Statistical mechanics of the lattice Boltzmann equation and an alternative approach to boundary conditions

27/06/2008, 14:15, D6-135

Ulf Schiller, MPI für Polymerforschung, Mainz

The lattice Boltzmann method has become a popular approach to simulate soft matter systems where hydrodynamic interactions play an important role. One major application is the coupling of particulate systems to a lattice Boltzmann fluid, whose purpose is to represent hydrodynamic interactions in a computationally efficient way. It has thus become possible to study complex fluids where the presence of additional ``mesoscopic'' length scales leads to many interesting phenomena. In systems like microfluidic devices the influence of confinement is of particular importance. We have explored a novel approach to implement boundary conditions that aims at modeling arbitrary slip length, while at the same time retaining locality and accuracy of the method.

The talk will be divided into two parts: In the first part, I will discuss the statistical mechanics of the fluctuating lattice Boltzmann equation. It is based on a generalized lattice gas model which is used to derive the probability distribution of the lattice Boltzmann populations. This allows to construct stochastic collision rules that satisfy detailed balance on the microscopic level and yield consistent thermalization. In the second part, this methodology will be used to systematically construct lattice Boltzmann models with reduced symmetry that allow implementation of boundary conditions in a completely local fashion. The applicability of these boundary conditions will be discussed with examples for simple flows.