Adaptation de maillages hybrides et application aux simulations d'equipements de combustion

The objectives of this thesis consist of developing a measure of mesh element quality which must be coherent for simplicial and non-simplicial elements.;The second published paper presents a vertex displacement algorithm which optimizes vertices positions by minimizing a cost function constructed from the non-conformity measure on the first order neighbourhood of the vertex to be moved. This smoothing algorithm, coupled with operations of refinement, unrefinement and topological modifications programmed in the adaptation library OORT , allows hybrid mesh adaptation by applying connectivity modification techniques on the unstructured regions of the mesh followed by non-conformity minimization mesh smoothing on the whole domain. Efficiency of the proposed approach to improve mesh quality is shown through multiple examples. In particular, the study of the transonic RAE2822 wing profile with a hybrid mesh shows that with an initial mesh that cannot capture the shock properly, mesh adaptation with non-conformity minimization generates a solution very close to the experimental results for this complex flow with a discontinuity.;The proposed adaptation algorithm is then applied to an industrial combustion test case. A mesh convergence study allowed a reference mesh to be determined and a reference solution to the problem to be obtained. The meshes used for this study are isotropic and refined over the whole domain equally in each case. The reference solution was obtained in 265 CPU hours and the mesh contains 825 000 elements. The initial mesh for the adaptation process contains 8011 isotropic elements. It is shown that the solution obtained with this mesh is imprecise and too inaccurate to reliably predict pollutant levels. After five global adaptation iterations, the mesh now contains 16 450 elements and the total time to obtain the solution from the initial mesh is about 1.5 hours. The final solution is comparable to the solution on the refined mesh and is accurate enough to use with pollutant prediction models.;The results obtained clearly show that the proposed hybrid mesh adaptation method based on Riemannian metric non-conformity minimization increases hybrid meshes quality for industrial combustion simulations. The result is a direct increase in solution accuracy for a fixed number of degrees of freedom. Even if the approach has only been validated on a single combustion problem with predetermined numerical models, it is possible to envision implementation of this approach to test a wider variety of combustion problems in the context of industrial equipment design to predict pollutant levels with greater accuracy while considerably reducing the time required for the design cycle. (Abstract shortened by UMI.);The first journal article presents a quality measure called the non-conformity to a Riemannian metric. The measure, previously defined for simplices of each dimension, quantifies the distance between the current metric tensor of an element and the specified metric tensor. The current metric is defined as the transformation of an element into its reference element while the specified metric contains the requested characteristics of the mesh. The use of a Riemannian metric notation allows for the control of all anisotropic characteristics of the mesh in a single matrix function. It is shown that the non-conformity measure is not directly applicable to non-simplicial elements without losing its capacity to detect element degeneration. An alternative in the form of subdivision of non-simplices into corner sub-simplices on which non-conformity is calculated is proposed. The use of the simplex, for which the transformation into the reference element is always constant, allows for detection of element degenerations which was not to case for the original formulation. A characterization of the non-conformity measure applied to non-simplices using the corner sub-simplices approach shows that it behaves similarly for all element types when submitted to different types of deformations with respect to a constant specified metric. The measure is continuous, differentiable, reaches zero for an element that satisfies the specification and tends towards infinity when the element approaches a degenerated state. Symmetry around the absolute conformity value can be observed in many types of deformations which gives, for example, the same non-conformity coefficient to an element which is two times too large as to an element which is two times too small.