Les arythmies auriculaires constituent une pathologie majeure en cardiologie, et leur étude constitue un vaste sujet de recherche. Pour les étudier, de nombreux modèles mathématiques de la propagation du potentiel d'action dans les oreillettes ont été développés. La plupart de ces modèles génériques permettent de reproduire des séquences d'activations typiques des oreillettes. De tels modèles peuvent avoir un intérêt expérimental, voir clinique, par exemple dans l'aide à la localisation des foyers arythmiques ou encore dans l'analyse des échecs du traitement de ces arythmies. Néanmoins, pour atteindre ce but, il faut être capable de recaler au mieux le modèle, dans ses dimensions géométriques ou fonctionnelles, sur des données individuelles. L'assimilation de données, discipline mathématique dans laquelle nous cherchons à combiner de manière optimale théorie et observations, est alors un bon candidat à la personnalisation des modèles de la propagation du potentiel d'action. Dans cette thèse, nous proposons d'étudier différentes méthodes d'assimilation de données -- séquentielles et variationnelles -- dans le but de combiner les modèles de propagation avec des données électroanatomiques. Plus précisément, nous nous intéressons à deux applications possible de l'assimilation de données que sont l'estimation d'état et l'estimation de paramètres. Dans un premier temps, nous étudions un observateur d'état permettant de corriger la position du front de propagation simulé en se basant sur la position du front observé. Cet observateur est alors utilisé afin de compléter une carte d'activation obtenue lors d'une procédure clinique. Ensuite, ce même observateur est combiné à un filtre de Kalman d'ordre réduit afin d'estimer les paramètres de conductivités du modèle mathématique de propagation du potentiel d'action. Une étude de la stratégie d'estimation liée état-paramètre est ensuite réalisée pour voir comment la méthode se comporte face aux erreurs de modélisation. La méthode est ensuite testée sur un jeu de données acquis cliniquement. Puis, nous regardons du côté des méthodes d'assimilation de données variationnelles qui permettent l'estimation de paramètres spatialement distribués. Plusieurs problèmes de minimisation, permettant d'estimer un paramètre de conductivité distribué dans l'espace, sont alors introduits et analysés. Nous montrons alors que la discrétisation de ces problèmes de minimisation, dans le but d'obtenir des méthodes numériques de résolution, peut s'avérer complexe. Une méthode numérique est ensuite mise en place pour un des problèmes de minimisation étudié, et trois cas tests unidimensionnels sont analysés.Enfin, nous démontrons l'existence d'un minimum pour une des fonctions objectif étudiées en nous basant sur des résultats d'analyse fonctionnelle de la littérature. / Atrial arrhythmias are a major pathology in cardiology, and their study is alarge research topic. To study them, many mathematical models of the actionpotential propagation in atria have been developed. Most of those generic models can be used to reproduce typical activation sequences of the atria. Such models may have an experimental or even clinical interest, for example in helping the location of arrhythmic foci or in the analysis of treatment failures for these arrhythmias. Nevertheless, to achieve this goal, it isnecessary to be able to adjust the model at best, based on experimental orclinical data. Data assimilation, a mathematical discipline in which we seek to optimally combine theory and observations, is then a good candidate for the customization of action potential propagation models.In this thesis, we propose to study different data assimilation methods-- sequential and variational -- in order to adjust action potential propagation model on electroanatomical data. More precisely, we are interested in two possible applications of data assimilation: state estimation and parameter estimation.First, we study a state observer which is able to correct the simulatedpropagation front localization based on the observed front localization. Thisobserver is then used to complete an activation map obtained during a clinical procedure.Then, this observer is combined with a reduced order Kalman filterin order to estimate the conductivity parameters of the action potentialpropagation model. A study of the joint state-parameter estimationstrategy is then realized to see how the method behaves faced with modelingerrors. The method is then tested on a clinically acquired dataset.Then, we look at variational data assimilation methods that allow the estimation of spatially distributed parameters. Several minimization problems, allowing to estimate a conductivity parameter distributed in space, are then introduced and analyzed. We then show that the discretization of these minimization problems, in order to obtain numerical methods of resolution, can be complex. A numerical method is then implemented for one of the studied minimization problems, and three 1D test cases are analyzed.Finally, we demonstrate the existence of a minimum for one of the studiedobjective function based on functional analysis results from theliterature.

Crystallization of polyethylene terephthalate in injection moulding : experiments, modelling and numerical simulation.

Crystallization of polyethylene terephthalate in injection moulding : experiments, modelling and numerical simulation.

Magnetohydrodynamics describes the motions of an electrically conducting fluid under the influence of magnetic fields. Such flows are encountered in a large variety of applications, from steel industry to heat exchangers of nuclear fusion reactors. Here we are concerned with situations where the magnetic field is relatively strong and the flow manifests turbulent motions. The interaction of the fluid with the electromagnetic field is still insufficiently understood and efficient predicting methods are lacking. Our goal is to provide more insight on this problem by making heavy use of numerical methods. In this work, two different classes of problem are investigated. First we consider that the turbulent character of the fluid is well developed and that solid boundaries are sufficiently far away to be completely neglected. The main effects of a strong magnetic field in that case are to damp the motion and to homogenize the flow along its direction, leading to a quasi two dimensional state. Using numerical simulations we have studied the dynamics of the flow in Fourier space and in particular the non linear energy transfers between turbulent eddies. Further we investigated the scale-by-scale anisotropy and compared various methods to address this quantity. Finally, the evolution of a passive scalar embedded in the flow was analyzed and it turned out that the characteristic anisotropy of the velocity field is reflected in the distribution of the scalar quantity. In the second problem, the flow in a duct of square cross section subject to a transverse magnetic field has been considered. Here, unlike in the previous situation, the magnetic field has globally a destabilizing effect on the flow, because of the strong inhomogeneities it produces. For instance, high velocity regions develop along the walls that are parallel to the magnetic field. There, we are mostly interested in the possible development of persistent time-dependent fluctuations. It is observed that the transition between laminar and turbulent regimes occurs through at least two distinct bifurcations. The first one takes place at moderate Reynolds number and is characterized by highly organized fluctuations. The second is encountered at higher Reynolds number and presents very strong and localized disturbances. /Il existe un grand nombre d'applications industrielles dans lesquelles un écoulement de métal liquide est soumis à un champ magnétique. La production d'acier par coulée continue, la fabrication de matériaux semi-conducteurs ou encore les échan-geurs de chaleur des futurs réacteurs à fusion nucléaire en sont de bons exemples. L'interaction du liquide conducteur avec le champ magnétique est à l'origine de nombreux phénomènes inhabituels en hydrodynamique classique et doit dès lors être décrite par la magnétohydrodynamique (ou MHD en abrégé). Le but de ce travail est d'étudier la physique de ces interactions, en se basant sur la résolution numérique des équations qui les gouvernent. Plusieurs aspects du problème ont été considérés indépendamment. Tout d'abord, l'étude de la turbulence homogène a permis de mettre en evidence les comportements du fluide loin de toute paroi solide. Ceci est mis un oeuvre dans un domaine spatial périodique, où les variables sont représentées par leur série de Fourier. L'influence du champ magnétique dans ce cas consiste à dissiper les fluctuations turbulentes et à rendre le champ de vitesse anisotrope. Les principaux résultats obtenus dans ce cadre concernent la distribution ainsi que le transfert d'énergie dans l'espace spectral, l'anisotropie des différentes échelles turbulentes de l'écoulement ainsi que le transport d'un scalaire passif au sein du fluide. Dans un deuxième temps, le travail a porté sur l'écoulement dans une conduite rectangulaire soumise à un champ magnétique et dont les parois sont conductrices d'électricité. La particularité de cet écoulement réside dans les zones de vitesse élevées qui se développent le long des parois parallèles au champ magnétique. Celles-ci donnent lieu à un intense cisaillement qui a généralement pour effet de rendre l'écoulement instable. La simulation numérique de ce problème a permis l'étude des instabilités au sein du fluide et de la transition du régime laminaire vers la turbulence.

This thesis deals with numerical simulation of turbulentflows in geometrically simple cases. Both plane and cylindricalgeometries are used. The simplicity of the geometry allows theuse of spectral methods which yield a very high accuracy usingrelatively few grid points. A spectral method for planegeometries is implemented on a parallel computer. Thetransitional Reynolds number for plane Couette flow is verifiedto be about 360, in accordance with earlier findings. TurbulentCouette flow at twice the transitional Reynolds number isstudied and the findings of large scale structures in earlierstudies of Couette flow are substantiated. These largestructures are shown to be of limited extent and give anintegral length scale of six half channel heights, or abouteight times larger than in pressure-driven channel flow.Despite this, they contain only about 10 \% of the turbulentenergy. This is demonstrated by applying a very smallstabilising rotation, which almost eliminates the largestructures. A comparison of the Reynolds stress budget is madewith a boundary layer flow, and it is shown that the near-wallvalues in Couette flow are comparable with high-Reynolds numberboundary layer flow. A new spectrally accurate algorithm isdeveloped and implemented for cylindrical geometries andverified by studying the evolution of eigenmodes for both pipeflow and annular pipe flow. This algorithm is a generalisationof the algorithm used in the plane channel geometry. It usesFourier transforms in two homogeneous directions and Chebyshevpolynomials in the third, wall-normal, direction. TheNavier--Stokes equations are solved with a velocity-vorticityformulation, thereby avoiding the difficulty of solving for thepressure. The time advancement scheme used is a mixedimplicit/explicit second order scheme. The coupling between twovelocity components, arising from the cylindrical coordinates,is treated by introducing two new components and solving forthem, instead of the original velocity components. TheChebyshev integration method and the Chebyshev tau method isboth implemented and compared for the pipe flow case.

No description available.

Finite-volume methods have been used for modeling of fluidflows involved in forced convection electrochemical coating androtating spray painting systems. Electrodeposition on a singlecircular cylinder under forced convection for Reynolds numbers10 and 200 was simulated. Comparisons with earlier numericaland theoretical results are presented and it is shown that theunsteady wake that appears for Reynolds numbers greater than 50affects the mass transfer from the surface of the cylinder onlyin an average sense. This result is compared with a heattransfer case, where unsteadiness is much more manifest. Theeffect of application of circulation movement around thecylinder surface was considered, showing that the use ofoptimal values for circulation can create a recirculation zonearound the cylinder and result in a remarkable improvement ofthe deposit uniformity. The magnetoelectrolysis researchdiscipline is presented with focus on magnetic fields uses onmass transfer processes. A classification of the governingdimensionless parameters that control the phenomena isproposed. Application of magnetoelectrolysis on electroplatingprocesses is done for the first time. It is found that the useof an alternating magnetically induced force around thecylinder can result in interesting improvement of quality andproductivity. Application of numerical methods is also studiedin another field of the surface finishing industry, thepainting atomizers. A critical situation of "reverse flow" isanalyzed. Different parameters of this phenomenon are studiedand suggestions for atomizers design are given and tested. <b>Keywords:</b>mass transfer, electrochemical coating, iontransport, forced convection, diffusion, magnetoelectrolysis,electrolyte, limiting current, numerical simulation,finite-volume methods, paint atomization, Coanda effect.

Modern industrial society is based on combustion with ever increasing standards on the efficiency of burning. One of the main combustion characteristics is the burning rate, which is influenced by intrinsic flame instabilities, external turbulence and flame interaction with walls of combustor and sound waves. In the present work we started with the problem how to include combustion along the vortex axis into the general theory of turbulent burning. We demonstrated that the most representative geometry for such problem is a hypothetic “tube” with rotating gaseous mixture. We obtained that burning in a vortex is similar to the bubble motion in an effective acceleration field created by the centrifugal force. If the intensity of the vortex is rather high then the flame speed is determined mostly by the velocity of the bubble. The results obtained complement the renormalization theory of turbulent burning. Using the results on flame propagation along a vortex we calculated the turbulent flame velocity, compared it to the experiments and found rather good agreement. All experiments on turbulent combustion in tubes inevitably involve flame interaction with walls. In the present thesis flame propagation in the geometry of a tube with nonslip walls has been widely studied numerically and analytically. We obtained that in the case of an open tube flame interaction with nonslip walls leads to the oscillating regime of burning. The oscillations are accompanied by variations of the curved flame shape and the velocity of flame propagation. If flame propagates from the closed tube end, then the flame front accelerates with no limit until the detonation is triggered. The above results make a good advance in solving one of the most difficult problems of combustion theory, the problem of deflagration to detonation transition. We developed the analytical theory of accelerating flames and found good agreement with results of direct numerical simulations. Also we performed analytical and numerical studies of another mechanism of flame acceleration caused by initial conditions. The flame ignited at the axis of a tube acquires a “finger” shape and accelerates. Still, such acceleration takes place for a rather short time until the flame reaches the tube wall. In the case of flame propagating from the open tube end to the closed one the flame front oscillates and therefore generates acoustic waves. The acoustic waves reflected from the closed end distort the flame surface. When the frequency of acoustic mode between the flame front and the tube end comes in resonance with intrinsic flame oscillations the burning rate increases considerably and the flame front becomes violently corrugated.

Coupled shape oscillations and translational motion of an incompressible gas bubble in a liquid container in response to forced vibration is studied numerically. Bond number (Bo) and the ratio of the vibration amplitude to the bubble diameter (A/D) are found to be the governing non-dimensional numbers. Bubble response is studied in both 2D and 3D. Different schemes are used for 2D and 3D simulations. In 2D, the flow solver is coupled to a Volume of Fluid (VOF) algorithm to capture the interface between the two phases while in 3D the interface is captured using a level set algorithm. The oscillation outcome ranges from small amplitude and regular oscillations for small Bo and A/D to large amplitude, nonlinear, and chaotic oscillations for large Bo and A/D. Chaotic behavior occurs due to the coupling between the nonlinear shape oscillations and large amplitude oscillatory translational motion. By further increase of the forcing, the inertia of the liquid results in the formation of a liquid jet which penetrates within the bubble core and pierces the bubble and a toroidal bubble shape is formed. The toroidal bubble shape then goes through large amplitude shape oscillations and smaller bubbles are formed. A summary of the 3D simulations provides a map which shows the bubble oscillation outcome as a function of Bo and A/D. The interaction between two bubbles is studied in 2D as well and the effect of vibration amplitude, frequency and liquid to gas density ratio on the interaction force is investigated.

Coupled shape oscillations and translational motion of an incompressible gas bubble in a liquid container in response to forced vibration is studied numerically. Bond number (Bo) and the ratio of the vibration amplitude to the bubble diameter (A/D) are found to be the governing non-dimensional numbers. Bubble response is studied in both 2D and 3D. Different schemes are used for 2D and 3D simulations. In 2D, the flow solver is coupled to a Volume of Fluid (VOF) algorithm to capture the interface between the two phases while in 3D the interface is captured using a level set algorithm. The oscillation outcome ranges from small amplitude and regular oscillations for small Bo and A/D to large amplitude, nonlinear, and chaotic oscillations for large Bo and A/D. Chaotic behavior occurs due to the coupling between the nonlinear shape oscillations and large amplitude oscillatory translational motion. By further increase of the forcing, the inertia of the liquid results in the formation of a liquid jet which penetrates within the bubble core and pierces the bubble and a toroidal bubble shape is formed. The toroidal bubble shape then goes through large amplitude shape oscillations and smaller bubbles are formed. A summary of the 3D simulations provides a map which shows the bubble oscillation outcome as a function of Bo and A/D. The interaction between two bubbles is studied in 2D as well and the effect of vibration amplitude, frequency and liquid to gas density ratio on the interaction force is investigated.