For the numerical simulation of many problems of engineering interest, it is desirable to have an automated mesh adaption tool. This is important especially for problems characterized by anisotropic features and require mesh clustering in the direction of high gradients. Another significant issue in meshing emerges in unsteady simulations with moving boundaries, where the boundary motion has to be accommodated by deforming the computational grid. Similarly, there exist problems where current mesh needs to be adapted to get more accurate solutions. To solve these problems, we propose three novel procedures. In the first part of this work, we present an optimization procedure for three-dimensional anisotropic tetrahedral grids based on metric-driven h-adaptation. Through the use of topological and geometrical operators, the mesh is iteratively adapted until the final mesh minimizes a given objective function. We propose an optimization process based on an ad-hoc application of the simulated annealing technique, which improves the likelihood of removing poor elements from the grid. Moreover, a local implementation of the simulated annealing is proposed to reduce the computational cost. Many challenging unsteady multi-physics problems are characterized by moving boundaries and/or interfaces. When the boundary displacements are large, degenerate elements are easily formed in the grid such that frequent remeshing is required. We propose a new r-adaptation technique that is valid for all types of elements (e.g., triangle, tet, quad, hex, hybrid) and deforms grids that undergo large imposed displacements at their boundaries. A grid is deformed using a network of linear springs composed of edge springs and a set of virtual springs. The virtual springs are constructed in such a way as to oppose element collapsing. Both frequent remeshing, and exact-pinpointing of clustering locations are great challenges of numerical simulations, which can be overcome by adaptive meshing algorithms. Therefore, we conclude this work by defining a novel mesh adaptation technique where the entire mesh is adapted upon application of a force field in order to comply with the target mesh or to get more accurate solutions. The method has been tested for two-dimensional problems of a-priori metric definitions as well as for oblique shock clusterings.

Gradient-based aerodynamic shape optimization, based on Computational Fluid Dynamics analysis of the flow, is a method that can automatically improve designs of aircraft components. The prospect is to reduce a cost function that reflects aerodynamic performances. When the shape is described by a large number of parameters, the calculation of one gradient of the cost function is only feasible by recourse to techniques that are derived from the theory of optimal control. In order to obtain the best computational efficiency, the so called adjoint method is applied here on the complete mapping, from the parameters of design to the values of the cost function. The mapping considered here includes the Euler equations for compressible flow discretized on unstructured meshes by a median-dual finite-volume scheme, the primal-to-dual mesh transformation, the mesh deformation, and the parameterization. The results of the present research concern the detailed derivations of expressions, equations, and algorithms that are necessary to calculate the gradient of the cost function. The discrete adjoint of the Euler equations and the exact dual-to-primal transformation of the gradient have been implemented for 2D and 3D applications in the code Edge, a program of Computational Fluid Dynamics used by Swedish industries. Moreover, techniques are proposed here in the aim to further reduce the computational cost of aerodynamic shape optimization. For instance, an interpolation scheme is derived based on Radial Basis Functions that can execute the deformation of unstructured meshes faster than methods based on an elliptic equation. In order to improve the accuracy of the shape, obtained by numerical optimization, a moving mesh adaptation scheme is realized based on a variable diffusivity equation of Winslow type. This adaptation has been successfully applied on a simple case of shape optimization involving a supersonic flow. An interpolation technique has been derived based on a mollifier in order to improve the convergence of the coupled mesh-flow equations entering the adaptive scheme. The method of adjoint derived here has also been applied successfully when coupling the Euler equations with the boundary-layer and parabolized stability equations, with the aim to delay the laminar-to-turbulent transition of the flow. The delay of transition is an efficient way to reduce the drag due to viscosity at high Reynolds numbers.

The work developed in this thesis focusses on the electrical activity of the heart, from the modeling of the action potential originating from cardiac cells and propagating through the heart, as well as its electrical manifestation at the body surface. The study is divided in two main parts: modeling the action potential, and numerical simulations. For modeling the action potential a dimensional and asymptotic analysis is done. The key advance in this part of the work is that this analysis gives the steps to reliably control the action potential. It allows predicting the time/space scales and speed of any action potential that is to say the shape of the action potential and its propagation. This can be done as the explicit relations on all the physiological constants are defined precisely. This method facilitates the integrative modeling of a complete human heart with tissue-specific ionic models. It even proves that using a single model for the cardiac action potential is enough in many situations. For efficient numerical simulations, a numerical method for solving the heart-torso coupling problem is explored according to a level set description of the domains. This is done in the perspective of using directly medical images for building computational domains. A finite element method is then developed to manage meshes not adapted to internal interfaces. Finally, an anisotropic adaptive remeshing methods for unstructured finite element meshes is used to efficiently capture propagating action potentials within complex, realistic two dimensional geometries.

Le projet ANR ICARE, dans lequel s'inscrit cette thèse, vise au développement de méthodes pour l'analyse de structures complexes et de grande taille. Le défi scientifique consiste à investiguer des zones très localisées, mais potentiellement critiques vis-à-vis de la tenue mécanique d'ensemble. Classiquement, sont mis en œuvre aux échelles globale et locale des représentations, discrétisations, modèles de comportement et outils numériques adaptés à des besoins de simulation gradués en complexité. Le problème global est traité avec un code généraliste dans le cadre d'idéalisations topologiques (formulation plaque, simplification géométrique) et comportementale (homogénéisation) ; l'analyse locale quant à elle demande la mise en œuvre d'outils spécialisés (routines, codes dédiés) pour une représentation fidèle de la géométrie et du comportement.L'objectif de cette thèse consiste à développer un outil efficace de couplage non-intrusif pour la simulation multi-échelles / multi-modèles en calcul de structures. Les contraintes de non-intrusivité se traduisent par la non modification de l'opérateur de rigidité, de la connectivité et du solveur du modèle global, ce qui permet de travailler dans un environnement logiciel fermé. Dans un premier temps, on propose une étude détaillée de l'algorithme de couplage global/local non-intrusif. Sur la base d'exemples et de cas-test représentatifs en calcul de structures (fissuration, plasticité, contact...), on démontre l'efficacité et la flexibilité d'un tel couplage. Aussi, une analyse comparative de plusieurs outils d'optimisation de l'algorithme est menée, et le cas de patchs multiples en interaction est traité. Ensuite le concept de couplage non-intrusif est étendu au cas de non-linéarités globales, et une méthode de calcul parallèle par décomposition de domaine avec relocalisation non-linéaire est développée. Cette méthode nous a permis de paralléliser un code industriel séquentiel sur un mésocentre de calcul intensif. Enfin, on applique la méthode de couplage au raffinement de maillage par patchs d'éléments finis. On propose un estimateur d'erreur en résidu explicite adapté au calcul de solutions multi-échelles via l'algorithme de couplage. Puis, sur la base de cet estimateur, on met en œuvre une procédure non-intrusive de raffinement local de maillage. Au travers de ces travaux, un outil logiciel de couplage non-intrusif a été mis au point, basé sur l'échange de données entre différents codes de calcul (protocole Message Passing Interface). Les développements effectués sont intégrés dans une surcouche Python, dont le rôle est de coupler plusieurs instances de Code_Aster, le code d'analyse de structures développé par EDF R&D, lequel sera utilisé dans l'ensemble des travaux présentés. / This PhD thesis, part of the ANR ICARE project, aims at developing methods for complex analysis of large scale structures. The scientific challenge is to investigate very localised areas, but potentially critical as of mechanical systems resilience. Classically, representation models, discretizations, mechanical behaviour models and numerical tools are used at both global and local scales for simulation needs of graduated complexity. Global problem is handled by a generic code with topology (plate formulation, geometric approximation...) and behaviour (homogenization) simplifications while local analysis needs implementation of specialized tools (routines, dedicated codes) for an accurate representation of the geometry and behaviour. The main goal of this thesis is to develop an efficient non-intrusive coupling tool for multi-scale and multi-model structural analysis. Constraints of non-intrusiveness result in the non-modification of the stiffness operator, connectivity and the global model solver, allowing to work in a closed source software environment. First, we provide a detailed study of global/local non-intrusive coupling algorithm. Making use of several relevant examples (cracking, elastic-plastic behaviour, contact...), we show the efficiency and the flexibility of such coupling method. A comparative analysis of several optimisation tools is also carried on, and the interacting multiple patchs situation is handled. Then, non-intrusive coupling is extended to globally non-linear cases, and a domain decomposition method with non-linear relocalization is proposed. Such methods allowed us to run a parallel computation using only sequential software, on a high performance computing cluster. Finally, we apply the coupling algorithm to mesh refinement with patches of finite elements. We develop an explicit residual based error estimator suitable for multi-scale solutions arising from the non-intrusive coupling, and apply it inside an error driven local mesh refinement procedure. Through this work, a software tool for non-intrusive coupling was developed, based on data exchange between codes (Message Passing Interface protocol). Developments are integrated into a Python wrapper, whose role is to connect several instances of Code_Aster, the structural analysis code developed by EDF R&D, which will be used in the following work.

Esta dissertação tem por objetivo a implementação de um método adaptativo anisotrópico de malhas e seu acoplamento a um programa de simulação de escoamentos de fluidos compressíveis numa faixa ampla de número de Mach utilizando o Método dos Elementos Finitos (Bubnov-Galerkin). Mais especificamente, implementa-se um código para simulação de escoamentos compressíveis utilizando o método das linhas ou direções características (CBS), o qual possui boa performance para uma amplo espectro de números de Mach. A discretização espacial é feita utilizando-se elementos finitos triangulares lineares e tetraédricos lineares para problemas bidimensionais e tridimensionais, respectivamente. A discretização temporal é feita por uma expansão em séries de Taylor. Implementa-se uma adaptação anisotrópica com capacidade de refinamento e desrefinamento do domínio computacional para se obter soluções precisas a baixos custos computacionais, onde a estimativa de erro é conduzida por uma métrica Riemanniana, a qual permite o tratamento contínuo do erro através de um tensor de erro anisotrópico. O código é modificado para possibilitar o uso de arquiteturas de memória compartilhada a fim de aumentar a velocidade de processamento da simulação. Por fim, diversos estudos, tanto para problemas bidimensionais quanto tridimensionais, são realizados, validando a metodologia e realizando estudos adicionais em problemas mais complexos. / The objectives of this dissertation are the implementation of an anisotropic mesh adaptation procedure and its coupling with a compressible flow simulation code with large Mach range using the Finite Element Method (Bubnov-Galerkin). Specifically, a computer code using the Characteristic Based Split method called CBS, which has a good performance for a wide range of Mach numbers, is implemented. The spatial discretization is performed using linear triangular and linear tetrahedral finite elements for two and three dimensional cases, respectively. The temporal discretization is done with Taylor series. An anisotropic mesh adaption technique, based on a Riemann metric to evaluate the errors (which allows continuous error analysis through an anisotropic error tensor evaluation), including mesh refinement and mesh coarsening procedures is also implemented looking for accurate and computationally cheaper solutions. The code is able to use shared memory architecture in order to reduce computer process time. Finally, two-dimensional and three-dimensional studies are performed in order to validate the proposed methodology and additional complex tests are also analysed.

Neste trabalho, é apresentada a simulação de escoamentos compressíveis turbulentos no entorno de corpos móveis rígidos ou deformáveis empregando-se técnicas adaptativas. As simulações numéricas são conduzidas utilizando-se o método dos elementos finitos. A discretização espaço-temporal é desenvolvida através do método das linhas ou direções características (Characteristic-Based Split - CBS) e a modelagem da turbulência é feita através de um modelo de Simulação de Grandes Escalas (SGE, ou na terminologia em inglês, Large Eddy Simulation – LES) com o coeficiente de Smagorinsky variável no tempo e espaço (SGE ou LES dinâmico). A análise estrutural de corpos deformáveis imersos no fluido é realizada através de um modelo de elementos finitos triangulares para análise de placas e cascas com não linearidade geométrica, usando materiais elásticos com comportamento linear. Conjuntamente, um método de adaptação anisotrópica transiente de malhas é empregado para obter resultados com boa resolução a baixos custos computacionais. A consideração do movimento relativo de corpos imersos no escoamento é feita através de um método híbrido de movimento da malha que emprega interpolação com funções de base radial. Exemplos bidimensionais e tridimensionais são apresentados de forma a validar cada uma das metodologias desenvolvidas. Por fim, exemplos de simulações complexas são investigados, comparando-se os resultados obtidos com resultados experimentais e numéricos presentes na literatura. / In this work, the simulation of compressible turbulent flows around rigid and flexible moving bodies is presented using adaptative techniques. The numerical simulations are solved employing the finite element method. The space-time discretization is performed using the Characteristic-Based Split scheme (CBS) and turbulence is modelled with Large Eddy Simulation (LES) and a dynamic Smagorinsky sub-grid model. The structural analysis of deformable bodies immersed on the flow is performed using a triangular finite element model for the analysis of geometrically non-linear elastic plates and shells. An anisotropic mesh adaptation algorithm for transient simulations is coupled with the solver to achieve results with good resolution and low computational costs. The consideration of the relative movement of immersed bodies on the flow is performed employing an hybrid method of mesh movement based on radial basis function interpolation. Twodimensional and three-dimensional examples are presented in order to validate the proposed methodologies. Finally, complex simulations are investigated, where results are compared with experimental and numerical data available in the literature.

Neste trabalho, é apresentada a simulação de escoamentos compressíveis turbulentos no entorno de corpos móveis rígidos ou deformáveis empregando-se técnicas adaptativas. As simulações numéricas são conduzidas utilizando-se o método dos elementos finitos. A discretização espaço-temporal é desenvolvida através do método das linhas ou direções características (Characteristic-Based Split - CBS) e a modelagem da turbulência é feita através de um modelo de Simulação de Grandes Escalas (SGE, ou na terminologia em inglês, Large Eddy Simulation – LES) com o coeficiente de Smagorinsky variável no tempo e espaço (SGE ou LES dinâmico). A análise estrutural de corpos deformáveis imersos no fluido é realizada através de um modelo de elementos finitos triangulares para análise de placas e cascas com não linearidade geométrica, usando materiais elásticos com comportamento linear. Conjuntamente, um método de adaptação anisotrópica transiente de malhas é empregado para obter resultados com boa resolução a baixos custos computacionais. A consideração do movimento relativo de corpos imersos no escoamento é feita através de um método híbrido de movimento da malha que emprega interpolação com funções de base radial. Exemplos bidimensionais e tridimensionais são apresentados de forma a validar cada uma das metodologias desenvolvidas. Por fim, exemplos de simulações complexas são investigados, comparando-se os resultados obtidos com resultados experimentais e numéricos presentes na literatura. / In this work, the simulation of compressible turbulent flows around rigid and flexible moving bodies is presented using adaptative techniques. The numerical simulations are solved employing the finite element method. The space-time discretization is performed using the Characteristic-Based Split scheme (CBS) and turbulence is modelled with Large Eddy Simulation (LES) and a dynamic Smagorinsky sub-grid model. The structural analysis of deformable bodies immersed on the flow is performed using a triangular finite element model for the analysis of geometrically non-linear elastic plates and shells. An anisotropic mesh adaptation algorithm for transient simulations is coupled with the solver to achieve results with good resolution and low computational costs. The consideration of the relative movement of immersed bodies on the flow is performed employing an hybrid method of mesh movement based on radial basis function interpolation. Twodimensional and three-dimensional examples are presented in order to validate the proposed methodologies. Finally, complex simulations are investigated, where results are compared with experimental and numerical data available in the literature.

Esta dissertação tem por objetivo a implementação de um método adaptativo anisotrópico de malhas e seu acoplamento a um programa de simulação de escoamentos de fluidos compressíveis numa faixa ampla de número de Mach utilizando o Método dos Elementos Finitos (Bubnov-Galerkin). Mais especificamente, implementa-se um código para simulação de escoamentos compressíveis utilizando o método das linhas ou direções características (CBS), o qual possui boa performance para uma amplo espectro de números de Mach. A discretização espacial é feita utilizando-se elementos finitos triangulares lineares e tetraédricos lineares para problemas bidimensionais e tridimensionais, respectivamente. A discretização temporal é feita por uma expansão em séries de Taylor. Implementa-se uma adaptação anisotrópica com capacidade de refinamento e desrefinamento do domínio computacional para se obter soluções precisas a baixos custos computacionais, onde a estimativa de erro é conduzida por uma métrica Riemanniana, a qual permite o tratamento contínuo do erro através de um tensor de erro anisotrópico. O código é modificado para possibilitar o uso de arquiteturas de memória compartilhada a fim de aumentar a velocidade de processamento da simulação. Por fim, diversos estudos, tanto para problemas bidimensionais quanto tridimensionais, são realizados, validando a metodologia e realizando estudos adicionais em problemas mais complexos. / The objectives of this dissertation are the implementation of an anisotropic mesh adaptation procedure and its coupling with a compressible flow simulation code with large Mach range using the Finite Element Method (Bubnov-Galerkin). Specifically, a computer code using the Characteristic Based Split method called CBS, which has a good performance for a wide range of Mach numbers, is implemented. The spatial discretization is performed using linear triangular and linear tetrahedral finite elements for two and three dimensional cases, respectively. The temporal discretization is done with Taylor series. An anisotropic mesh adaption technique, based on a Riemann metric to evaluate the errors (which allows continuous error analysis through an anisotropic error tensor evaluation), including mesh refinement and mesh coarsening procedures is also implemented looking for accurate and computationally cheaper solutions. The code is able to use shared memory architecture in order to reduce computer process time. Finally, two-dimensional and three-dimensional studies are performed in order to validate the proposed methodology and additional complex tests are also analysed.

Esta dissertação tem por objetivo a implementação de um método adaptativo anisotrópico de malhas e seu acoplamento a um programa de simulação de escoamentos de fluidos compressíveis numa faixa ampla de número de Mach utilizando o Método dos Elementos Finitos (Bubnov-Galerkin). Mais especificamente, implementa-se um código para simulação de escoamentos compressíveis utilizando o método das linhas ou direções características (CBS), o qual possui boa performance para uma amplo espectro de números de Mach. A discretização espacial é feita utilizando-se elementos finitos triangulares lineares e tetraédricos lineares para problemas bidimensionais e tridimensionais, respectivamente. A discretização temporal é feita por uma expansão em séries de Taylor. Implementa-se uma adaptação anisotrópica com capacidade de refinamento e desrefinamento do domínio computacional para se obter soluções precisas a baixos custos computacionais, onde a estimativa de erro é conduzida por uma métrica Riemanniana, a qual permite o tratamento contínuo do erro através de um tensor de erro anisotrópico. O código é modificado para possibilitar o uso de arquiteturas de memória compartilhada a fim de aumentar a velocidade de processamento da simulação. Por fim, diversos estudos, tanto para problemas bidimensionais quanto tridimensionais, são realizados, validando a metodologia e realizando estudos adicionais em problemas mais complexos. / The objectives of this dissertation are the implementation of an anisotropic mesh adaptation procedure and its coupling with a compressible flow simulation code with large Mach range using the Finite Element Method (Bubnov-Galerkin). Specifically, a computer code using the Characteristic Based Split method called CBS, which has a good performance for a wide range of Mach numbers, is implemented. The spatial discretization is performed using linear triangular and linear tetrahedral finite elements for two and three dimensional cases, respectively. The temporal discretization is done with Taylor series. An anisotropic mesh adaption technique, based on a Riemann metric to evaluate the errors (which allows continuous error analysis through an anisotropic error tensor evaluation), including mesh refinement and mesh coarsening procedures is also implemented looking for accurate and computationally cheaper solutions. The code is able to use shared memory architecture in order to reduce computer process time. Finally, two-dimensional and three-dimensional studies are performed in order to validate the proposed methodology and additional complex tests are also analysed.

La simulation numérique des écoulements (CFD) est largement utilisée aujourd'hui dans l'industrie aéronautique, de l'avant-projet à la conception des appareils. En parallèle, la puissance des calculateurs s'est accrue, permettant d'effectuer des simulations résolvant les équations de Navier-Stokes moyennées (RANS) dans un délai de restitution acceptable du point de vue industriel. Cependant, les configurations simulées sont de plus en plus complexes géométriquement, rendant la réalisation du maillage très coûteuse en temps humain. Notre objectif est de proposer une méthode permettant de simplifier la génération de maillages autour de géométries complexes, en exploitant les avantages de la méthode Chimère, tout en levant les difficultés principales rencontrées par cette méthode dans le calcul des connectivités. Dans notre approche, le domaine de calcul est découpé en régions proches et en régions éloignées des corps. Des grilles curvilignes de faible extension décrivent les régions autour des corps. Le maillage de fond est défini par un ensemble de grilles cartésiennes superposées aux grilles de corps, qui sont engendrées et adaptées automatiquement selon les caractéristiques de l'écoulement. Afin de traiter des maillages recouvrants autour de géométries complexes sans surcoût humain, les différentes grilles sont regroupées par composant Chimère. Des relations d'assemblage sont alors définies entre composants, en s'inspirant de la Géométrie de Construction des Solides (CSG), où un solide peut être construit par opérations booléennes successives entre solides primitifs. Le calcul des connectivités Chimère est alors réalisé de manière simplifiée. Des simulations RANS sont effectuées autour d'un fuselage d'hélicoptère avec mât de soufflerie et autour d'une aile NACA0015 en incidence, afin de mettre en oeuvre la méthode. / Computational fluid dynamics (CFD) is widely used today in aeronautics, while the computing power has increased, enabling to perform simulations solving Reynolds-averaged Navier-Stokes equations (RANS) within an acceptable time frame from the industrial point of view. However, the configurations are more and more geometrically complex, making the mesh generation step prohibitive. Our aim is here to propose a method enabling a simplification of the mesh generation over complex geometries, taking advantage of the Chimera method and overcoming the major difficulties arising when performing overset grid connectivity. In our approach, the computational domain is partitioned into near-body regions and off-body regions. Near-body regions are meshed by curvilinear grids of short extension describing the obstacles involved in the simulation. Off-body mesh is defined by a set of adaptive Cartesian grids, overlapping near-body grids. In order to consider overset grids over complex geometries with no additional cost, grids are gathered by Chimera component, and assembly relations are defined between them, inspired by Constructive Solid Geometry, where a solid can result from boolean operations between primitive solids. The overset grid connectivity is thus simplified. RANS simulations are performed over a helicopter fuselage with a strut, and over a NACA0015 wing.