You tube link : https://youtu.be/E9aSeMW1QgM
This PhD study intends to evaluate Lattice Boltzmann Methods (LBM) applied to multiphase flows. First, a general review of statistical physics for Lattice Boltzmann Methods is conducted, as well as a particular review of LBM methods for two-phase flows. General principals are presented, and the Color Gradient, Pseudo-Potential, Free Energy and HCZ, are successively presented. Lattice Boltzmann Methods advanced notions are then introduced, in particular, a Taylor expansion allowing to determine Lattice Boltzmann schemes equivalent macroscopic equation is described.
A Color Gradient method theoretical study is then proposed. First, an original reformulation of the algorithm allowing to improve the computational efficiency is proposed. The Taylor expansion method then allows to determine the high order errors induced by the numerical scheme. This underlines the relationships between the degree of isotropy of LBM operators and the numerical scheme stability. In particular, a numerical isotropic operator allowing to introduce an equation of state is proposed. This operator efficiency is illustrated on academical test cases. The Taylor expansion method is also applied to demonstrate that the Color Gradient Method allows to solve an Allen-Cahn phase field equation. This Allen-Cahn equation allows a perfect control of the diffuse interface thickness. This theoretical result is then validated numerically. Finally, an original improved version of the Gradient Color Method is proposed. In this formulation, our isotropic Equation of State operator is used, and an original temporal correction term is proposed. This temporal correction improves the scheme numerical stability and allows to expands the method application range to higher density ratios. Finally, this method is validated through academical testcases.
François Dubois, Laboratoire de mathématiques d'Orsay – Referee
Florian de Vuyst, Université de Technologie de Compiègne – Referee
Umberto d'Ortona, M2P2 – Member
Rémi Abgrall, University of Zurich – Member
Bénédicte Cuenot, CERFACS – Director
Pierre Boivin, M2P2 – co-director
Nicolas Odier, CERFACS – co-advisor
Stefano Puggeli, SafranTech – co-advisor