Lubrication correction for simulating particle- uid interaction with the lattice Boltzmann method

Ausführungen, die wörtlich oder sinngemäÿ übernommen wurden, sind als solche gekennzeichnet. The lubrication force is an important problem in simulations of suspended particles with the lattice Boltzmann method. When two particles approach each other and get near contact, closer than the lattice spacing, the thin layer of uid, still left between the particles, cannot be suciently simulated, which even results in the particles sticking together. In order to get realistic results, there are dierent means to calculate and apply lubrication forces to the particles. The goal of this thesis is to explain the derivation and implementation of a technique presented by Ding and Aidun: the ALD' method. As it follows a link-wise approach, the terms of force applied per link are derived. Another feature is that the gap between the particles near contact is treated in a way, which always leaves a layer of uid in the discretised grid. This is explained and shown, as well. Furthermore the concept of virtual uid is presented. The Chair for System Simulation already has developed a framework for these kinds of simulations, the widely applicable Lattice Boltzmann solver from Erlangen (waLBerla), thus the implementation only enhances the current code. Conclusively some comparisons between analytical estimations and results of special test cases are presented.