1998-10-21
10:15 at ML H 43

The Lattice Boltzmann Method and the Numerical Simulation of Viscoelastic Fluids

Laurent Giraud

Centre for Systems Engineering and Applied Mechanics (CESAME), Universite catholique de Louvain, Louvain-la-Neuve -- Belgium

The Lattice Boltzmann Method is a technique based on a discretisation of the Boltzmann equation, with the BGK approximation, and has been used for a decade for the numerical simulation of various fluid flows. This method deals with populations of mesoscopic particles that propagate and collide on the links of a regular lattice and can also be seen as a relaxation method towards a local equilibrium. Viscoelastic effects appear when the relaxation time given to the viscous modes is large enough. The connection between the free parameters of the model and the Jeffreys constitutive law was made with the help of a modified Chapman-Enskog expansion. The extension to a non linear model (Oldroyd-B) is obtained by adding non linearity in the local equilibrium distribution. In this talk, I will present first the basic theory of the method and then as an exemple of the possibilities of the method, I will present the very first results in the field of mixing different kind of fluids (the mixing of viscous and viscoelastic fluids).