stochastic nature of the outputs produced by TRIPOLI-4, uncertainties are inherent to our coupling scheme and propagate along the coupling iterations. Moreover, thermal-hydraulics equations are non linear, so the prediction of the propagation of the uncertainties is not straightforward.

L’objectif de cette thèse est l’étude des méthodes de couplage entre neutronique, thermique et mécanique. Après une revue générale des techniques de couplage, on s’est intéressé à la prise en compte de déformations mécaniques dans les simulations neutroniques. Les codes actuels de neutronique utilisant des méthodes déterministes ne sont généralement pas capables de traiter une géométrie déformée. Ce type de calcul a pourtant un intérêt fort pour la filière rapide et est un prérequis indispensable pour l’étude du couplage envisagée.Deux approches ont été identifiées et implémentées pour répondre à cette problématique, selon que l’on utilise un maillage de calcul mobile ou fixe. Elles ont été testées et confrontées sur les essais de gerbage du réacteur Phénix. Le couplage a été étudié ensuite, avec l’approche à maillage mobile, sur l’expérience Godiva qui présente un couplage à la fois conceptuellement simple et fort entre les physiques qui nous intéressent. Ces travaux ont permis de mettre en avant l’utilisation de la méthode de factorisation quasi-statique en neutronique qui permet de coupler efficacement un solveur de neutronique cinétique avec une autre discipline. Travail plus amont, le développement d’un solveur directement multiphysique a également été exploré. L’utilisation de l’algorithme de Newton sur les formes discrétisées des équations couplées a donné de bons résultats et semble être une approche généralisable à d’autres couplages.Cette thèse débouche ainsi à la fois sur une meilleure compréhension de la physique des cœurs déformés et sur des outils opérationnels pour leur simulation, mais aussi sur des recommandations très générales pour la mise en œuvre de calculs couplés. / The objective of this thesis is to study coupling techniques between neutron transport, heat transfer and mechanics. First, a very general review of coupling techniques in the literature was done. Then we worked on neutron transport simulations in wrapped cores. Most of current deterministic codes for neutron transport are not able to deal with deformed geometry. This kind of computations is however of special interest for fast neutrons reactors and is a prerequisite for our planned coupling study.Two approaches were identified and implemented to take into account core deformations, using respectively mobile and fixed meshing. They were tested and compared on the flowering tests of the reactor Phenix. The coupling itself was studied afterwards, on the Godiva experiment. It was chosen because of the direct, strong and time-dependent coupling it involves. On this case, the “quasi-static” factorization of neutron flux was shown to be an effective way to couple a space- and time-dependent neutron transport solver with another discipline. We also investigated the development of a unique multiphysics solver. The well-known Newton algorithm applied to the discretized forms of the coupled equations was shown to be an efficient tool, which could be generalized to other couplings.This thesis therefore leads, on the one hand, to a better understanding of the physics of deformed cores and to operational tools to simulate these effects, and on the other hand, to very general advices for multiphysics calculations.

L’accès aux données de base, que sont les sections efficaces, constitue le principal goulot d’étranglement aux performances dans la résolution des équations du transport neutronique par méthode Monte Carlo (MC). Ces sections efficaces caractérisent les probabilités de collisions des neutrons avec les nucléides qui composent le matériau traversé. Elles sont propres à chaque nucléide et dépendent de l’énergie du neutron incident et de la température du matériau. Les codes de référence en MC chargent ces données en mémoire à l’ensemble des températures intervenant dans le système et utilisent un algorithme de recherche binaire dans les tables stockant les sections. Sur les architectures many-coeurs (typiquement Intel MIC), ces méthodes sont dramatiquement inefficaces du fait des accès aléatoires à la mémoire qui ne permettent pas de profiter des différents niveaux de cache mémoire et du manque de vectorisation de ces algorithmes.Tout le travail de la thèse a consisté, dans une première partie, à trouver des alternatives à cet algorithme de base en proposant le meilleur compromis performances/occupation mémoire qui tire parti des spécificités du MIC (multithreading et vectorisation). Dans un deuxième temps, nous sommes partis sur une approche radicalement opposée, approche dans laquelle les données ne sont pas stockées en mémoire, mais calculées à la volée. Toute une série d’optimisations de l’algorithme, des structures de données, vectorisation, déroulement de boucles et influence de la précision de représentation des données, ont permis d’obtenir des gains considérables par rapport à l’implémentation initiale.En fin de compte, une comparaison a été effectué entre les deux approches (données en mémoire et données calculées à la volée) pour finalement proposer le meilleur compromis en termes de performance/occupation mémoire. Au-delà de l'application ciblée (le transport MC), le travail réalisé est également une étude qui peut se généraliser sur la façon de transformer un problème initialement limité par la latence mémoire (« memory latency bound ») en un problème qui sature le processeur (« CPU-bound ») et permet de tirer parti des architectures many-coeurs. / Monte Carlo (MC) neutron transport simulations are widely used in the nuclear community to perform reference calculations with minimal approximations. The conventional MC method has a slow convergence according to the law of large numbers, which makes simulations computationally expensive. Cross section computation has been identified as the major performance bottleneck for MC neutron code. Typically, cross section data are precalculated and stored into memory before simulations for each nuclide, thus during the simulation, only table lookups are required to retrieve data from memory and the compute cost is trivial. We implemented and optimized a large collection of lookup algorithms in order to accelerate this data retrieving process. Results show that significant speedup can be achieved over the conventional binary search on both CPU and MIC in unit tests other than real case simulations. Using vectorization instructions has been proved effective on many-core architecture due to its 512-bit vector units; on CPU this improvement is limited by a smaller register size. Further optimization like memory reduction turns out to be very important since it largely improves computing performance. As can be imagined, all proposals of energy lookup are totally memory-bound where computing units does little things but only waiting for data. In another word, computing capability of modern architectures are largely wasted. Another major issue of energy lookup is that the memory requirement is huge: cross section data in one temperature for up to 400 nuclides involved in a real case simulation requires nearly 1 GB memory space, which makes simulations with several thousand temperatures infeasible to carry out with current computer systems.In order to solve the problem relevant to energy lookup, we begin to investigate another on-the-fly cross section proposal called reconstruction. The basic idea behind the reconstruction, is to do the Doppler broadening (performing a convolution integral) computation of cross sections on-the-fly, each time a cross section is needed, with a formulation close to standard neutron cross section libraries, and based on the same amount of data. The reconstruction converts the problem from memory-bound to compute-bound: only several variables for each resonance are required instead of the conventional pointwise table covering the entire resolved resonance region. Though memory space is largely reduced, this method is really time-consuming. After a series of optimizations, results show that the reconstruction kernel benefits well from vectorization and can achieve 1806 GFLOPS (single precision) on a Knights Landing 7250, which represents 67% of its effective peak performance. Even if optimization efforts on reconstruction significantly improve the FLOP usage, this on-the-fly calculation is still slower than the conventional lookup method. Under this situation, we begin to port the code on GPGPU to exploit potential higher performance as well as higher FLOP usage. On the other hand, another evaluation has been planned to compare lookup and reconstruction in terms of power consumption: with the help of hardware and software energy measurement support, we expect to find a compromising solution between performance and energy consumption in order to face the "power wall" challenge along with hardware evolution.

No description available.

The F_N method, originated by C. E. Siewert, is developed for a bare, axially infinite critical cylinder. The full-range completeness and orthogonality properties of the singular eigenfunctions are used to derive an expression for the emerging angular flux, which is represented by a power series. The resulting equations are reduced to matrix form and computer solved. Examples of the results of this method for different parameters are presented. Comparisons with other models are made. A fourth order approximation was found to be sufficient to achieve up to four digit agreement with benchmark values. / Master of Science

In reactor core design, a gap exists between the manual calculation of few-group constants and the many-group calculation, by large computer programs. A method is needed by which group constants may be calculated easily and quickly. The FASPEC program is designed to reduce the amount of manual calculation and to complement the large program by reducing the number of times the large program must be run to achieve desired results. The program calculates group constants from 940 microgroups, collapsing to any user-specified number of macrogroups up to 47. FASPEC is based on group-averaged flux calculations by a solution of the Infinite medium neutron transport equation. Flux contributions from inelastic scatter are included while those from neutron up-scatter are not. The energy spectrum considered is from 10 MeV to 0.625 eV. Required input is the atomic number density of each isotope, the number of macrogroups desired and the upper and lower microgroup numbers of each macrogroup. Input is facilitated by prompting in each case. Cross section look-up tables were provided by the Very Improved Monte Carlo code (VIM) for a mid-range Infinite hexagonal lattice. Self-shielding effects are included indirectly. A brief user's guide is provided. Group constants calculated and stored for either terminal display or printed output are group number, lowest energy of the group, macroscopic removal cross section, macroscopic absorption cross section, diffusion coefficient, flux, macroscopic fission cross section, v, the average number of neutrons emitted per fission, and vΣ_f. / Master of Science

Um método de matriz resposta (RM) é descrito para gerar soluções numéricas livres de erros de truncamento espacial para problemas de transporte de nêutrons monoenergéticos e com fonte fixa, em geometria unidimensional na formulação de ordenadas discretas (SN). O método RM com esquema iterativo de inversão parcial por região (RBI) converge valores numéricos para os fluxos angulares nas fronteiras das regiões que coincidem com os valores da solução analítica das equações SN, afora os erros de arredondamento da aritmética finita computacional. Desenvolvemos um esquema numérico de reconstrução espacial, que fornece a saída para os fluxos escalares de nêutrons em qualquer ponto do domínio definido pelo usuário, com um passo de avanço também escolhido pelo usuário. Resultados numéricos são apresentados para ilustrar a precisão do presente método em cálculos de malha grossa. / Presented here is a response matrix (RM) method, which solves numerically fixedsource one-speed slab-geometry neutron transport problems in the discrete ordinates (SN) formulation. The numerical solutions are completely free from spatial truncation errors. Therefore, the RM method with the RBI iterative scheme converges numerical values for the region-edge angular fluxes, which coincide with the numerical values generated from the analytical solution, apart from computational finite arithmetic considerations. A spatial reconstruction scheme has also been developed to yield the detailed profile of the scalar flux using a fixed step defined by the code user. Numerical results are given to illustrate the offered methods accuracy.

Nesta dissertação, são apresentados os seguintes modelos matemáticos de transporte de nêutrons: a equação linearizada de Boltzmann e a equação da difusão de nêutrons monoenergéticos em meios não-multiplicativos. Com o objetivo de determinar o período fluxo escalar de nêutrons, é descrito um método espectronodal que gera soluções numéricas para o problema de difusão em geometria planar de fonte fixa, que são livres de erros de truncamento espacial, e que conjugado com uma técnica de reconstrução espacial intranodal gera o perfil detalhado da solução. A fim de obter o valor aproximado do fluxo angular de nêutrons em um determinado ponto do domínio e em uma determinada direção de migração, descreve-se também um método de reconstrução angular baseado na solução analítica da equação unidimensional de transporte de nêutrons monoenergéticos com espalhamento linearmente anisotrópico com aproximação sintética de difusão nos termos de fonte por espalhamento. O código computacional desenvolvido nesta dissertação foi implementado na plataforma livre Scilab, e para ilustrar a eficiência do código criado,resultados numéricos obtidos para três problemas-modelos são apresentados / We describe a method to determine the neutron scalar flux in a slab using monoenergetic diffusion model. To achieve this goal we used three ingredients in the computational code that we developed on the Scilab platform: (i) a spectral nodal method that generates numerical solution for the one-speed slab-geometry fixed-source difusion problem with no spatial truncation errors; (ii) a spatial reconstruction scheme to yield detailed proile of the coarse-mesh solution; and (iii) an angular reconstruction scheme to yield approximately the neutron angular flux profile within the slab. The angular reconstruction scheme is based on the analytical solution of the neutron transport equation in slab geometry with linearly anisotropic scattering and diffusion approximation for the scattering source terms. Numerical results are given to illustrate the efficiency of the offered code

Conselho Nacional de Desenvolvimento Científico e Tecnológico / Um método de Matriz Resposta (MR) é descrito para gerar soluções numéricas livres de erros de truncamento espacial para problemas multigrupo de transporte de nêutrons com fonte fixa e em geometria unidimensional na formulação de ordenadas discretas (SN). Portanto, o método multigrupo MR com esquema iterativo de inversão nodal parcial (NBI) converge valores numéricos para os fluxos angulares nas fronteiras das regiões que coincidem com os valores da solução analítica das equações multigrupo SN, afora os erros de arredondamento da aritmética finita computacional. É também desenvolvido um esquema numérico de reconstrução espacial, que fornece a saída para os fluxos escalares de nêutrons em cada grupo de energia em um intervalo qualquer do domínio definido pelo usuário, com um passo de avanço também escolhido pelo usuário. Resultados numéricos são apresentados para ilustrar a precisão do presente método em cálculos de malha grossa.

In this work, an analytical approach is used along with nodal schemes for the solution of xed source two-dimensional neutron transport problems, in Cartesian geometry, de ned in heterogeneous medium, with anisotropic scattering. The methodology is developed from the discrete ordinates version of the two-dimensional transport equation along with the level symmetric angular quadrature set. One-dimensional equations for the averaged angular uxes are obtained by transverse integration of the original problem. Such equations are solved by the ADO method. Explicit expressions in spatial variables are derived for averaged uxes in each region in which the domain is subdivided. The solution in each region is coupled with that of its neighbouring regions to provide the solution in the whole domain, without resorting to using iterative methods. As usual in nodal schemes, auxiliary equations are needed. Here two di erent treatments were given to this issue: one based on relations between the unknown ows in the contours of the regions and the average angular uxes, and another in which these ows are approximated by polynomials of order zero being in this case, incorporated into the source term. Numerical results were compared with available literature showing the solution preserve the computational e ciency which has been a good feature of the ADO method when applied to different problems. / Neste trabalho, uma abordagem analítica é utilizada juntamente com esquemas nodais na resolução de problemas bidimensionais de transporte de nêutrons de fonte fixa, em geometria cartesiana, definidos em meio heterogêneo, com espalhamento anisotrópico. A metodologia proposta é desenvolvida a partir da versão em ordenadas discretas da equação de transporte bidimensional, juntamente com o esquema de quadratura simétrica de nível. As equações em ordenadas discretas são integradas transversalmente, originando equações unidimensionais para os fluxos angulares médios. Tais equações unidimensionais são resolvidas pelo método ADO (Analytical Discrete Ordinates). Expressões explícitas nas variáveis espaciais são derivadas para os fluxos angulares médios em cada região em que o domínio foi subdividido. A solução em cada região é acoplada às regiões vizinhas, para fornecer a solução no domínio todo, sem a utilização de métodos iterativos. Como usual em esquemas nodais, equações auxiliares são necessárias, recebendo neste estudo dois tratamentos distintos: um em que os fluxos desconhecidos nos contornos das regiões assumem relações de proporcionalidade, com os fluxos angulares médios; e, outro, em que esses fluxos são aproximados por polinômios de ordem zero sendo, nesse caso, incorporados ao termo fonte. Resultados numéricos obtidos e comparados com disponíveis na literatura mostram a viabilidade da formulação, mantendo a eficiência computacional já verificada no tratamento de outros problemas, com o uso do método ADO.