The modelling of the processes of advection and dispersion-diffusion is the most crucial factor in solute transport simulations. It is generally appreciated that the first order upwind difference scheme gives rise to excessive numerical diffusion, whereas the conventional second order central difference scheme exhibits severe oscillations for advection dominated transport, especially in regions of high solute gradients or discontinuities. Higher order schemes have therefore become increasingly used for improved accuracy and for reducing grid scale oscillations. Two such schemes are the QUICK (Quadratic Upwind Interpolation for Convective Kinematics) and TOASOD (Third Order Advection Second Order Diffusion) schemes, which are similar in formulation but different in accuracy, with the two schemes being second and third order accurate in space respectively for finite difference models. These two schemes can be written in various finite difference forms for transient solute transport models, with the different representations having different numerical properties and computational efficiencies. Although these two schemes are advectively (or convectively) stable, it has been shown that the originally proposed explicit QUICK and TOASOD schemes become numerically unstable for the case of pure advection. The stability constraints have been established for each scheme representation based upon the von Neumann stability analysis. All the derived schemes have been tested for various initial solute distributions and for a number of continuous discharge cases, with both constant and time varying velocity fields. The 1-D QUICKEST (QUICK with Estimated Streaming Term) scheme is third order accurate both in time and space. It has been shown analytically and numerically that a previously derived quasi 2-D explicit QUICKEST scheme, with a reduced accuracy in time, is unstable for the case of pure advection. The modified 2-D explicit QUICKEST, ADI-TOASOD and ADI-QUICK schemes have been developed herein and proved to be numerically stable, with the bility sta- region of each derived 2-D scheme having also been established. All these derived 2-D schemesh ave been tested in a 2-D domain for various initial solute distributions with both uniform and rotational flow fields. They were further tested for a number of 2-D continuous discharge cases, with the corresponding exact solutions having also been derived herein. All the numerical tests in both the 1-D and 2-D cases were compared with the corresponding exact solutions and the results obtained using various other difference schemes, with the higher order schemes generally producing more accurate predictions, except for the characteristic based schemes which failed to conserve mass for the 2-D rotational flow tests. The ADI-TOASOD scheme has also been applied to two water quality studies in the U. K., simulating nitrate and faecal coliform distributions respectively, with the results showing a marked improvement in comparison with the results obtained by the second order central difference scheme. Details are also given of a refined numerical representation of flooding and drying of tidal flood plains for hydrodynamic modelling, with the results showing considerable improvements in comparison with a number of existing models and in good agreement with the field measured data in a natural harbour study.

There is a growing need to better understand the dynamics of small and medium Mediterranean low-inflow estuaries (LIEs), which is addressed here by characterizing a heat budget and associated heat transfer processes. A one-dimensional deterministic model was developed from the advection-diffusion equation and applied to Morro Bay, CA using 15-minute water property (temperature, salinity, pressure) and meteorological (wind speed and direction, air temperature, relative humidity, air pressure, irradiance) data collected over a two-year period (2020 – 2021). Seasonal variability is observed in meteorological components, water temperature, and salinity. There is strong seasonal variability in head-mouth temperature and salinity differences. Temperature differences peak in summer (daily mean 2.52 ºC, June – Sept.). Daily average salinity difference is 0.33 (hyposaline, Sept. – Apr.) with strongest gradients observed during the winter storm season following enhanced freshwater discharge. Inverse salinity develops intermittently May – Aug. Subtidal heat flux is dominated by surface heating, whose daily average is always positive (heat input). The developed model does not quantify adequate heat export from the estuary, however, a sensitivity analysis indicates that diffusive flux may be a significant heat export component. Excess heat appears to be exported to the ocean, allowing ocean-estuary temperatures to remain similar. Characterizing estuarine dynamics like these enables us to predict how Morro Bay, and other similar estuarine systems, may respond to long and short-term environmental changes, and how these responses influence estuarine circulation and environmental health.

The geological sequestration of carbon dioxide (CO2) is one of the options of controlling the greenhouse gas emissions. However, leakage of CO2 from the storage reservoir is a risk associated with geological sequestration. Over longer times, large-scale groundwater motion may cause leakage of dissolved CO2 (CO2aq). The objectives of this thesis are twofold. First, the modelling study analyzes the leakage of CO2aq along the conducting pathways. Second, a relatively safer mode of geological storage is investigated wherein CO2aq is injected in a carbonate reservoir. A reactive transport model is developed that accounts for the coupled hydrological transport and the geochemical reactions of CO2aq in the porous media. The study provides a quantitative assessment of the impact of advection, dispersion, diffusion, sorption, geochemical reactions, temperature, and heat transport on the fate of leaking CO2aq. The mass exchange between the conducting pathway and the rock matrix plays an important role in retention and reactions of leaking CO2aq. A significant retention of leaking CO2aq is caused by its mass stored in aqueous and adsorbed states and its consumption in reactions in the rock matrix along the leakage pathway. Advection causes a significant leakage of CO2aq directly from the reservoir through the matrix in comparison to the diffusion alone in the rock matrix and advection in a highly conducting, but thin fracture. Heat transport by leaking brine also plays an important role in geochemical interactions of leaking CO2aq.  Injection of CO2aq is simulated for a carbonate reservoir. Injected CO2-saturated brine being reactive causes fast dissolution of carbonate minerals in the reservoir and fast conversion of CO2aq through considered geochemical reactions. Various parameters like dispersion, sorption, temperature, and minerals reaction kinetics are found to play important role in the consumption of CO2aq in reactions. / <p>Research Funders:</p><p>(i) Higher Education Commission (HEC) of Pakistan</p><p>(ii) Lars Erik Lundberg Scholarship Foundation, Sweden</p>

Dans cette thèse, nous analysons une méthode de Galerkine discontinue (GD) et deux estimateurs d'erreur a posteriori pour l'équation d'advection-diffusion-réaction linéaire et stationnaire avec diffusion hétérogène. La méthode GD considérée, la méthode SWIP, utilise des moyennes pondérées dont les poids dépendent de la diffusion. L'analyse a priori montre que la convergence est optimale en le pas du maillage et robuste par rapport aux hétérogénéités de la diffusion, ce qui est confirmé par les tests numériques. Les deux estimateurs d'erreur a posteriori sont obtenus par une analyse par résidus et contrôlent la (semi-)norme d'énergie de l'erreur. L'analyse d'efficacité locale montre que presque tous les estimateurs sont indépendants des hétérogénéités. Le deuxième estimateur d'erreur est plus précis que le premier, mais son coût de calcul est légèrement plus élevé. Cet estimateur est basé sur la construction d'un flux H(div)-conforme dans l'espace de Raviart-Thomas-Nédéléc.

A novel study on the investigation of three very common atmospheric sulphur species relevant to the Mpumalanga Highveld subregion was conducted. Long-term in situ measurements were applied in the diurnal and seasonal evaluation of the observed sulphur species. Ambient pollutant concentrations and surface meteorological data were collected at an air quality monitoring station at Elandsfontein. Elandsfontein air quality monitoring station was ideal for the observations due to its high elevation within the Mpumalanga Province surrounded by few rolling hills and negligible windbreaks which easily allows for extensive plume-contact with the surface during convective daytime mixing. The temporal characteristics of the sulphur species have been assessed relative to one another with varying meteorological conditions. The diurnal and seasonal concentration variations were used to describe the physical characteristics exhibited by the compounds over Elandsfontein. Pollution roses were used to target the source of the major release points and areas of these sulphur species relative to the Elandsfontein monitoring station. Gas and particle concentrations were analysed in relation to varying meteorological parameters with a view to ascertaining the sulphur transformation and concentration distribution in the planetary boundary layer. Particulate sulphate distribution has been modelled through multivariate regression analyses in relation to three meteorological parameters, namely, wind speed, relative humidity and ambient temperature for the various seasons observed over southern Africa. This study has shown that hydrogen sulphide, sulphur dioxide and sulphate species are present throughout the year in the Mpumalanga Highveld at notably significant levels. The presence of ambient particulate sulphate has been shown to result from the combination of chemical interactions during long-range aerosol transport; atmospheric recirculation processes shown from back trajectories over the southern Africa sub-region, as well as the variation in the removal mechanisms and rates for the different seasons throughout the year. These transport and removal processes all contribute to the overall sulphur mass balance in the planetary boundary layer. Dosage of the three sulphur species was evaluated to provide data for sulphur pollution loading that could form a basis for health and vii environmental impact assessments over the area. In view of the characteristic patterns displayed by particulate sulphate, multivariate mathematical models have been developed on a seasonal basis with variations in meteorological parameters. This was seen to predict an accuracy of up to 70 % of the particulate sulphate loading for different seasons over the South African Highveld. In order to understand the chemical interactions of atmospheric sulphur species, it is important to be able to predict the route taken and expected products of transformation on any given condition. Theoretical analyses of the chemical thermodynamic properties of the known reacting species and a well-established approach were used in predicting reaction paths and establishing the possible and feasible products of chemical transformation in relation to the ambient temperature. The determination of reaction paths and possible products of chemical transformation provides a measure of the relative importance of the reacting species and the mechanism of reaction. Gas-, aqueous-phase and radical reactions involving sulphur (IV) were investigated with a view to establishing their relative importances. Thermochemical properties of several sulphur-containing compounds not available in the literature have been generated for evaluation of Gibbs free energy (ΔG) and enthalpy (ΔH). An electronic energy structural approach has been applied to model for ΔG and ΔH of 88 sulphur species in 90 chemical reactions comprising gas-phase, aqueousphase and radical reactions. Modelling was evaluated for their relative importances over a temperature range of –100 °C to +100 °C. The temperature range is well above the known tropospheric temperature range to account for variations in the atmospheric environment. To further comprehend the chemistry of sulphur with regards to distribution of the species in the atmosphere, a kinetic model is developed and incorporated into a dispersion model. The kinetic evaluation of the oxidation rate of SO2 to sulphate has been determined with advection and dispersion over the Elandsfontein area. Gas-phase transformation with advection and dispersion has been used to evaluate the extent of the distribution of SO2 relative to the major contributing sources. The dry deposition was considered to be the dominant removal mechanism. It was assumed that the reaction rate was second order in concentration and that the rate of deposition was first order. The oxidation rates obtained for the seasons were 10.9 % h-1 for summer; 8.83 % h-1 for autumn; 6.56 % h-1 for winter; viii 10.8 % h-1 for spring, while an overall rate of 9.6 % h-1 was obtained for the one year study period. The transformation rate model produced a reaction constant and an activation energy of 4.92 x 10-6 μg m-3 s-1 and 36.54 kJ kg-1 for summer; 3.939 x 10-6 μg m-3 s-1 and 43.89 kJ kg-1 for autumn; 2.90 x 10-6 μg m-3 s-1 and 115.69 kJ kg-1 for winter; 4.82 x 10-6 μg m-3 s-1 and 43.29 kJ kg-1 for spring, while for the year 4.29 x 10-6 μg m-3 s-1 and 34.31 kJ kg-1. A Gaussian puff unsteady state Lagrangian dispersion model with reflection at the surface and inversion layer was applied for concentration diffusion. The Lagrangian dispersion model with dry deposition was a better prediction of the observed data than the models from previous studies using a first order rate constant with or without deposition rate.

O modelo numérico Delft3D-Flow foi utilizado nos estudos da distribuição e variabilidade de propriedades termohalinas, e da circulação tridimensional do sistema estuarino dos rios Caravelas e Peruípe-SERCP. Os resultados do modelo foram validados quantitativamente usando dados experimentais de marés de quadratura e de sizígia de correntes e salinidades em quatro estações fixas (duas em cada um dos estuários de Caravelas e Nova Viçosa). No processamento foram aplicadas inicialmente condições iniciais homogêneas da salinidade, densidade e dos coeficientes cinemáticos de viscosidade e difusividade vertical, e após quatro semanas de simulação foram extraídos resultados de diferentes condições. Esses resultados foram utilizados como condições iniciais mais realistas, tendo o campo espacial variado das propriedades termohalinas, e dos parâmetros físicos. Essas novas condições iniciais permitiram pular o tempo transiente otimizando assim as simulações subsequentes. A validação das simulações foi feita com base nas medições da campanha de verão, por causa do atraso do período chuvoso a vazão do rio Peruípe foi bem representativa para condições de inverno e, portanto, seria redundante usar as forçantes dos rios com valores tão próximos na validação, além da necessidade da demanda de um tempo muito maior nas analise comparativas dos resultados. Durante o verão (janeiro de 2008), os dados de vazão do rio Peruípe obtidos na Agência Nacional de Águas (ANA) levaram a estimativa da descarga fluvial de ~ 20 m3.s-1, com a extrapolação de ~ 4 m3.s-1 para vazão conjunta dos dois principais afluentes do canal estuarino do rio Caravelas (rios Cúpido e Jaburuna). As oscilações da maré foram simuladas satisfatoriamente para as quatro estações de controle utilizadas na validação, com valores médios do parâmetro Skill superiores a 0,97. As amplitudes da maré calculadas numericamente foram de aproximadamente 1,3 m e 2,5 m na quadratura e sizígia, respectivamente. Os resultados numéricos das simulações das velocidades foram melhores em condições de sizígia com valores médios do parâmetro Skill entre 0,77 e 0,93, enquanto que na quadratura esse parâmetro variou entre 0,38 a 0,65. Para a estrutura de salinidade durante as condições de maré de sizígia, melhores resultados no SERCP do skill e, portanto abrangendo as quatro estações de controle, foram confirmados pelos parâmetros Skill médios superiores a 0,83. Na maré de quadratura os correspondentes valores médios também foram relativamente altos, variando entre 0,73-0,85. Entretanto, houve dificuldades em simular adequadamente a alta estratificação (vertical e longitudinal) do estuário de Nova Vicosa, podendo-se atribuir esse fato à maior vazão do rio Peruípe, que é muito maior do que a do rio de Caravelas. Com os resultados da estrutura de salinidade a intrusão da massa de Água Tropical (AT) foi adequadamente representada nos quilômetros iniciais do canal estuarino do rio Caravelas, e na parte interna da desembocadura na região de Nova Viçosa. Movimentos bidirecionais foram observados nos resultados das simulações na preamar e baixamar, na região de desembocadura dos estuários da Caravelas e Nova Viçosa, movimentos estes forçados pela componente baroclínica da força de gradiente de pressão. Vale ressaltar que o efeito baroclínico ficou mais visível nos instantes da baixamar. Na preamar para a maior parte destas duas regiões verificou-se apenas um pequeno desvio no sentido das correntes entre superfície (Z = -0,1) e fundo (Z = -0,9) e em geral inferior a 30 graus. Usando os traçadores lagrangeanos virtuais lançados ao longo dos canais estuarinos das entradas norte (Caravelas) e sul (Nova Viçosa) do SERCP foi obtido como resultado um tempo de residência relativamente pequeno e comparável ao estuário tropical do rio Curimataú. No trecho analisado no canal estuarino do rio Caravelas, a ~ 3 km e ~ 12 km distantes da Boca do Tomba o tempo de residência médio foi ~ 4,2 dias e ~10,3 dias, respectivamente. Já no estuário de Nova Viçosa, ou canal estuarino do rio Peruípe, apenas o trecho inicial de 5 km foi considerado para o lançamento dos traçadores, e os tempos de residência de ~ 1,5 dias e 2,5 dias foram estimados para as posições de ~2,5 km e 5,0 km distantes da desembocadura. O modelo analítico proposto e usado no cálculo de tempo de residência teve resultados comparáveis aos obtidos pelas simulações pelo método lagrangeano do Delft-3D Flow. Diferentemente, o modelo LOICZ apresentou valores bem diferentes do tempo de residência para os seis estuários analisados (Caravelas, Nova Viçosa, Curimataú, Hudson, Conwy and Mersey), em geral bem inferiores aos do modelo proposto, indicando assim uma possível estimativa maior do fluxo difusivo na formulação do modelo LOICZ. / The numerical model Delft-Flow was used to study the spatial distribution and variability of the termohaline properties, and the tridimensional circulation in the estuarine system of the rivers Caravelas and Peruípe. The model results were validated quantitatively using field data of tidal oscilation and currents, and salinity measurements during neap and spring tides at four mooring stations, two in each estuary. In the data processing homogeneous conditions were used initially for the fields of salinity, density and the vertical kinematic coeficients of viscosity and diffusivity, then after four weeks of running simulation those fields were saved with spatially varied conditions. Those results were used for a more realistic initial condition, thus having a varied field of the termohaline properties, and of the physical parameters. The new initial conditions allowed avoiding the transient time and thus optimizing the following simulations. The model evaluation was done based on measurements undertaken during the summer season, because of the delay in the raining season, the Peruípe river discharge was low and more representative of dry season condition, for those reasons we just used the measurement taken in the January 2008. In the summer the measurements of the Peruíbe river discharge taken from the Agência Nacional de Águas (ANA), and the river flow of was estimated at ~ 20 m3.s-1, with the extrapolation of ~ 4 m3.s-1 for the unified flow from the rivers Cúpido and Jaburuna, with contribute to the flow in the Caravelas estuary. Tidal oscillation at neap and spring tides were well simulated for the 4 controling sites used to the validation, and with the mean skill values over 0.97. The tidal amplitudes were numerical calculated and nearly between 1.3 and 2.5 meters at neap and spring tides, respectively. The numerical results of the velocities were better simulated in spring tides with the mean skill values in the range of 0.77 and 0.93, while at neap tides this parameter varied between 0.38 and 0.65. For the salinity structure at spring tides good results in the estuarine system were achieved, hence comprising all the controling station for validation, with all mean skill values over 0.83. At neap tides the corresponding mean skill values were relatively high, varing in the range of 0.73-0.85. In addition, there were difficulties in simulation adequately the highly vertical and longitudinal stratification of the Nova Vicosa estuary. That was caused by the stronger river inflow of the Peruípe River, which is much higher than the inflow by Caravelas River. The intrusion of the Tropical Water mass (TW) was properly simulated given the right distribution of the salinity along the first quilometers of the estuarine channel of Caravelas, and the internal part of the Nova Viçosa estuarine mouth. Bidirectional movements were observed from the model outputs at the high and low tides, at the region near the mouth of both, Caravelas and Nova Viçosa estuary. Those moviments are forced by the baroclinic component of the pressure gradient. Is worth to mention the the baroclinic effect was better observed at the low tides of these regions. At high tide most of areas showed only a small change in the current direction between surface (Z = -0.1) and bottom (Z = -0.9) and usually smaller than 30 degrees. The virtual lagrangian drifters released along the estuarine channels of Caravelas (north) and Nova Viçosa (south) have shown a residence time relatively short, and comparable to the Curimataú tropical estuary. In the released location between 3 and 12 km of distance from the Caravelas mouth, the residence time was in the range of 4.2 and 10.3 days. Differently, at the Nova Viçosa estuary, only the first 5 km were studied and the residence time of 1.5 and 2.5 days was estimated for the respectives positions of 2.5 and 5.0 km away from the mouth. The analytical model proposed and used to calculate the residence time leaded to results comparable to the results from the numerical simulation using the Lagrangian method of the Delft-3D Flow. Differently, the LOICZ model has shown results really different of the residence time for all the six estuaries (Caravelas, Nova Viçosa, Curimataú, Hudson, Conwy and Mersey), and in general much smaller then the results from the proposed formula, thus indicating a possible overestimation of the diffusive flux assumed in the LOICZ formulation.

O estudo do transporte de partículas tem uma importância fundamental em diversas áreas de pesquisas como, por exemplo, na formação de gelo em uma aeronave pois pode afetar a sua sustentação e estabilidade. Tamanha é a preocupação com a segurança de vôo que diversos estudos têm sido realizados, resultando em códigos computacionais como o LEWICE nos Estados Unidos, TRAJICE no Reino Unido, ONERA na França e CANICE no Canadá. No Brasil, um dos estudo é feito pela EMBRAER em parceria com algumas instituições. O objetivo deste trabalho é desenvolver um algoritmo que possa ser empregado na trajetória das partículas, utilizando uma formulação euleriana que elimina a dificuldade da semeadura de partículas específica da formulação lagrangiana na determinação da fração de volume da partícula. O método empregado é dos volumes finitos em malhas não-estruturadas cuja principal chave está na reconstrução mínimos quadrados de alta ordem com restrição nos contornos. O desenvolvimento do trabalho engloba 3 etapas: definição da geometria e geração das malhas; utilização de um solver para o tratamento do escoamento do ar e obtenção do campo de velocidade; implementação e utilização do esquema numérico com reconstrução mínimos quadrados de alta ordem para simular o cálculo da fração de volume com imposição de condições limites apropriadas no contorno do corpo. Os resultados dos testes realizados mostram que o esquema numérico com reconstrução mínimos quadrados pode ser empregado na resolução de equações que apresentam uma região de descontinuidade, como é o caso da região de sombra, reduzindo a largura da banda de difusão numérica e overshoots. / The particle transport study has a fundamental importance in diverse research area like in the icing accretion on an aircraft because that can affect its sustentation and stability. The concern is so big that many researches have been carried through, resulting in computational codes like the LEWICE in the United States, TRAJICE in the United Kingdom, ONERA in France and CANICE in Canada. In Brazil, one of the study has been made by the EMBRAER with some institutes. The goal of this work is to develop an algorithm that can be used in the particles trajectory study, using an Eulerian method that eliminates the difficulty particle sowing, particular of the Lagrangian method, in the determination of the droplet fraction volume. This is made by the finite volume method on unstructured meshes whose main key is the high order reconstruction with restriction on the boundary. The development of the work involves 3 stages: geometry definition and mesh generation; using code for the treatment of the air flow and obtained flow velocity; use of the high order numerical scheme least square reconstruction to simulate the droplet fraction volume result with imposition of appropriate limit conditions in the body contour. The realized simulations shown that Least Square method can be used in problem resolution that present descontinuos region like is shadow region reducing numerical diffusion and overshoots.

La circulation sanguine joue un rôle vital en microcirculation, et ce pour le transport de l'oxygène, le dioxide de carbone et d'autres nutriments. Les globules rouges (GR) constituent la majorité des cellules du sang, c'est pourquoi par "écoulement sanguin", nous entendrons "écoulement d'une suspension de GR". Pendant longtemps l'écoulement sanguin était vu comme un phénomène passif où les GR sont considérés comme des cargos d'oxygène. La vision moderne est tout autre: l'écoulement sanguin est bel et bien un phénomène actif. Les GR ainsi que les cellules endothéliales (qui tapissent les faces internes des vaisseaux sanguins) sont impliquées dans un grand nombre de signalisations biochimiques induites par les contraintes hydrodynamiques, la route vers des régulations vasomotrices sans l'intervention du système nerveux. Par exemple, les GR ne transportent pas que l'oxygène, mais également de l'ATP (adenosine triphosphate), qui est libérée suite à des changements de conformation de protéines membranaires induite par les contraintes hydrodynamiques. Cette thèse est dédiée à la circulation sanguine et son couplage avec la signalisation biochimique ayant lieu en microcirculation. Plus précisément, les questions traités dans cette thèse sont i) la dynamique des GR, ii) le problème de la diffiusion-advection d'espèces chimiques au sein des écoulements sanguins, et iii) le rôle de la géométrie des réseaux vasculaires dans le processus de la signalisation biochimique mentionnés plus haut. Dans un premier temps nous analysons la dynamique de GR dans un écoulement de Poiseuille en présence de valeurs réalistes de contraste de viscosité. Dans un deuxième temps nous développons un modèle de diffusion-advection et le couplons aux écoulements sanguins en adoptant la méthode de Boltzmann sur réseaux; nous exploitons ensuite formulation en l'appliquant au problème de la libération de l'ATP par les GR sous écoulement. Enfin nous présentons des résultats préliminaires pour la problématique générale de l'écoulement sanguin mettant en jeu l'ATP libéré par les GR et la signalisation de calcium par les cellules endothéliales. Cette étude constitue un premier pas vers le problème général et ambitieux de la régulation locale mechano-biochimique impliquée dans la microcirculation. / Blood flow in microcirculation is vital for oxygen, carbon dioxide and nutrients transport. Most of blood cells are red blood cells (RBCs), so that by blood flow we mean flow of a suspension of RBCs. For long time blood flow has been mainly considered as a passive phenomenon, in which RBCs are viewed as passive carriers of oxygen. The modern view is completely different: blood flow is more active than we thought. The RBCs as well as vascular endothelial cells covering the internal walls of blood vessels are involved in a number of biochemical signaling processes that are triggered by shear stress eliciting a number of biochemical events, and ultimately resulting into vasomotor regulation without participation of the nerve system. For example, RBCs do not only carry oxygen but also ATP (adenosine triphosphate) , the release of which occurs thanks to changes of RBC membrane protein conformations caused by shear stress. Released ATP reacts with some endothelial membrane receptors leading to vasodilation. This thesis is devoted to blood flow and its coupling to biochemical signaling. More precisely, we investigate i) the dynamics of RBCs, ii) the advection diffusion of chemicals in blood flow and the role of iii) the geometry of vessel networks, in the mentioned signaling processes in microcirculations. Firstly, we study the RBC dynamics in a pipe flow with realistic viscosity contrast values, where a link between shape dynamics and rheology is established. Secondly, we develop an advection-diffusion solver that can handle general moving curved boundaries based on lattice-Boltzmann method (LBM); we then implement it for the study of the problem of ATP release from RBCs under shear flow. Membrane tension and deformation induced by shear stress together with vessel network geometry contribute to ATP release. Finally we demonstrate the capability of applying our model and our numerical tool to the complete problem of blood under flow involving ATP release from RBCs and endothelial calcium signaling as a preliminary step to the ambitious task of mechano-involved local regulation events in microcirculation.

Das globale Klimasystem ist ein ausgesprochen komplexes und hochgradig nichtlineares System mit einer Vielzahl von Einflüssen und Interaktionen zwischen Variablen und Parametern. Komplementär zu der Beschreibung des Systems mit globalen Klimamodellen, kann Klima anhand der Interaktionsstruktur des Gesamtsystems durch Netzwerke beschrieben werden. Statt Details so genau wie möglich zu modellieren, werden hier Zeitreihendaten verwendet um zugrundeliegende Strukturen zu finden. Die Herausforderung liegt dann in der Interpretation dieser Strukturen. Um mich der Frage nach der Interpretation von Netzwerkmaßen zu nähern, suche ich nach einem allgemeinen Zusammenhang zwischen Eigenschaften der Netzwerktopologie und Eigenschaften des zugrundeliegenden physikalischen Systems. Dafür werden im Wesentlichen zwei Methoden entwickelt, die auf der Analyse von Temperaturentwicklungen gemäß der Advektions-Diffusions-Gleichung (ADE) basieren. Für die erste Methode wird die ADE mit offenen Randbedingungen und δ-peak Anfangsbedingungen gelöst. Die resultierenden lokalen Temperaturprofile werden verwendet um eine Korrelationsfunktion und damit ein Netzwerk zu definieren. Diese Netzwerke werden analysiert und mit Klimanetzen aus Daten verglichen. Die zweite Methode basiert auf der Diskretisierung der stochastischen ADE. Die resultierende lineare, stochastische Rekursionsgleichung wird verwendet um eine Korrelationsmatrix zu definieren, die nur von der Übergangsmatrix und der Varianz des stochastischen Störungsterms abhängt. Ich konstruiere gewichtete und ungewichtete Netzwerke für vier verschiedene Fälle und schlage Netzwerkmaße vor, die zwischen diesen Systemen zu unterscheiden helfen, wenn nur das Netzwerk und die Knotenpositionen gegeben sind. Die präsentierten Rekonstruktionsmethoden generieren Netzwerke, die konzeptionell und strukturell Klimanetzwerken ähneln und können somit als "proof of concept" der Methode der Klimanetzwerke, sowie als Interpretationshilfe betrachtet werden. / The earth’s climate is an extraordinarily complex, highly non-linear system with a multitude of influences and interactions between a very large number of variables and parameters. Complementary to the description of the system using global climate models, in recent years, a description based on the system’s interaction structure has been developed. Rather than modelling the system in as much detail as possible, here time series data is used to identify underlying large scale structures. The challenge then lies in the interpretation of these structures. In this thesis I approach the question of the interpretation of network measures from a general perspective, in order to derive a correspondence between properties of the network topology and properties of the underlying physical system. To this end I develop two methods of network construction from a velocity field, using the advection-diffusion-equation (ADE) for temperature-dissipation in the system. For the first method, the ADE is solved for δ-peak-shaped initial and open boundary conditions. The resulting local temperature profiles are used to define a correlation function and thereby a network. Those networks are analysed and compared to climate networks from data. Despite the simplicity of the model, it captures some of the most salient features of climate networks. The second network construction method relies on a discretisation of the ADE with a stochastic term. I construct weighted and unweighted networks for four different cases and suggest network measures, that can be used to distinguish between the different systems, based on the topology of the network and the node locations. The reconstruction methods presented in this thesis successfully model many features, found in climate networks from well-understood physical mechanisms. This can be regarded as a justification of the use of climate networks, as well as a tool for their interpretation.

O estudo do transporte de partículas tem uma importância fundamental em diversas áreas de pesquisas como, por exemplo, na formação de gelo em uma aeronave pois pode afetar a sua sustentação e estabilidade. Tamanha é a preocupação com a segurança de vôo que diversos estudos têm sido realizados, resultando em códigos computacionais como o LEWICE nos Estados Unidos, TRAJICE no Reino Unido, ONERA na França e CANICE no Canadá. No Brasil, um dos estudo é feito pela EMBRAER em parceria com algumas instituições. O objetivo deste trabalho é desenvolver um algoritmo que possa ser empregado na trajetória das partículas, utilizando uma formulação euleriana que elimina a dificuldade da semeadura de partículas específica da formulação lagrangiana na determinação da fração de volume da partícula. O método empregado é dos volumes finitos em malhas não-estruturadas cuja principal chave está na reconstrução mínimos quadrados de alta ordem com restrição nos contornos. O desenvolvimento do trabalho engloba 3 etapas: definição da geometria e geração das malhas; utilização de um solver para o tratamento do escoamento do ar e obtenção do campo de velocidade; implementação e utilização do esquema numérico com reconstrução mínimos quadrados de alta ordem para simular o cálculo da fração de volume com imposição de condições limites apropriadas no contorno do corpo. Os resultados dos testes realizados mostram que o esquema numérico com reconstrução mínimos quadrados pode ser empregado na resolução de equações que apresentam uma região de descontinuidade, como é o caso da região de sombra, reduzindo a largura da banda de difusão numérica e overshoots. / The particle transport study has a fundamental importance in diverse research area like in the icing accretion on an aircraft because that can affect its sustentation and stability. The concern is so big that many researches have been carried through, resulting in computational codes like the LEWICE in the United States, TRAJICE in the United Kingdom, ONERA in France and CANICE in Canada. In Brazil, one of the study has been made by the EMBRAER with some institutes. The goal of this work is to develop an algorithm that can be used in the particles trajectory study, using an Eulerian method that eliminates the difficulty particle sowing, particular of the Lagrangian method, in the determination of the droplet fraction volume. This is made by the finite volume method on unstructured meshes whose main key is the high order reconstruction with restriction on the boundary. The development of the work involves 3 stages: geometry definition and mesh generation; using code for the treatment of the air flow and obtained flow velocity; use of the high order numerical scheme least square reconstruction to simulate the droplet fraction volume result with imposition of appropriate limit conditions in the body contour. The realized simulations shown that Least Square method can be used in problem resolution that present descontinuos region like is shadow region reducing numerical diffusion and overshoots.