Résolution des équations de Navier-Stokes linéarisées pour l'aéroélasticité, l’optimisation de forme et l’aéroacoustique

Abstract : The linearized Navier-Stokes equations are solved at Dassault Aviation within numerical simulations for aerodynamic shape optimisation, flutter calculations and aeroacoustics. In order to improve the robustness and efficiency of the Navier-Stokes solver, this thesis followed two complementary paths. The first is work on the iterative methods used to solve linear systems, and the second is the improvement of the numerical scheme underlying these linear systems. In the first part, the extension to multiple right-hand sides of the GMRES algorithm with spectral deflation was tested on industrial test cases. The use of the ILU(k) preconditioner within an additive Schwarz method led to a reduction of the time needed to solve the systems with GMRES by a factor ten. It also enabled the convergence of some numerically very difficult cases which could not be solved by the software available before this thesis. The second part of the manuscript begins with work on the SUPG method used to stabilise the finite element scheme. A new way of computing the stabilisation matrix gave promising results on non-linear cases, which were however not observed for linear cases. A study on Dirichlet boundary conditions concludes this part. An algebraic method to impose non homogeneous Dirichlet boundary conditions on non-trivial variables is introduced. It enables the use, in an industrial context, of linearized Navier-Stokes for aeroacoustics. Moreover, the transparent behaviour of a homogeneous Dirichlet boundary conditions on all variables is proved to be due to the SUPG stabilisation.
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Aloïs Bissuel. Résolution des équations de Navier-Stokes linéarisées pour l'aéroélasticité, l’optimisation de forme et l’aéroacoustique. Equations aux dérivées partielles [math.AP]. Université Paris-Saclay, 2018. Français. ⟨NNT : 2018SACLX019⟩. ⟨tel-01791103⟩

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