Este trabalho tem como principal objetivo o desenvolvimento de um método numérico para simulação das grandes escalas de escoamentos turbulentos tridimensionais utilizando uma modelagem de turbulência baseada em filtragem temporal (denominada TLES - Temporal Large Eddy Simulation). O método desenvolvido combina discretizações temporais com ordem de mínima precisão 2 (Adams-Bashforth, QUICK, Runge-Kutta), um método de projeção de ordem 2, com discretizações espaciais também de ordem 2 obtidas pelo método de volumes finitos. Esta metodologia foi empregada na simulação de problemas teste turbulentos como o canal e a cavidade impulsionada, sendo este último resultado simulado pela primeira vez com modelagem TLES. Os resultados mostram uma excelente concordância quando comparado com resultados de simulações diretas (DNS) e dados experimentais, superando resultados clássicos obtidos com formulação LES com filtragem espacial. / The main objective of this work is to develop a numerical method for large eddy simulation of tridimensional turbulent flows using a model based on temporal filtering (TLES - Temporal Large Eddy Simulation). The developed method combines at least 2nd order temporal discretizations (Adams-Bashforth, QUICK, Runge-Kutta), a 2nd order projection method, and 2nd order spatial discretizations obtained by the finite volume method. This methodology was employed to the simulation of turbulent benchmark problems such as channel and lid-driven cavity flows. The latter is simulated for the first time using a TLES turbulence modelling. Results show excellent agreement when compared to Direct Numerical Simulations (DNS) and experimental data, with better results than classical results produced by standard LES formulation with spatial filtering.

Le but de cette thèse est de faire l'étude de méthodes de volumes finis pour des équations aux dérivées partielles déterministes et stochastiques; nous effectuons des simulations numériques et démontrons des résultats de convergence d'algorithmes.Au Chapitre 1, nous appliquons un schéma semi-implicite en temps combiné avec la méthode de volumes finis généralisés SUSHI pour la simulation d'écoulements à densité variable en milieu poreux; il vient à résoudre une équation de convection-diffusion parabolique pour la concentration couplée à une équation elliptique en pression. Nous présentons ensuite une méthode de simulation numérique pour un problème d'écoulements à densité variable couplé à un transfert de chaleur.Au Chapitre 2, nous effectuons une étude numérique de l'équation de Burgers non visqueuse en dimension un d'espace, avec des conditions aux limites périodiques, un terme source stochastique de moyenne spatiale nulle et une condition initiale déterministe. Nous utilisons un schéma de volumes finis combinant une intégration en temps de type Euler-Maruyama avec le flux numérique de Godunov. Nous effectuons des simulations par la méthode de Monte-Carlo et analysons les résultats pour différentes régularités du terme source. Il apparaît que la moyenne empirique des réalisations converge vers la moyenne en espace de la condition initiale déterministe quand t → ∞. Par ailleurs, la variance empirique converge elle aussi en temps long, vers une valeur qui dépend de la régularité et de l'amplitude du terme stochastique.Au Chapitre 3, nous démontrons la convergence d'une méthode de volumes finis pour une loi de conservation du premier ordre avec une fonction de flux monotone et un terme source multiplicatif faisant intervenir un processus Q-Wiener. Le terme de convection est discrétisé à l'aide d'un schéma amont. Nous présentons des estimations a priori pour la solution discrète dont en particulier une estimation de type BV faible. A l'aide d'une interpolation en temps, nous démontrons deux inégalité entropiques vérifiées par la solution discrète, ce qui nous permet de prouver que la solution discrète converge selon une sous-suite vers une solution stochastique faible entropique à valeurs mesures de la loi de conservation.Au Chapitre 4, nous obtenons des résultats similaires à ceux du Chapitre 3 dans le cas où la fonction flux n'est pas monotone; le terme de convection est discrétisé à l'aide d'un schéma monotone. / This thesis bears on numerical methods for deterministic and stochastic partial differential equations; we perform numerical simulations by means of finite volume methods and prove convergence results.In Chapter 1, we apply a semi-implicit time scheme together with the generalized finite volume method SUSHI for the numerical simulation of density driven flows in porous media; it amounts to solve a nonlinear convection-diffusion parabolic equation for the concentration coupled with an elliptic equation for the pressure. We then propose a numerical scheme to simulate density driven flows in porous media coupled to heat transfer. We use adaptive meshes, based upon square or cubic volume elements.In Chapter 2, We perform Monte-Carlo simulations in the one-dimensional torus for the first order Burgers equation forced by a stochastic source term with zero spatial integral. We suppose that this source term is a white noise in time, and consider various regularities in space. We apply a finite volume scheme combining the Godunov numerical flux with the Euler-Maruyama integrator in time. It turns out that the empirical mean converges to the space-average of the deterministic initial condition as t → ∞. The empirical variance also stabilizes for large time, towards a limit which depends on the space regularity and on the intensity of the noise.In Chapter 3, we study a time explicit finite volume method with an upwind scheme for a first order conservation law with a monotone flux function and a multiplicative source term involving a Q-Wiener process. We present some a priori estimates including a weak BV estimate. After performing a time interpolation, we prove two entropy inequalities for the discrete solution and show that it converges up to a subsequence to a stochastic measure-valued entropy solution of the conservation law in the sense of Young measures.In Chapter 4, we obtain similar results as in Chapter 3, in the case that the flux function is non-monotone, and that the convection term is discretized by means of a monotone scheme.

The issue this master’s thesis discusses the cooling synchronous machines. Specifically, the calculation of cooling induction motor using the finite volume method. Using Autodesk Inventor will create a 3D model of a real electric machine, ie asynchronous motor and then ANSYS WORKBENCH perform system analysis CFX, based on the finite volume method. Furthermore, we realize the air speed measurements on a particular machine and the individual results obtained by measuring and calculating the actual compared with each other. The master’s thesis also deals marginally with closely related to it. For the same machine model, we apply the calculation of the temperature fields using the finite volume method and them perform a thermal analysis. Next, we can carry out the measurement of the temperature on the motor itself and calculate the measured values and the measured compare each other.

The present thesis is concerned with air flow over lightweight footbridge. Special attention is paid to flow-induced instabilities. The thesis opens with a theoretical elaboration on the phenomena related to the research matter. The next part investigates air flow over footbridge in a specific situation using numerical simulation in the Ansys CFX software. Finally, results are discussed in the light of chosen theoretical framework and relevant conclusions are presented.

Presented work deals with heat transfer and its methods. At the beginning thesis describes the theory and the ways of heat transfer with connected quantities and equations. Then it explains the stack effect and impact of temperature on electro technical device. In work is also described ABB driver ACS line and calculation of heat transfer according to IEC 60890 standard. In the practical part there is the calculation of heat transfer in Flow Simulation simulating CFD program solved and finite element method is mentioned. Important part of work is devoted to setting and optimization of simulation. In conclusion are made some changes of construction of driver, dependence on heat transfer is inspected.

This master thesis deals with problematic of the heat convection in phase change materials (PCM) and PCM with nanoparticles. The derivation of stationary and non-stationary equations for 1D, 2D and 3D heat convection are described in detail. The finite element volume method is used for solution to these equations, of which principle is described carefully. The aim of this thesis is model development for 2D solution to temperature distribution at heat convection in PCM and influence assessment of nanoparticle implementation into material on given temperature distribution. Software MATLAB was used for model development, solution and plotting graphs.

Les travaux de cette thèse portent sur la modélisation et la discrétisation des écoulements diphasiques dans les milieux poreux fracturés. On se place dans le cadre des modèles dits dimensionnels hybrides couplant l'écoulement dans la matrice 3D à l'écoulement dans un réseau de fractures modélisées comme des surfaces 2D. La discrétisation s'appuie sur le cadre abstrait des schémas gradients. Dans cette étude nous présentons deux classes de schémas de types Gradient Schemes sur ces modèles en monophasique et en diphasique. Les objectifs sont motivés par l'application cible de la thèse qui concerne les procédés de récupération assistée de gaz par fracturation hydraulique dans les réservoirs de très faibles perméabilités / This thesis presents the work on modelling and discretisation of two-phase flows in the fractured porous media. These models couple the flow in the fractures represented as the surfaces of codimension one with the flow in the surrounding matrix. The discretisation is made in the framework of Gradient schemes which accounts for a large family of conforming and nonconforming discretizations. The test cases are motivated by the target application of the thesis concerning the gas recovery under the hydraulic fracturing process in low-permeability reservoirs

La compréhension des écoulements souterrains est importante pour de nombreuses applications comme l’énergie ou le stockage des déchets nucléaires. Cette thèse, effectuée en collaboration avec le Bureau de Recherches Géologiques et Minières (BRGM), est dédiée à la simulation des écoulements diphasiques compositionnels thermiques en milieux poreux et ses applications à la géothermie haute énergie et plus particulièrement au champ géothermique de Bouillante (Guadeloupe). Tout d’abord, deux formulations à variables persistantes sont comparées en termes d’implémentation et de convergence numérique. Dans ces deux formulations, les fractions molaires d’une phase absente sont étendues par celles à l’équilibre thermodynamique avec la phase présente. Il en résulte que l’ensemble des variables principales et des équations ne dépend pas de l’ensemble de phases présentes. De plus, l’équilibre thermodynamique est exprimé par une contrainte de complémentarité pour chacune des phases, ce qui permet l’utilisation de méthodes de type semi-smooth Newton pour résoudre les systèmes non-linéaires. D’autre part, cette thèse présente une nouvelle méthodologie combinant des discrétisations centrées aux noeuds (le schéma Vertex Approximate Gradient - VAG) et aux faces (le schéma Hybrid Finite Volume - HFV) sur une partition arbitraire des ensembles de mailles ou de faces, dans le but d’adapter le choix du schéma aux différentes parties du maillage. En effet, les maillages hybrides composés de différents types de mailles sont plus adaptés à la discrétisation de la géologie et de la géométrie des différents domaines d’un système géothermique. Ainsi le schéma peut être choisi localement en fonction de la géométrie de la maille et des propriétés pétrophysiques. L’analyse de convergence est effectuée dans le cadre des discrétisations Gradient pour des problèmes de diffusion du second ordre et la convergence est confirmée numériquement sur différents types de maillages hybrides 3D. Ensuite la discrétisation VAG-HFV est étendue au cas des écoulements de Darcy diphasiques non-isothermes compositionnels et est appliquée au cas test 2D représentant le plan de faille vertical du réservoir géothermique de Bouillante. Un autre aspect important de la modélisation des flux géothermiques consiste à prendre en compte les interactions entre le flux dans le milieu poreux et l’atmosphère. Puisque le couplage entre le modèle poreux et un modèle 2D surfacique ou 3D atmosphérique n’est pas réaliste en terme de coût de calcul aux échelles spatiale et temporelle géologiques, l’interaction sol-atmosphère est modélisée grâce à une condition limite prenant en compte l’équilibre de matière et d’énergie à l’interface. Ce modèle considère une couche limite atmosphérique avec transfert convectif molaire et thermique (en supposant l’évaporation de la phase liquide), une condition de débordement liquide aux surfaces d’infiltration, ainsi que le rayonnement thermique et la recharge en eau douce due aux précipitations. Cette condition limite est évaluée à l’aide d’une solution de référence couplant les écoulements non-isothermes liquide-gaz en milieu poreux et le gaz dans le milieu libre. Elle est ensuite étudiée numériquement en terme de convergence et de solution sur des cas tests géothermiques, dont le plan de faille vertical du réservoir géothermique de Bouillante. En complément est présenté le travail issu d’une collaboration lors de l’école d’été du CEMRACS 2016. Le projet consistait à ajouter un modèle de puits multi-branche thermique au code ComPASS, un nouveau simulateur géothermique parallèle basé sur des maillages non-structurés avec la possibilité de représenter des fractures. / The study of the subsurface flows is important for various applications such as energy or nuclear waste storage. This thesis, performed in collaboration with the French Geological Survey (BRGM), is dedicated to the simulation of non-isothermal compositional two-phase flows in porous media and its applications to high-energy geothermal fields and more precisely to the Bouillante field (Guadeloupe, French West Indies). First of all, two persistent variable formulations are compared in terms of implementation and numerical convergence. In these two formulations, the choice of the principal variables is based on with the extension of the phase molar fractions by the one at thermodynamic equilibrium with the present phase. It results that the set of principal variables and equations does not depend on the set of present phases. It also has the advantage to express the thermodynamic equilibrium as complementarity constraints, which allows the use of semi-smooth Newton methods to solve the non-linear systems. Moreover, this thesis presents a new methodology to combine a node-centered discretization (the Vertex Approximate Gradient scheme - VAG) and a face-centered discretization (the Hybrid Finite Volume scheme - HFV) on arbitrary subsets of cells or faces in order to choose the best-suited scheme in different parts of the mesh. Indeed, hybrid meshes composed of different types of cells are best suited to discretize the geology and geometry of the different parts of the geothermal system. Then, the scheme is adapted locally to the type of mesh/ cells and to petrophysical properties. The convergence analysis is performed in the gradient discretization framework over second order diffusion problems and the convergence is checked numerically on various types of hybrid three-dimensional meshes. Then, the VAG-HFV discretization is extended to non-isothermal compositional liquid-gas Darcy flows and is applied on the two dimensional cross-section of the Bouillante high temperature geothermal reservoir. Another important aspect of the geothermal flows modelling consists in considering the interactions between the porous medium and the atmosphere. Since the coupling between the porous medium and the 2D surface of 3D atmospheric flows is not computationally realistic at the space and time scales of a geothermal flow, the soil-atmosphere interaction is modelled using an advanced boundary condition accounting for the matter (mole) and energy balance at the interface. The model considers an atmospheric boundary layer with convective molar and energy transfers (assuming the vaporization of the liquid phase in the atmosphere), a liquid outflow condition at seepage surfaces, as well as the heat radiation and the precipitation influx. This boundary condition is assessed using a reference solution coupling the Darcy flow to a full-dimensional gas free flow. Then, it is studied numerically in terms of solution and convergence of the Newton-min non-linear solvers on several geothermal test cases including two-dimensional simulations of the Bouillante geothermal field. In addition is presented the collaborative project which took place during the CEMRACS summer school 2016. The project consisted in adding a multibranch thermal well model into the ComPASS code, a new geothermal simulator based on unstructured meshes and adapted to parallel distributed architectures with the ability to represent fractures.

Hydraulic piston accumulators play a major role especially within the field of stationary hydraulics. The calculation of the amount of hydraulic energy which can be stored in such an accumulator is crucial when it comes to a precise system design. The knowledge of the temperature and pressure within the accumulator is required in order to calculate the amount of energy to be stored. The state of the art solution to estimate the state of change of such an accumulator is the implementation of a costly measurement system within the accumulator which tracks the position of the piston. The goal of this paper is to develop and to analyse a time efficient simulation approach for the gaseous phase within a piston accumulator depending on the accumulator’s load cycle. Temperature, pressure, density and velocity profiles inside of the gaseous phase are calculated transiently in order to achieve that goal. The simulation model is derived in one dimensional environment to save computational effort. Having derived a valid model of the gaseous phase it will be possible in future works to replace the expensive position measurement system by pressure and temperature transducers and then use the model to calculate the position of the piston and therefore estimate the state of change.

3D environment reconstruction has received great interest in recent years in areas such as city planning, virtual tourism and flood hazard warning. With the rapid development of computer technologies, it has become possible and necessary to develop new methodologies and techniques for real time simulation for virtual environments applications. This thesis proposes a novel dynamic simulation scheme for flood hazard warning. The work consists of three main parts: digital terrain modelling; 3D environmental reconstruction and system development; flood simulation models. The digital terrain model is constructed using real world measurement data of GIS, in terms of digital elevation data and satellite image data. An NTSP algorithm is proposed for very large data assessing, terrain modelling and visualisation. A pyramidal data arrangement structure is used for dealing with the requirements of terrain details with different resolutions. The 3D environmental reconstruction system is made up of environmental image segmentation for object identification, a new shape match method and an intelligent reconstruction system. The active contours-based multi-resolution vector-valued framework and the multi-seed region growing method are both used for extracting necessary objects from images. The shape match method is used with a template in the spatial domain for a 3D detailed small scale urban environment reconstruction. The intelligent reconstruction system is designed to recreate the whole model based on specific features of objects for large scale environment reconstruction. This study then proposes a new flood simulation scheme which is an important application of the 3D environmental reconstruction system. Two new flooding models have been developed. The first one is flood spreading model which is useful for large scale flood simulation. It consists of flooding image spatial segmentation, a water level calculation process, a standard gradient descent method for energy minimization, a flood region search and a merge process. The finite volume hydrodynamic model is built from shallow water equations which is useful for urban area flood simulation. The proposed 3D urban environment reconstruction system was tested on our simulation platform. The experiment results indicate that this method is capable of dealing with complicated and high resolution region reconstruction which is useful for many applications. When testing the 3D flood simulation system, the simulation results are very close to the real flood situation, and this method has faster speed and greater accuracy of simulating the inundation area in comparison to the conventional flood simulation models