Simulating transient compressible flows involving shock waves presents challenges to the CFD practitioner in terms of the mesh quality required to resolve discontinuities and prevent smearing. This document discusses a novel two-dimensional Cartesian anisotropic mesh adaptation technique implemented for transient compressible flow. This technique, originally developed for laminar incompressible flow, is efficient because it refines and coarsens cells using criteria that consider the solution in each of the cardinal directions separately. In this document the method will be applied to compressible flow. The procedure shows promise in its ability to deliver good quality solutions while achieving computational savings. Transient shock wave diffraction over a backward step and shock reflection over a forward step are considered as test cases because they demonstrate that the quality of the solution can be maintained as the mesh is refined and coarsened in time. The data structure is explained in relation to the computational mesh, and the object-oriented design and implementation of the code is presented. Refinement and coarsening algorithms are outlined. Computational savings over uniform and isotropic mesh approaches are shown to be significant.

Simulating transient compressible flows involving shock waves presents challenges to the CFD practitioner in terms of the mesh quality required to resolve discontinuities and prevent smearing. This document discusses a novel two-dimensional Cartesian anisotropic mesh adaptation technique implemented for transient compressible flow. This technique, originally developed for laminar incompressible flow, is efficient because it refines and coarsens cells using criteria that consider the solution in each of the cardinal directions separately. In this document the method will be applied to compressible flow. The procedure shows promise in its ability to deliver good quality solutions while achieving computational savings. Transient shock wave diffraction over a backward step and shock reflection over a forward step are considered as test cases because they demonstrate that the quality of the solution can be maintained as the mesh is refined and coarsened in time. The data structure is explained in relation to the computational mesh, and the object-oriented design and implementation of the code is presented. Refinement and coarsening algorithms are outlined. Computational savings over uniform and isotropic mesh approaches are shown to be significant.

Afin d'anticiper les effets du vieillissement des enceintes de confinement des centrales électronucléaires, l'IRSN effectue des recherches avancées sur le vieillissement du béton. Les problématiques de fissuration liées au vieillissement sont abordées à l'aide d'une méthode micromécanique basée sur des Modèles de Zones Cohésives Frottantes et à l'aide de la méthode d'<<Eigen-Erosion >> basée sur des considérations énergétiques. L'objectif de la thèse est de réduire les temps de calcul liés à ces deux approches, tout en conservant une bonne précision dans les zones d'intérêt, en adaptant la discrétisation en espace à l'aide de techniques de raffinement local adaptatif. La méthode de raffinement retenue est la méthode CHARMS (Conforming Hierarchical Adaptive Refinement Methods). Cette méthode, basée sur le raffinement des fonctions de base, permet un raffinement sans dégradation de la qualité des mailles initiales. En particulier, les non conformités géométriques sont naturellement prises en compte. Initialement appliquée à la Mécanique des Fluides, cette méthode est d'abord étendue à la Mécanique des Milieux Dé-formables en proposant un critère de raffinement général, puis elle est appliquée à la méthode d'<< Eigen-Erosion >> et aux Modèles de Zones Cohésives. Enfin, l'influence de la morphologie des inclusions d'un Volume Elémentaire Représentatif de béton numérique sur le comportement apparent et sur la fissuration est étudiée. / In order to anticipate effects of ageing in confinement structures of nuclear power plant, the IRSN develops research programs to study the ageing of concrete. A micromechanical approach, based on Cohesive Zone Models, and the "Eigen-Erosion" method, based on energetics consideration, are used. The aim of this study is to reduce the computational cost while keeping simulations with good accuracy in the areas of interest. The strategy is to adapt the spatialdiscretization in the areas of interest using local adaptive refinement technics. The selected refinement method is called CHARMS (Conforming Hierarchical Adaptive Refinement Methods). CHARMS is based on the refinement of basis functions and enables refinement without any loss of the inital mesh quality. The geometrical non conformities are implicitly handled. Initialyapplied to Fluid Mechanics, the method is first extended to Solid Mechanics with a specific refinement criterion. It is then applied to "Eigen-Erosion" and to Cohesive Zone Models. The inclusion's shape of a Representative Elementary Volume of numerical concrete is studied in order to determine the influence over the apparent behaviour and the crack propagation.