Fluid ow simulations using the lattice Boltzmann method with multiple relaxation times

In this thesis, the multiple-relaxation-time model of the collision operator in the lattice Boltzmann method is presented. In contrast to the simple Bhatnagar-GrossKrook approximation, not only a single but various relaxation parameters are available and can be used to optimise the simulation results. The main idea behind this approach is the construction of a space based on the moments of the particle distribution functions and the usage of a collision matrix. The consequently increased flexibility allows independent control over certain physical properties, like the kinematic and bulk viscosity of the fluid and the placement of the walls represented by no-slip boundary conditions. To compare different collision models and to obtain more insight into the effect of the various relaxation parameters, simulations featuring a Poiseuille flow, a lid-driven cavity flow and a flow past a square cylinder are carried out. The results allow to identify those relaxation parameters that influence certain flow properties the most. Finally, some guidelines are formulated on how to choose the parameters to achieve accurate and stable outcomes.