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Abstract

This thesis is dedicated to the derivation and the validation of a new collision model as a stabilization technique for high-order lattice Boltzmann methods (LBM). More specifically, it intends to stabilize simulations of: (1) isothermal and weakly compressible flows at high Reynolds numbers, and (2) fully compressible flows including discontinuities such as shock waves.

The new collision model relies on an enhanced regularization step. The latter includes a recursive computation of nonequilibrium Hermite polynomial coefficients. These recursive formulas directly derive from the Chapman-Enskog expansion, and allow to properly filter out second- (and higher-) order nonhydrodynamic contributions in underresolved conditions. This approach is even more interesting since it is compatible with a very large number of velocity sets.

This high-order LBM is first validated in the isothermal case, and for high-Reynolds number flows. The coupling with a shock-capturing technique allows to further extend its validity domain to the simulation of fully compressible flows including shock waves. The present work ends with the linear stability analysis (LSA) of the new approach, in the isothermal case. This leads to a proper quantification of the impact induced by each discretization (velocity and numerical) on the spectral properties of the related set of equations. The LSA of the recursive regularized LBM finally confirms the drastic stability gain obtained with this new approach.

Keywords : Lattice Boltzmann Method, Regularization, Compressible, Linear Stability

Jury
François DUBOIS                         University of Paris Sud, Orsay                       Referee
Florian DE VUYST                       University of Technology, Compiègne            Referee
Nicolas GOURDAIN                     ISAE, Toulouse                                               Member
Irina GINZBURG                          IRSTEA, Antony                                             Member
Jonas LATT                                  University of Geneva                                      Member
Guillaume PUIGT                         CERFACS, Toulouse                                       Advisor