Les modèles aux moments angulaires constituent des descriptions intermédiaires entre les modèles cinétiques et les modèles fluides. Dans ce manuscrit, les modèles aux moments angulaires basés sur un principe de minimisation d'entropie sont étudiés pour des applications en physique des plasmas. Ce mémoire se découpe en trois parties. La première est une contribution à la modélisation en physique des plasmas à travers le formalisme des modèles aux moments angulaires. Dans celle-ci, le domaine de validité de ces modèles est étudié en régimes non-collisionels. Il est également montré que les opérateurs de collisions proposés pour le modèle M1 permettent de retrouver des coefficients de transport plasma précis. La deuxième partie de ce document concerne la dérivation de méthodes numériques pour l'étude du transport de particules en temps long. Dans ce cadre, des schémas numériques appropriés pour le modèle M1, préservant l'asymptotique, sont construits et validés numériquement. La troisième partie représente un premier pas significatif vers la modélisation multi-espèces. Ici, le modèle aux moments angulaire M1, construit dans un référentiel mobile, est appliqué à la dynamique des gaz raréfiés. Les propriétés de ce modèle sont détaillées, un schéma numérique est proposé et une validation numérique est menée. / Angular moments models represent alternative descriptions situated in between the kinetic and the fluid models. In this work, angular moments models based on an entropy minimisation principle are considered for plasma physics applications. This manuscript is organised in three parts. The first one is a contribution to plasma physics modelling within the formalism of angular moments models. The validity domain of angular moments models in collisionless regimes is studied. It is also shown that the collisional operators proposed for the M1 angular moments model enable to recover accurate plasma transport coefficients. The second part of this document deals with the derivation of numerical methods for the long timescales particle transport. Appropriate asymptotic-preserving numerical schemes are designed for the M1 angular moments model and numerical validations are performed. The third part represents a first important step toward multi-species modelling. The M1 angular moments model in a moving frame is introduced and applied to rarefied gas dynamics. The model properties are highlighted, a numerical scheme is proposed and a numerical validation is carried out.

Ionizing radiation has a harmful potential to humans, so the protection of workers and public individuals is fundamental for the safe use of radiation in different practical purpose. Therefore, is necessary to set exposure limits to radiation using dosimetric quantities such as equivalent dose and effective dose. However equivalent and effective dose are not directly measured, so it is necessary calculate conversion coefficients (CCs) which relates this quantities with measured quantities such as particles fluence. In the literature exposure scenarios are, in general, built with simulator in the standing posture, but exposure of individuals to radiation can occur in other posture, so the aim of this work is calculate and compare the absorbed dose-to-fluence conversion coefficients (DT/ ) and effective dose-to-fluence conversion coefficients (E/ ) for the female hybrid simulator (UFHADF) in the standing and sitting posture and for the male hybrid simulator (UFHADM) in the standing posture using the Monte Carlo code MCNPX for monoenergetic protons from 2 MeV to 10 GeV and in the antero posterior (AP), postero anterior (PA), right lateral (RLAT), left lateral (LLAT), rotational (ROT) and isotropic (ISO) exposure scenarios. Comparing the CCs between standing and sitting posture of UFHADF simulator, it was observed that in the AP and PA irradiation geometry the relative differences in the head, chest and the superior abdomen organs were not relevant. However in the others irradiation geometries, for some organs in the abdomen and chest region differences in CCs were observed. The organs that presented more differences in CCs were uterus (538 % in RLAT geometry), bladder (80 % in ROT geometry) and ovaries (2861 % in LLAT geometry) since this organs are located in the lower abdominal region, in which the position of legs and arms are different between standing and sitting posture. Calculate the DT/ e E/ nconversion coefficients using simulator in the sitting posture is important to estimate more precisely the dose in individuals exposed to radiation in actual scenarios. / As radiacoes ionizantes tem um potencial danoso aos seres humanos e, por isso, a protecao de trabalhadores e de individuos do publico e essencial para o uso seguro das mesmas nos diversos fins praticos. Desta forma, e necessario estabelecer limites de exposicao com relacao a estes tipos de radiacao e, para tanto, sao utilizadas grandezas dosimetricas como a dose equivalente e a dose efetiva. Como a dose equivalente e a dose efetiva nao sao medidas diretamente faz-se necessario o calculo de coeficientes de conversao (CCs) em ambito computacional, pois eles relacionam estas grandezas com grandezas mensuraveis, como a fluencia de particulas. Como na literatura os cenarios de exposicao sao, em geral, construidos com simuladores implementados na postura vertical e nem sempre a exposicao de individuos a radiacao ocorre nessa postura, esse trabalho tem como finalidade, utilizar o codigo de transporte de radiacao Monte Carlo MCNPX e o simulador antropomorfico adulto feminino UFHADF nas posturas vertical e sentada e o simulador masculino UFHADM na postura vertical para obter e comparar os coeficientes de conversao para dose absorvida (DT) e dose efetiva (E) em termos da fluencia (X) (DT/X e E/X) para protons monoenergeticos de 2 MeV ate 10 GeV, para os cenarios de irradiacao antero-posterior (AP), postero-anterior (PA), lateral direito (RLAT), lateral esquerdo (LLAT), rotacional (ROT) e isotropico (ISO). Na comparacao dos CCs entre o simulador UFHADF nas posturas vertical e sentada, foi observado que a diferenca relativa entre os CCs nos orgaos da regiao da cabeca, do torax e do abdomen superior nao foram relevantes nas geometrias de irradiacao AP e PA. Ja nas demais geometrias de irradiacao, para alguns orgaos da regiao do abdomen e torax diferencas nos CCs foram observadas. Os orgaos que mais apresentaram diferencas nos CCs foram o utero (538 % na geometria RLAT), a bexiga (80 % na geometria ROT) e os ovarios (2861 % na geometria LLAT) que se localizam na regiao abdominal inferior, regiao onde ha a diferenca na posicao das pernas e bracos do simulador. Assim, o calculo dos coeficientes de conversao DT/ e E/ utilizando simuladores antropomorficos na postura sentada e importante para uma estimativa mais precisa da dose em individuos submetidos a cenarios reais de exposicao a radiacao.

L’érosion éolienne est un phénomène complexe avec des interactions entre la couche limite atmosphérique, le transport des particules et la déformation des dunes. Dans cette thèse des simulations numériques de transport de particules solides sur des dunes fixes ou déformables sont effectuées. L’écoulement turbulent est calculé par des simulations des grandes échelles (LES) couplée avec une méthode de frontières immergées. Les particules solides sont tractées par une approche Lagrangienne. L’entraînement des particules, leur interaction avec la surface et leur dépôt sont pris en compte par des modèles physiques complets d’érosion. D’un point de vue numérique, une méthode de frontières immergées a été introduite pour simuler les écoulements turbulents sur des frontières mouvantes. Le nouveau solveur a été validé en effectuant des comparaison avec les résultats expérimentaux de Simoens et al. (2015) dans le cas d’une colline Gaussienne. D’un point de vue physique, des modèles complets ont été développés pour l’érosion éolienne en se basant sur les forces agissant sur les particules. Des modèles instantanés pour l’envol, le roulement et le glissement des particules sont développés pour initier le mouvement des particules. Leur rebond et le splash sont également pris en compte. Des équations Lagrangiennes sont utilisées pour simuler la trajectoire des particules solides dans l’air. Une équation de transport d’un lit de particules a également été développée pour les cas de glissement et de roulement des particules sur la surface. La déformation de la dune est effectuée en faisant le bilan des particules qui s’envolent et se déposent. Ces modèles ont été validés en comparant les résultats de simulation avec les résultats expérimentaux de Simoens et al. (2015) sur les profils de concentration autour d’une colline Gaussienne. Enfin, des simulations numériques d’une dune sinusoïdale déformable sont effectuées. La forme de la dune simulée est comparée avec les résultats expérimentaux de Ferreira and Fino (2012). Un bon agrément est obtenu a t = 2.0 min, par contre la hauteur de la dune est sous-estimée entre 4.0 min et 6.0 min. Les résultats numériques montrent que la zone de recirculation diminue progressivement quand la dune se déforme. L’érosion, due à l’envol et au splash, est important a l’avant de la dune tandis que les particules se déposent a l’arrière de la dune. Le modèle de splash a été modifié pour prendre en compte l’effet de la pente, ce qui a permis une meilleure estimation de la hauteur de la dune a t = 4.0 min. / Wind erosion is a complex dynamic process consisting in an atmospheric boundary layer, aeolian particle transport, sand dune deformation and their intricate interactions. This thesis undertakes this problems by conducting three-dimensional numerical simulations of solid particle transport over a fixed or deformable sand dune. Turbulent flow is calculated by a developed numerical solver (Large-eddy simulation (LES) coupled with immersed boundary method (IBM)). Solid particle trajectories are tracked by a Lagrangian approach. Particle entrainment, particle-surface interactions and particle deposition are taken into account by physical comprehensive wind erosion models. Firstly, a new numerical solver has been developed to simulate turbulent flows over moving boundaries by introducing the IBM into LES. Two canonical simulation cases of a turbulent boundary layer flow over a Gaussian dune and over a sinusoidal dune are performed to examine the accuracy of the developed solver. Recirculation region characteristics, mean streamwise velocity profiles, Reynolds stress profiles as well as the friction velocity over the dune are presented. In the Gaussian case, a good agreement between experimental data and simulated results demonstrates the numerical ability of the improved solver. In the sinusoidal case, the developed solver with wall modeling over the immersed boundary shows a better performance than the pure one, when a relatively coarse grid is used. Secondly, physical comprehensive modeling of wind erosion is described in detail, based on the forces acting an individual particle. An instantaneous entrainment model for both lifting and rolling-sliding modes is proposed to initialize particle incipient motions. Lagrangian governing equations of aeolian particle motion are presented and used to simulate the trajectories of solid particles. Particularly, Lagrangian governing equations of bed-load particle motion are originally deduced and applied to model the particle rolling-sliding movement on the bed surface. In addition, particle-surface interactions are taken into account by probabilistic rebound/splash models. Thirdly, numerical simulations of particle transport over a fixed Gaussian dune and over a deformable sinusoidal dune are carried out. In the fixed Gaussian case, an overall good agreement on the particle concentration profiles over the dune between the simulated results and the experimental data of Simoens et al. (2015) preliminarily validates the ability and accuracy of the developed numerical solver coupled with physical comprehensive wind erosion models. In the deformable sinusoidal case, the simulated dune shapes are compared with the experimental ones of Ferreira and Fino (2012). A good agreement between them is observed at t = 2.0 min and an obvious underestimate of the dune shape is shown at t = 4.0 min and t = 6.0 min. By analyzing the simulated results, it is shown that the recirculation zone behind the dune is gradually reduced as the dune deforms and that windward erosion and lee side deposition is observed. It is also shown after testing that the splash entrainment is important for the lee side erosion. Moreover, a preliminary attempt is presented to apply an improved splash model with accounting for the bed slope effect to the simulation of sand dune deformation. A better performance on the simulated dune shape is achieved at t = 4.0 min in comparison with the experimental one.

Les milieux poreux font partie des formations géologiques assez répandue dans la nature et son sujet d'études intensives. L'engouement de ce sujet vient des multiples secteurs d'applications de ces recherches et leur importance dans notre société. Que ce soit de la part des sociétés pétrolières qui souhaitent optimiser leurs moyens de productions, les agences de contrôles environnementaux qui veulent prévenir la contamination de nappe phréatique et la fuite de déchets nucléaires ou encore des industriels avec des problèmes de drainages et de réhabilitation de mines, tous ces acteurs dépendent des recherches faites dans ce domaine. Cependant, un des principaux problèmes de ce sujet est l'inaccessibilité des milieux que nous voulons étudier. Pour palier à cela de nombreuses équipes se sont tournées vers la simulation numérique. Cette thèse s'inscrit dans ce cadre et utilise le module PARADIS du logiciel d'hydrogéologie H2olab pour modéliser le transport de particules dans des milieux poreux fortement hétérogènes. Grâce aux données obtenues et à des comparaisons avec la littérature nous montrerons l'effet du passage au 3D sur la topologie de l'écoulement et les répercussions sur le transport de particules ainsi que l'effet de la diffusion moléculaire sur les coefficients de macro-dispersion. Enfin nous proposerons deux lois de transport reliant macrodispersion, variance du champ de perméabilité et diffusion moléculaire. / Heterogeneous porous media have been intensively studied these last fifty years. The popularity of this subject come from the multiple areas where these researches can be applied and their importance to our society. Whether from the oil companies that want to optimize their methods of production, environmental control agencies who want to prevent contamination of ground water and leakage of nuclear waste or industrial with drainage issues and mine rehabilitation, all these actors depend on research done in this area. However, one of the main problems of this subject is the accessibility of these porous media which are often several hundred meters underground. To overcome this, many teams have turned to computer simulation. This thesis is among them and uses the PARADIS module from the hydrogeology software H2olab to model particle transport in highly heterogeneous porous media. Thanks to the data obtained and comparisons with the literature, we show the impact of switching from a 2D to a 3D porous media on the ow topology and the repercussions on the particle transport. Furthermore, we also investigated the effect of molecular diffusion coefficients on macro-dispersion. Finally, we will propose two empirical functions linking macro-dispersion variance of the permeability field and molecular diffusion.

Im Grundwasser mobile Feststoff-Partikel stehen im Verdacht, den Transport schwerlöslicher Schadstoffe zu begünstigen. Die Partikel-Konzentration im Wasser lässt sich aber nur mittels einer aufwändigen Probenahme bestimmen. Vor diesem Hintergrund wurden im Rahmen dieser Arbeit Feld- und Laborversuche durchgeführt. In Feldversuchen zur Probenahme wurde festgestellt, dass für eine Stabilisierung der Partikel-Anzahl-Konzentration (CN in Partikel>Nachweisgrenze/L) die Dauer der Probenahme ausschlaggebend ist, nicht das insgesamt geförderte Volumen. Eine hohe Förderrate hat dabei nicht automatisch eine stärkere Mobilisierung von Partikeln aus dem Partikel-Depot im Umfeld der Messstelle zur Folge, wie es häufig postuliert wird. Die Gewinnung einer repräsentativen Partikelprobe macht eine Probenahme-Dauer von mindestens 5, häufig sogar über 10 oder 12 Stunden erforderlich. Empfehlungen zur Probenahme wurden erarbeitet. Es wurde aber festgestellt, dass sich stabilisierte Werte für CN als Funktion der Förderdauer (t in min) nach CN = a ? t^(-½) ungefähr abschätzen lassen, wenn der Parameter a über CN nach ca. 60 Minuten ermittelt wird. Bei Wässern mit Sauerstoff-Konzentrationen über ca. 1 mg/L kann überdies auch die Verteilung der Partikel auf einzelne Größenklassen bereits nach dieser Zeit ermittelt werden; bei sauerstoffärmeren Wässern verändert sie sich später noch. Angesichts einer starken Variation von CN einer Messstelle ist es generell aber nur möglich, eine Größenordnung für die Hintergrundkonzentration anzugeben. Von Messstelle zu Messstelle sind große Unterschiede bei CN festzustellen. Die Konzentration ist dabei nicht eindeutig abhängig von der Lithologie des Grundwasserleiters oder der Zusammensetzung des Grundwassers. Allerdings konnte eine schwache Korrelation mit dem Redox-Potential (Eh in mV) des Wassers gefunden werden (CN = 1,8?10^6?e^( 0,0087?Eh) [Partikel>2,58µm/L]; r² ≈ 0,46). Hierüber besteht die Möglichkeit, CN eines Grundwassers auch ohne Partikelmessung abzuschätzen. Insgesamt bewegen sich die Partikel-Massen-Konzentrationen (C in mg/L) der beprobten Wässer meist im Bereich von <1 mg/L, öfters sogar <0,1 mg/L, wenn die im Verlaufe von Probenahme und Messung ausgefällten Fe- und Mn-Oxide nicht berücksichtigt werden. Solche Konzentrationen sind vermutlich kaum in der Lage, relevante Mengen selbst sehr hydrophober Schadstoffen aufzunehmen und zu transportieren. Versuche mit Phenanthren ergaben zudem, dass es anscheinend weniger an bereits in Suspension befindliche Partikel sorbiert, sondern vielmehr in sorbiertem oder kristallinen Zustand aus dem Depot erodiert wird. In Laborversuchen wurde weiter gezeigt, dass in natürlichen Sedimenten ein großes Depot mobilisierbarer Partikel vorhanden ist, das Partikel über einen sehr langen Zeitraum kontinuierlich abgeben kann. Durchbruchsversuche ergaben außerdem, dass ein Großteil zugegebener Partikel bei der Passage durch eine Sedimentprobe zurückgehalten und nur sehr allmählich wieder abgegeben wird. Allerdings war auch ein schneller (präferentieller) Durchbruch zu verzeichnen. In Modellrechnungen konnte gezeigt werden, dass sich ein solcher Partikeltransport weder über eine Filterfunktion noch über die Transportgleichung zufrieden stellend berechnen lässt. Daher ist es nötig, einerseits einen bevorzugten Transport und andererseits eine starke Retardation zu berücksichtigen. Letzteres kann am besten über verschiedene Retardationsfaktoren oder ein dynamisches Partikel-Depot mit Anlagerungs- und Ablösungskonstanten geschehen. / Solid particles that are mobile in groundwater are suspected to enhance the transport of hardly soluble contaminants. But particle concentrations in water can only be measured using time-consuming sampling-procedures. On this background field- and laboratory-experiments were conducted in this work. In field experiments on sampling it turned out, that sampling time is crucial for stabilizing particle number-concentration (CN in particles>detection limit/L), not the volume sampled. A high sampling rate does not -as often argued- automatically result into higher mobilization of particles from the particle-depot in the vicinity of the sampling-well. Obtaining a representative particle sample requires a sampling-time of at least 5, often even more than 10 or 12 hours. In this work recommendations on sampling are given. It was noticed that stabilized values of CN can be estimated as function of sampling time (t in min) by CN = A ? t^(-½), if parameter A is calculated using CN after about 60 minutes. In waters having oxygen-concentrations above approximately 1 mg/L even distribution of the particles into size classes can be estimated after this time; in oxygen-poor waters size-distributions stabilized much later. Because of strong variations of CN in a single measuring well it is generally only possible to give the magnitude of the background-particle-concentration. But among several measuring wells CN may differ by several magnitudes. The concentrations do neither definitely depend upon the lithology of the aquifer nor on the groundwater-composition. But a weak correlation to the redox-potential (Eh in mV) can be found (CN = 1.8 ? 10^6 ? e^( 0.0087 ? Eh) [particles>2.58µm/L]; r² ≈ 0,46). Using this connection it is possible to estimate a magnitude of CN of a groundwater without even measuring particles. Over all particle mass-concentrations (C in mg/L) of all sampled groundwaters were almost always <1 mg/L, often even <0.1 mg/L, at least if iron- and manganese-oxides that precipitated during measurements were ignored. Such particle concentrations are probably hardly capable of adsorbing and carrying relevant amounts of contaminants, even very hydrophobic ones. Experiments using phenanthrene in contaminated sand additionally showed that it is probably hardly adsorbed onto already suspended particles, but mostly eroded from the particle depot in adsorbed or crystalline state. In laboratory experiments it was further shown that there is a huge depot of mobilizable particles in natural sediments that can continually release particles over a very long period of time. Break-through-experiments showed in addition that a large part of particles fed into the system are retained during the passage through a sediment sample and that they are re-released only very slowly. However, there also was a fast (preferential) break-through. In model calculations it could be shown that such a particle transport can neither be sufficiently described by the filter-function nor by the transport equation. Because of that it is necessary to take into consideration a preferential transport on the one hand and a strong retardation on the other. The last one can at the best be described by several retardation-factors or a dynamic particle-depot having constant attachment- and detachment rates.

<p>This study, motivated by biomedical applications such as drug delivery and adsorption, is aimed at describing magneto- and dielectro-phoretic systems via dimensional analysis to quantitatively assess the relative contribution of hydrodynamics, electromagnetism, and particle dynamics. Magnetophoresis and dielectrophoresis, phenomena of magnetic and dielectric particle transports, respectively, have been used in various applications requiring selective collecting or separating magnetic particles, especially in microfluidic systems.</p> <p>A multiphysics computational model for a magnetophoretic system was developed to assess magnetophoretic characteristics. The magnetically induced mobility of the magnetic particles was simulated for a range of parameters relevant in biomedical applications, including the particle and fluid properties, fluid velocity, and geometries of the particle, flow channel, and magnet. With the help of dimensional analysis, dimensionless numbers were introduced to reduce the number of parameters characterizing the transport of the particles suspended in an electrically non-conducting fluid exposed to an external magnetic field. As a result, 14 relevant variables determining the particle capture were reduced to only 3 dimensionless numbers describing the magnetophoretic system. The results from multiphysics models supported this analysis, suggesting a scaling law. The functional relationship among the dimensionless numbers resulted in prediction curves to assess the particle capture. The performance of the magnetophoretic system predicted with the dimensional analysis was verified in comparison with the available experimental data. In addition, the dimensionless numbers introduced here were compared with established numbers in magnetohydrodynamics (MHD).</p> <p>These theoretical and parametrical analyses of the magnetophoretic system were applied to the novel magnetic filter proposed to capture the drug-loaded small magnetic particles (MPs) from the bloodstream during the Intra-Arterial Chemotherapy (IAC). The IAC is a preferred treatment for unresectable hepatocellular carcinoma (HCC), the primary liver cancer. In the IAC procedure, chemotherapeutic agents, e.g. doxorubicin (Dox), are administered via a catheter placed in an artery supplying the tumor. The effectiveness of the IAC, however, is limited due to the passage of excessive chemotherapy agents to the blood circulation after their effect on the tumor, causing systemic toxicity. To remove the excessive drugs, the endovascular filtration devices have been developed. The proposed magnetic filtration device could be deployed from a catheter placed in the hepatic vein or inferior vena cava (IVC) to remove the excessive Dox from the bloodstream. The Ferumoxytol approved by the FDA is one of the types of the ultrasmall superparamagnetic iron oxide (USPIO) particles. The excessive Dox-coated USPIO can be filtered by a magnetic catheter-based device generating an external magnetic field. The filter utilizing magnetic fields is a promising method for therapeutic applications since an influence of magnetic field reaches comparatively wide ranges and magnetic fields do not affect biological tissues. To optimize the design, efficacy, and performance of the proposed magnetic filtration device, numerical models were developed based on the proposed dimensionless numbers characterizing drug transport and binding. Drug adsorption can be optimized by modifying magnetic field distribution and device configuration. To enhance the filtering up to 70-80 % of the excessive drug, multi-stage filters were developed by optimizing magnet configuration and flow patterns. By decreasing the concentration of toxins in the cardiovascular system, the drug dosage can be increased while reducing side effects, thus improving the effectiveness of the IAC treatment.</p> <p>In addition, new dimensionless numbers for dielectrophoresis analogous to magnetophoresis were introduced for a range of applications. The proposed dimensionless numbers for dielectrophoresis were evaluated for several conditions and compared with the previously established numbers in electrohydrodynamics (EHD). </p> <p>This study provides a promising framework for analyzing and predicting performance of various magneto- and dielectro-phoretic systems for a range of applications, particularly in biomedicine such as –drug filtering, targeted drug delivery, or small particle separation–, thus providing a reliable methodology for predicting particle manipulation. </p>

<p>To extract metals and increase the pH value of water around a historical mine waste deposit a series of barrels are used. Polluted water is forced to pass inside these barrels where different filter materials purify the water. This research project is carried out in Sweden by MTM at Örebro University and Bergkraft in Kopparberg, titled “Methods for characterisation and remediation of historical mine waste”.</p><p> </p><p>The fluid flow trough the filter materials in the barrels are needed to be understood, in order to improve the extracting process.</p><p> </p><p>In this work a small transparent model filled with sand was made to visualise the fluid flow. In that model coloured water is representing the polluted water. To describe the flow in the transparent model a mathematical model is presented. The theory used in this work is the complex variable method in fluid dynamics together with numerical methods and computer programming. There is a pretty good match between the theoretical and experimental results presented in two dimensions. Continuing work could result in a three dimensional model with different geometries using the same technique.</p>

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Neste trabalho, três técnicas para resolver numericamente problemas inversos de transporte de partículas neutras a uma velocidade para aplicações em engenharia nuclear são desenvolvidas. É fato conhecido que problemas diretos estacionários e monoenergéticos de transporte são caracterizados por estimar o fluxo de partículas como uma função-distribuição das variáveis independentes de espaço e de direção de movimento, quando os parâmetros materiais (seções de choque macroscópicas), a geometria, e o fluxo incidente nos contornos do domínio (condições de contorno), bem como a distribuição de fonte interior são conhecidos. Por outro lado, problemas inversos, neste trabalho, buscam estimativas para o fluxo incidente no contorno, ou a fonte interior, ou frações vazio em barras homogêneas. O modelo matemático usado tanto para os problemas diretos como para os problemas inversos é a equação de transporte independente do tempo, a uma velocidade, em geometria unidimensional e com o espalhamento linearmente anisotrópico na formulação de ordenadas discretas (SN). Nos problemas inversos de valor de contorno, dado o fluxo emergente em um extremo da barra, medido por um detector de nêutrons, por exemplo, buscamos uma estimativa precisa para o fluxo incidente no extremo oposto. Por outro lado, nos problemas inversos SN de fonte interior, buscamos uma estimativa precisa para a fonte armazenada no interior do domínio para fins de blindagem, sendo dado o fluxo emergente no contorno da barra. Além disso, nos problemas inversos SN de fração de vazio, dado o fluxo emergente em uma fronteira da barra devido ao fluxo incidente prescrito no extremo oposto, procuramos por uma estimativa precisa da fração de vazio no interior da barra, no contexto de ensaios não-destrutivos para aplicações na indústria. O código computacional desenvolvido neste trabalho apresenta o método espectronodal de malha grossa spectral Greens function (SGF) para os problemas diretos SN em geometria unidimensional para gerar soluções numéricas precisas para os três problemas inversos SN descritos acima. Para os problemas inversos SN de valor de contorno e de fonte interior, usamos a propriedade da proporcionalidade da fuga de partículas; ademais, para os problemas inversos SN de fração de vazio, oferecemos a técnica a qual nos referimos como o método físico da bissecção. Apresentamos resultados numéricos para ilustrar a precisão das três técnicas, conforme descrito nesta tese. / In this work, three techniques for numerically solving one-speed neutral particle inverse transport problems for nuclear engineering applications are developed. It is well known that direct steady-state monoenergetic transport problems are characterized by estimating the flux of particles as a distribution function of space and direction-of-motion independent variables, when the material parameters (cross sections), the geometry, and the incoming flux at the boundaries of the domain (boundary conditions), as well as the interior source distribution are known. Conversely, inverse problems, in this work, seek for estimates to the incident boundary flux, or interior source, or void fractions in homogeneous slabs. The mathematical model used for direct and inverse problems is the time-independent one-speed slab-geometry transport equation with linearly anisotropic scattering in the discrete ordinates (SN) formulation. In the boundary-value inverse problems, given the existing flux at one boundary of the slab, as measured by a neutron detector, for example, we seek for accurate estimate for the incident flux at the opposite boundary. On the other hand, in the interior source inverse SN problems, we seek for accurate estimate for the interior source stored within the slab for shielding purpose, given the exiting flux at the boundary of the slab. Furthermore, as with the void fraction inverse SN problems, given the exiting flux at one boundary of the slab due to prescribed incident flux at the opposite boundary, we seek for accurate estimate of the void fraction within the slab in the context of non-destructive testing applications in industry. The computer code developed in this work presents the coarse-mesh spectral Greens function (SGF) nodal method for direct SN problems in slab geometry to generate accurate numerical solutions to the three inverse SN problems described above. For the boundary-value and interior source inverse SN problems, we use the proportionality property of the leakage of particles; moreover, for the void fraction inverse SN problems, we offer the technique that we refer to as the physical bisection method. We present numerical results to illustrate the accuracy of the three techniques, as described in this dissertation.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Neste trabalho, três técnicas para resolver numericamente problemas inversos de transporte de partículas neutras a uma velocidade para aplicações em engenharia nuclear são desenvolvidas. É fato conhecido que problemas diretos estacionários e monoenergéticos de transporte são caracterizados por estimar o fluxo de partículas como uma função-distribuição das variáveis independentes de espaço e de direção de movimento, quando os parâmetros materiais (seções de choque macroscópicas), a geometria, e o fluxo incidente nos contornos do domínio (condições de contorno), bem como a distribuição de fonte interior são conhecidos. Por outro lado, problemas inversos, neste trabalho, buscam estimativas para o fluxo incidente no contorno, ou a fonte interior, ou frações vazio em barras homogêneas. O modelo matemático usado tanto para os problemas diretos como para os problemas inversos é a equação de transporte independente do tempo, a uma velocidade, em geometria unidimensional e com o espalhamento linearmente anisotrópico na formulação de ordenadas discretas (SN). Nos problemas inversos de valor de contorno, dado o fluxo emergente em um extremo da barra, medido por um detector de nêutrons, por exemplo, buscamos uma estimativa precisa para o fluxo incidente no extremo oposto. Por outro lado, nos problemas inversos SN de fonte interior, buscamos uma estimativa precisa para a fonte armazenada no interior do domínio para fins de blindagem, sendo dado o fluxo emergente no contorno da barra. Além disso, nos problemas inversos SN de fração de vazio, dado o fluxo emergente em uma fronteira da barra devido ao fluxo incidente prescrito no extremo oposto, procuramos por uma estimativa precisa da fração de vazio no interior da barra, no contexto de ensaios não-destrutivos para aplicações na indústria. O código computacional desenvolvido neste trabalho apresenta o método espectronodal de malha grossa spectral Greens function (SGF) para os problemas diretos SN em geometria unidimensional para gerar soluções numéricas precisas para os três problemas inversos SN descritos acima. Para os problemas inversos SN de valor de contorno e de fonte interior, usamos a propriedade da proporcionalidade da fuga de partículas; ademais, para os problemas inversos SN de fração de vazio, oferecemos a técnica a qual nos referimos como o método físico da bissecção. Apresentamos resultados numéricos para ilustrar a precisão das três técnicas, conforme descrito nesta tese. / In this work, three techniques for numerically solving one-speed neutral particle inverse transport problems for nuclear engineering applications are developed. It is well known that direct steady-state monoenergetic transport problems are characterized by estimating the flux of particles as a distribution function of space and direction-of-motion independent variables, when the material parameters (cross sections), the geometry, and the incoming flux at the boundaries of the domain (boundary conditions), as well as the interior source distribution are known. Conversely, inverse problems, in this work, seek for estimates to the incident boundary flux, or interior source, or void fractions in homogeneous slabs. The mathematical model used for direct and inverse problems is the time-independent one-speed slab-geometry transport equation with linearly anisotropic scattering in the discrete ordinates (SN) formulation. In the boundary-value inverse problems, given the existing flux at one boundary of the slab, as measured by a neutron detector, for example, we seek for accurate estimate for the incident flux at the opposite boundary. On the other hand, in the interior source inverse SN problems, we seek for accurate estimate for the interior source stored within the slab for shielding purpose, given the exiting flux at the boundary of the slab. Furthermore, as with the void fraction inverse SN problems, given the exiting flux at one boundary of the slab due to prescribed incident flux at the opposite boundary, we seek for accurate estimate of the void fraction within the slab in the context of non-destructive testing applications in industry. The computer code developed in this work presents the coarse-mesh spectral Greens function (SGF) nodal method for direct SN problems in slab geometry to generate accurate numerical solutions to the three inverse SN problems described above. For the boundary-value and interior source inverse SN problems, we use the proportionality property of the leakage of particles; moreover, for the void fraction inverse SN problems, we offer the technique that we refer to as the physical bisection method. We present numerical results to illustrate the accuracy of the three techniques, as described in this dissertation.

To extract metals and increase the pH value of water around a historical mine waste deposit a series of barrels are used. Polluted water is forced to pass inside these barrels where different filter materials purify the water. This research project is carried out in Sweden by MTM at Örebro University and Bergkraft in Kopparberg, titled “Methods for characterisation and remediation of historical mine waste”.   The fluid flow trough the filter materials in the barrels are needed to be understood, in order to improve the extracting process.   In this work a small transparent model filled with sand was made to visualise the fluid flow. In that model coloured water is representing the polluted water. To describe the flow in the transparent model a mathematical model is presented. The theory used in this work is the complex variable method in fluid dynamics together with numerical methods and computer programming. There is a pretty good match between the theoretical and experimental results presented in two dimensions. Continuing work could result in a three dimensional model with different geometries using the same technique.