### 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.