La modélisation du transport réactif est utilisée dans de nombreuses applications énergétiques et environnementales liées aux écoulements souterrains. La modélisation de tels problèmes conduit à un système hautement non linéaire d'EDP couplées à des équations différentielles ordinaires ou algébriques. Deux types d'approches pour la résolution numérique des problèmes de transport réactif sont largement utilisés dans la littérature. L'une est l'approche de séparation des opérateurs qui consiste à découpler les problèmes d'écoulement et de transport réactif. Ces derniers sont résolus séquentiellement à chaque pas de temps. L'autre stratégie est basée sur une approche entièrement couplée dans laquelle le système entier est résolu simultanément. Le but de la thèse de doctorat est le développement d'un schéma implicite en volumes finis pour la modélisation numérique d'écoulements multicomposants monophasiques et diphasiques avec transport réactif en milieu poreux.Deux nouveaux modules de transport réactif seront implémentés dans DuMuX, un simulateur libre pour les problèmes d'écoulements et de transport dans les milieuw poreux. Des simulations numériques bi et tridimensionnels comprenant des benchmarks et du calcul haute performance, seront effectuées pour valider les modules. / Reactive transport modeling is used in many energy and environmental applications related to subsurface flows. Modeling such problems leads to a highly nonlinear system of PDEs coupled with algebraic or ODEs. Two types of approaches for the numerical solving of reactive transport problems are widely used in the literature. One is the operator-splitting approach which consists in splitting the flow and reactive transport problems. These latter are solved sequentially at each time step. The other strategy is based on the fully coupled approach in which the entire system is solved simultaneously. The goal of the PhD thesis is the development of a fully coupled fully implicit finite volume scheme for numerical modeling of single and two-phase multicomponent flows with reactive transport in porous media. New reactive transport modules will be implemented in DuMuX, a free and open-source simulator for flow and transport processes in porous media. Numerical simulations for 2D and 3D including benchmark tests and high performance computing will be performed to validate the modules.

En simulation dynamique des réservoirs, un des artéfacts les plus gênants pour la prédiction de production est l’effet de l’orientation du maillage. Bien que celui-ci soit « normal » pour tout schéma numérique, il se trouve amplifié par l’instabilité du modèle physique, ce qui a lieu lorsque le contraste de mobilités entre l’eau (fluide poussant, utilisé dans les procédés de récupération secondaires) et l’huile (fluide poussé, contenant les hydrocarbures) dépasse un certain seuil critique. On parle alors d’écoulements à rapport de mobilités défavorable. Connu depuis longtemps, ce problème a fait l'objet de nombreux travaux dans les années 1980 ayant abouti au schéma dit à neuf points. Actuellement implanté dans PumaFlow, logiciel développé et commercialisé par IFPEN, ce schéma fonctionne relativement bien en maillages carrés et dépend d’un paramètre scalaire dont le réglage varie selon les auteurs sur la base de considérations heuristiques. Dans cette thèse, nous proposons une nouvelle démarche méthodologique afin non seulement d’ajuster ce paramètre libre de manière optimale mais aussi de généraliser le schéma aux maillages rectangulaires. La stratégie que nous préconisons repose sur une analyse d’erreur du problème, à partir de laquelle il est possible de définir une notion d’erreur angulaire et de garantir que le comportement du schéma obtenu soit le « moins anisotrope » possible via une minimisation de son écart par rapport à un comportement idéal. Cette procédure de minimisation est ensuite appliquée à deux autres familles de schémas numériques~ : (1) un schéma multidimensionnel proposé par Kozdon, dans lequel le paramètre libre est une fonction~ ; (2) un autre schéma à neuf points faisant intervenir deux paramètres scalaires. C’est ce dernier qui réduit le mieux l’effet de l’orientation lorsque le rapport des pas de maillage s’éloigne de 1. Enfin, une extension de la méthode à des modèles physiques plus complets est envisagée. / In dynamic reservoir simulation, one of the most troublesome artifacts for the prediction of production is the grid orientation effect. Although this normally arises from any numerical scheme, it happens to be amplified by the instability of the physical model, which occurs when the mobility contrast between the water (pushing fluid, used in the processes of secondary recovery) and the oil (pushed fluid, containing the hydrocarbons) exceeds a some critical threshold. We then speak of flows with adverse mobility ratio. This GOE issue has received a lot of attention from the engineers. Numerous works dating back to the 1980s have resulted in the so-called nine-point scheme. Currently implemented in the IFPEN software PumaFlow, this scheme performs relatively well in square meshes and depends on a scalar parameter whose value varies from one author to another, on the grounds of heuristic considerations. In this thesis, we propose a new methodological approach in order not only to optimally adjust this free parameter, but also to extend the scheme to rectangular meshes. The strategy that we advocate is based on an error analysis of the problem, from which it is possible to define a notion of angular error and to guarantee that the behavior of the obtained scheme is the "least anisotropic" possible through a minimization of its deviation from some ideal behavior. This minimization procedure is then applied to two other families of numerical schemes: (1) a multidimensional scheme proposed by Kozdon, in which the free parameter is a function; (2) another nine-point scheme involving two scalar parameters. The latter provides the best results regarding GOE reduction when the ratio of the mesh steps is far away from 1. Finally, an extension of the method to more sophisticated physical models is envisaged.

The theses is focused on efficient use of numerical methods in development of low-voltage switching devices, namely to create a physically correct and reliable numerical model of the temperature field to find an application in the design of the current path of a device for various operating conditions. The creation of this numerical model requires not only correct inclusion of all modes of heat transfer - conduction, convection and radiation, but also correct solution of problematic transient resistance - both electrical and thermal in electrical contacts at different stages of usage. Therefore an essential part of the theses forms a thorough experimental analysis of the necessary material properties and dependencies which forms input data for the numerical model that is based on the finite volume method. The last part of the theses deals with debugging and verification of numerical model to correspond with experimentally obtained data. The result of the theses is the numerical model which is able to solve correctly both steady and various transient states of swiching devices.

This master`s thesis analyzes the pressure distribution on the premises of scintillation detector secondary electron in the variant with three aperture. The aim of this study is analyzing the fluid flow depending on the application of the third aperture in the entrance of the detector, thus creating more self-pumped chamber, which is responsible for ensuring a better distribution of pressure in the premises of the detector. The result of the analysis would be determining how to change parameters within the detector. If it is found that application of the third aperture has a positive effect on water flow in the premises of the detector, this arrangement may be used for improvement of the detector. Master`s thesis is divided into several chapters. First describes the basic principles of electron microscopy, including sample preparation, conditions for the proper functioning of microscopes and sharing different types of electron microscopes. The next chapters describe briefly the physical descriptions of gases flow in low pressures and small apertures, the mathematical models and simulation software used in this analysis. The analysis is done in SolidWorks with the module called Cosmos FloSimulation. The conclusion summarizes the results of the analysis, including graphical representations of simulation.

The aim of this thesis is to study the issue of eniveromental scanning electron microscopy and pumping gas to create vacuum in the newly designed scintillation detector. Further, creating a model of recently proposed scintillation detector and simulating and analyzing pumping gas in differentially pumped chamber of detector. The theoretical part deals with electron microscopy, electron sources, electron optics and secondary electrons detectors. It is also presented which signals are generated by the electron beam on the surface of a solid. Further fluid flow issues and equations describing the flow in the solved chamber are dismantled. Furthermore, the impact of gaseous environment on the trajectory of primary electrons, because there are collisions of primary beam with atoms and molecules of gas. The following section discusses creating, quality and importance of the network in mathematical modelling. A method of a final volume used to calculate the differential equations describing the flow of gas at the premises of the detector is described . The practical part consists in creating a model of scintillation detector and analyzing the gas flow in drawing a vacuum in the newly designed scintillation detector. At the end the simulation results of gas flow are compared for different variants of apertures and various pressures on the neck of a scintillation detector designed for optimum performance of the detector. The outcome of this thesis is model of newly designed scintillation detector with optimized shapes of apertures according to functional requirements.

This thesis deals with the optimization of the concentrate photovoltaic cell cooling system through the CAE system. In the theoretical part, the thesis treats there the problematic of the photovoltaics and focuses on the concentrator cell and its problems coupled with the cooling system and the sink of heat. In the next theoretic part, it also analyses there the problematic of the conduit and transfer of heat. Moreover, the mathematical description of the fluid flow, the finite-volume method that is used in the SolidWorks Flow Simulation for the calculations, are also described there. In the practical part, the models and steps which depict precisely all the process of the heat cooling optimization are mentioned. All the proposed variants are mutually compared and put up for the discussion about their advantages and disadvantages. Lastly, the resultant model was also put through the simulation with the suggested radiational component that gave precision to the results. In the end of the thesis, there was made out the documentation of the final model drawings.

Thesis is concerned with modeling fluid dynamics and computing wind load on thin-walled structure of cooling tower. Two models for computational fluid dynamics are presented – one with singleton cooling tower and second with group of four cooling tower. Thesis includes also a structural model of cooling tower and methodology of wind load transfer is presented.

Práce je zaměřena na vytvoření numerického modelu 1D experimentálního reaktoru pro spalování tuhých paliv. Metodou konečných objemů je provedena diskretizace řídících rovnic a takto formulovaná úloha je implementována do programu v prostředí MATLAB. V závěru jsou uvedeny výsledky několika simulací hoření slámy.

The aim of this thesis is to study the issue of eniveromental scanning electron microscopy and pumping gas to create a vacuum in the newly designed scintillation detector. Further, creating a model of recently proposed scintillation detector and simulating and analyzing pumping gas in differentially pumped chamber of detector and the results compare with the previous model. The theoretical part deals with electron microscopy, electron sources, electron optics and secondary electrons detectors. It is also presented which signals are generated by the electron beam on the surface of a solid. Further fluid flow issues and equations describing the flow in the solved chamber are dismantled. Furthermore, the impact of gaseous environment on the trajectory of primary electrons, because there are collisions of primary beam with atoms and molecules of gas. The following section discusses creating, quality and importance of the network in mathematical modelling. A method of a final volume used to calculate the differential equations describing the flow of gas at the premises of the microscope is described . The practical part consists in creating a model of scintillation detector and analyzing the gas flow in drawing a vacuum in the newly designed scintillation detector. Furthermore, the simulation results are compared with the results of simulations on the older type of scintillation detector. The output of this thesis is model of recently proposed scintillation detector with visualized simulation results.

On s’intéresse dans cette thèse à montrer que la solution approchée, par la méthode des volumes finis, converge vers la solution renormalisée de problèmes elliptiques ou paraboliques à donnée L1. Dans la première partie nous étudions une équation de convection-diffusion ellliptique à donnée L1. En adaptant la stratégie développée pour les solutions renormaliséesà la méthode des volumes finis, nous montrons que la solution approchée converge vers l’unique solution renormalisée.Dans la deuxième partie nous nous intéressons à un problème parabolique nonlinéaire à donnée L1. En utilisant une version discrète de résultats de compacité classiques, nous montrons que les résultats obtenues dans le cas elliptique restentvrais dans le cas parabolique. Dans la troisième partie nous montrons des résultats similaires pour une équationparabolique doublement non-linéaire à donnée L1. Le caractère doublement nonlinéaire de l’équation crée des difficultés supplémentaires par rapport à la partie précédente, notamment car la règle de dérivation en chaîne ne s’applique pas dansle cas discret. Enfin, dans la quatrième partie, nous utilisons les résultats établis précédemment pour étudier un système de type thermoviscoélasticité. Nous montrons que la solution approchée, obtenue par un schéma éléments finis-volumes finis, converge vers une solution faible-renormalisée du système. / In this thesis we are interested in proving that the approximate solution, obtained by the finite volume method, converges to the unique renormalized solution of elliptic and parabolic equations with L1 data. In the first part we study an elliptic convection-diffusion equation with L1 data. Mixing the strategy developed for renormalized solution and the finite volume method,we prove that the approximate solution converges to the unique renormalized solution. In the second part we investigate a nonlinear parabolic equation with L1 data. Using a discrete version of classical compactness results, we show that the results obtaines previously in the elliptic case hold true in the parabolic case. In the third part we prove similar results for a doubly nonlinear parabolic equation with L1 data. The doubly nonlinear character of the equation makes new difficulties with respect to the previous part, especially since the chain rule formula does not apply in the discrete case. Finaly, in the fourth part we use the results established previously to investigate a system of thermoviscoelasticity kind. We show that the approximate solution,obtaines by finite element-finite volume scheme, converges to a weak-renormalized solution of the system.