Colloque des sciences mathématiques du Québec

12 octobre 2007 de 16 h 00 à 18 h 00 (heure de Montréal/HNE) Sur place

A Lattice Boltzmann Model for Single- and Multi-Phase Fluid Flows

Colloque par Tim Phillips (Cardiff University, UK)

The fundamental philosophy of the lattice Boltzmann method (LBM) is to construct simplified kinetic type models that preserve the conservation laws and necessary symmetries so that the macroscopically averaged properties obey the desired continuum equations. The LBM and its historical development, including the derivation of the Navier-Stokes equations, are presented. The treatment of boundary conditions within the LBM framework is described. The flow of a Newtonian fluid past a confined cylinder is investigated and comparisons made with existing results in the literature. An extension of the LBM to axisymmetric flows is presented. The resulting method is validated for the classical problem of flow past a sphere. Excellent agreement is found with analytical and empirical expressions for the drag. The LBM is then developed for immiscible binary fluids with different viscosities and densities. The model is shown to recover the Navier-Stokes equations for two-phase flow in the macroscopic limit. A theoretical expression for surface tension is derived and the validity of the analysis is confirmed by comparing numerical and theoretical predictions of surface tension as a function of density. Finally, a formal perturbation analysis of the generalized LBE is presented. The generalized LBE overcomes some of the shortcomings of the single relaxation parameter LBM such as its ability to model complex fluids.


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