Fundamental aspects of turbulence and turbulent mixing are investigated using direct numerical simulations (DNS) of stationary isotropic turbulence, with Taylor-scale Reynolds numbers ranging from 8 to 650 and Schmidt numbers from 1/8 to 1024. The primary emphasis is on important scaling issues that arise in the study of intermittency, mixing and turbulence under solid-body rotation. Simulations up to 2048^3 in size have been performed using large resource allocations on Terascale computers at leading supercomputing centers. Substantial efforts in algorithmic development have also been undertaken and resulted in a new code based on a two-dimensional domain decomposition which allows the use of very large number of processors.Benchmark tests indicate very good parallel performance for resolutions up to 4096^3 on up to 32768 processors. Investigation of intermittency through the statistics of dissipation and enstrophy in a series of simulations at the same Reynolds number but different resolution indicate that accurate results in high-order moments require a higher degree of fine-scale resolution than commonly practiced. At the highest Reynolds number in our simulations (400 and 650) dissipation and enstrophy exhibit extreme fluctuations of O(1000) the mean which have not been studied in the literature before and suggest a universal scaling of small scales. Simulations at Reynolds number of 650 on 2048^3 grids with scalars at Sc=1/8 and 1 have allowed us to obtain the clearest evidence of attainment of inertial-convective scaling in the scalar spectrum in numerical simulations to date whereas results at high Sc support k^{-1} viscous-convective scaling. Intermittency for scalars as measured by the tail of the PDF of scalar dissipation and moments of scalar gradient fluctuations is found to saturate at high Sc. Persistent departures from isotropy are observed as the Reynolds number increases. However, results suggest a return to isotropy at high Schmidt numbers, a tendency that appears to be stronger at high Reynolds numbers. The effects of the Coriolis force on turbulence under solid-body rotation are investigated using simulations on enlarged solution domains which reduce the effects of periodic boundary conditions.

Au cours des dernières décennies, des progrès remarquables ont été réalisés au niveau de la simulation d’écoulements sanguins dans des modèles anatomiques réalistes construits à partir de données d'imagerie médicale 3D en vue de simulation hémodynamique et physiologique 3D à grande échelle. Alors que les modèles anatomiques précis sont d'une importance primordiale pour simuler le flux sanguin, des conditions aux limites réalistes sont également importantes surtout lorsqu’il s’agit de calculer des champs de vitesse et de pression. La première cible de cette thèse était d'étudier l'analyse de convergence des inconnus pour différents types de conditions aux limites permettant un cadre flexible par rapport au type de données d'entrée (vitesse, pression, débit, ...). Afin de faire face au grand coût informatique associé, nécessitant un calcul haute performance, nous nous sommes intéressés à comparer les performances de deux préconditionneurs par blocs; le preconditionneur LSC (Least-Squared Commutator et le preconditionneur PCD (Pressure Convection Diffusion). Dans le cadre de cette thèse, nous avons implémenté ce dernier dans la bibliothèque Feel++. Dans le but de traiter l'interaction fluide-structure, nous nous sommes focalisés sur l'approximation de la force exercée par le fluide sur la structure, un champ essentiel intervenant dans la condition de continuité pour assurer le couplage du modèle de fluide avec le modèle de structure. Enfin, afin de valider nos choix numériques, deux cas tests ont été réalisés et une comparaison avec les données expérimentales et numériques a été établie et validée (le benchmark FDA et le benchmark Phantom). / Towards a large scale 3D computational model of physiological hemodynamics, remarkable progress has been made in simulating blood flow in realistic anatomical models constructed from three-dimensional medical imaging data in the past few decades. When accurate anatomic models are of primary importance in simulating blood flow, realistic boundary conditions are equally important in computing velocity and pressure fields. Thus, the first target of this thesis was to investigate the convergence analysis of the unknown fields for various types of boundary conditions allowing for a flexible framework with respect to the type of input data (velocity, pressure, flow rate, ...). In order to deal with the associated large computational cost, requiring high performance computing, we were interested in comparing the performance of two block preconditioners; the least-squared commutator preconditioner and the pressure convection diffusion preconditioner. We implemented the latter, in the context of this thesis, in the Feel++ library. With the purpose of handling the fluid-structure interaction, we focused of the approximation of the force exerted by the fluid on the structure, a field that is essential while setting the continuity condition to ensure the coupling of the fluid model with the structure model. Finally, in order to assess our numerical choices, two benchmarks (the FDA benchmark and the Phantom benchmark) were carried out, and a comparison with respect to experimental and numerical data was established and validated.