Multiple Relaxation Times in the Lattice Boltzmann Method

Since its introduction about two decades ago the lattice-Boltzmann (LB) method has been developed into a viable numerical tool for computational fluid dynamics and beyond. With its roots in kinetic theory this special version of a cellular automaton concept allows to obtain continuum flow quantities from simple and local update rules based on particle interactions.
Instead of solving the Navier-Stokes equation directly (DNS), the discrete Boltzmann equation is solved by using simple models for the collision operator. The simplest such operator is the lattice Bhatnagar-Gross-Krook (BGK) model, where only one collisional relaxation time is related to the shear and bulk viscosity of the fluid. More complex models featuring multiple relaxation times (MRT) can rectify some of the shortcomings of the basic BGK-model.
In this seminar I will outline the basic principles of the LB method and the BGK-model, introduce the more general MRT-form of the collision operator and show how multiple relaxation times are directly related to physical observables and permit different shear and bulk viscosities.