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.

Dans de nombreux réservoirs géothermiques profonds, l'échangeur thermique est un massif de roches chaudes fracturées. Comment la morphologie des fractures influence-t-elle le flux hydraulique et le champ de température lorsque de l'eau froide est injectée dans ce milieu ? Cette question est abordée à l'échelle de la fracture, de manière numérique, à l'aide de deux méthodes : par différences finies, en 2D, et par méthode de Boltzmann sur réseau, en 3D. Les calculs en différences finies montrent qu'une ouverture auto-affine induit une variabilité spatiale du flux hydraulique et du champ de température. Dans certains cas, il se crée une chenalisation du fluide, qui réduit l'efficacité du transfert thermique entre la roche et le fluide. Ces caractéristiques hydro-thermiques sont essentiellement engendrées par les plus grandes longueurs d'ondes de ces ouvertures auto-affines. Une première application à grande échelle, dimensionnée suivant les caractéristiques du site géothermique de Soultz-sous-Forêts (Alsace, France), est proposée. Une deuxième application consiste à évaluer la perméabilité du sous-sol de Draix (Alpes, France). Pour cela, la géométrie de fractures présentes dans le sous-sol est caractérisée précisément à partir de carottes géologiques. La topographie des fractures, mesurée avec un laser, est utilisée pour reconstituer la morphologie de l'ouverture des fractures. Ces données sont utilisées pour quantifier la perméabilité, ici élevée -- de l'ordre de 10^-9-10^-8 m^2. À l'aide de méthodes de Boltzmann sur réseau, la modélisation du comportement hydro-thermique dans des fractures présentant une topographie avec de fortes pentes est abordée. Au voisinage d'une aspérité de forme simple, le comportement hydro-thermique modélisé est très différent (recirculation) de celui dans le reste de la fracture. L'ensemble de ces modélisations suggère qu'il est nécessaire de prendre en compte la morphologie des fractures pour estimer le comportement hydro-thermique en géothermie.

The construction of compact high-order Residual Distribution schemes for the discretizationof steady multidimensional advection-diffusion problems on unstructuredgrids is presented. Linear and non-linear scheme are considered. A piecewise continuouspolynomial approximation of the solution is adopted and a gradient reconstructionprocedure is used in order to have a continuous representation of both thenumerical solution and its gradient. It is shown that the gradient must be reconstructedwith the same accuracy of the solution, otherwise the formal accuracy ofthe numerical scheme is lost in applications in which diffusive effects prevail overthe advective ones, and when advection and diffusion are equally important. Thenthe method is extended to systems of equations, with particular emphasis on theNavier-Stokes and RANS equations. The accuracy, efficiency, and robustness of theimplicit RD solver is demonstrated using a variety of challenging aerodynamic testproblems.

Na presente tese é apresentada uma nova solução analítica para a equação de ad-vecção-difusão bidimensional transiente para simular a dispersão de poluentes na atmosfera. Para tanto, a equação de advecção-difusão é resolvida pela combinação da transformada de Laplace e da técnica GILTT (Generalized Integral Laplace Transform Technique). O fechamento da turbulência para os casos Fickiano e não-Fickiano é considerado. É investigado o problema de modelagem da dispersão de poluentes em condições de ventos fortes e fracos considerando, para o caso de ventos fracos, a difusão longitudinal na equação de advecção-difusão. Além disso, foi incluída no modelo a velocidade vertical e avaliada sua influência considerando-se o campo de velocidades constante e também geradas via LES (Large Eddy Simulation), para poder simular uma camada limite turbulenta mais realística. Os resultados obtidos por essa metodologia são validados com resultados experimentais disponíveis na literatura. / In the present thesis it is presented a new analytical solution for the transient two- dimensional advection-diffusion equation to simulate the pollutant dispersion in atmosphere. For that, the advection-diffusion equation is solved combining the Laplace transform and the GILTT (Generalized Integral Laplace Transform Technique) techniques. The turbulence closure for Fickian and non-Fickian cases is considered. It is investigated the problem of modeling the pollutant dispersion in strong and weak winds considering, for the case of low wind conditions, the longitudinal diffusion in the advection-diffusion equation. Moreover, it was considered in the model the vertical velocity and its influence was evaluated considering velocities field constant and also generated by means of LES (Large Eddy Simulation), to simulate a more realistic turbulent boundary layer. The results attained by this methodology are validated with experimental results available in literature.

Na presente tese é apresentada uma nova solução analítica para a equação de ad-vecção-difusão bidimensional transiente para simular a dispersão de poluentes na atmosfera. Para tanto, a equação de advecção-difusão é resolvida pela combinação da transformada de Laplace e da técnica GILTT (Generalized Integral Laplace Transform Technique). O fechamento da turbulência para os casos Fickiano e não-Fickiano é considerado. É investigado o problema de modelagem da dispersão de poluentes em condições de ventos fortes e fracos considerando, para o caso de ventos fracos, a difusão longitudinal na equação de advecção-difusão. Além disso, foi incluída no modelo a velocidade vertical e avaliada sua influência considerando-se o campo de velocidades constante e também geradas via LES (Large Eddy Simulation), para poder simular uma camada limite turbulenta mais realística. Os resultados obtidos por essa metodologia são validados com resultados experimentais disponíveis na literatura. / In the present thesis it is presented a new analytical solution for the transient two- dimensional advection-diffusion equation to simulate the pollutant dispersion in atmosphere. For that, the advection-diffusion equation is solved combining the Laplace transform and the GILTT (Generalized Integral Laplace Transform Technique) techniques. The turbulence closure for Fickian and non-Fickian cases is considered. It is investigated the problem of modeling the pollutant dispersion in strong and weak winds considering, for the case of low wind conditions, the longitudinal diffusion in the advection-diffusion equation. Moreover, it was considered in the model the vertical velocity and its influence was evaluated considering velocities field constant and also generated by means of LES (Large Eddy Simulation), to simulate a more realistic turbulent boundary layer. The results attained by this methodology are validated with experimental results available in literature.

No description available.

Na presente tese é apresentada uma nova solução analítica para a equação de ad-vecção-difusão bidimensional transiente para simular a dispersão de poluentes na atmosfera. Para tanto, a equação de advecção-difusão é resolvida pela combinação da transformada de Laplace e da técnica GILTT (Generalized Integral Laplace Transform Technique). O fechamento da turbulência para os casos Fickiano e não-Fickiano é considerado. É investigado o problema de modelagem da dispersão de poluentes em condições de ventos fortes e fracos considerando, para o caso de ventos fracos, a difusão longitudinal na equação de advecção-difusão. Além disso, foi incluída no modelo a velocidade vertical e avaliada sua influência considerando-se o campo de velocidades constante e também geradas via LES (Large Eddy Simulation), para poder simular uma camada limite turbulenta mais realística. Os resultados obtidos por essa metodologia são validados com resultados experimentais disponíveis na literatura. / In the present thesis it is presented a new analytical solution for the transient two- dimensional advection-diffusion equation to simulate the pollutant dispersion in atmosphere. For that, the advection-diffusion equation is solved combining the Laplace transform and the GILTT (Generalized Integral Laplace Transform Technique) techniques. The turbulence closure for Fickian and non-Fickian cases is considered. It is investigated the problem of modeling the pollutant dispersion in strong and weak winds considering, for the case of low wind conditions, the longitudinal diffusion in the advection-diffusion equation. Moreover, it was considered in the model the vertical velocity and its influence was evaluated considering velocities field constant and also generated by means of LES (Large Eddy Simulation), to simulate a more realistic turbulent boundary layer. The results attained by this methodology are validated with experimental results available in literature.

No description available.