Numerical simulation of nanoparticles in Brownian motion using the lattice Boltzmann method

In many bio-molecular and nano-technological processes, the physical phenomenon of Brownian motion plays an important role. At this, nano-sized particles suspended in a fluid move in a random manner due to collisions with single fluid molecules. The present diploma thesis describes the theory and algorithmic realisation of a fluctuating multiplerelaxation-time lattice Boltzmann scheme which was originally developed by Dünweg, Schiller and Ladd in [9] and accounts for these random influences in nanofluids. In addition to this, the correct limit of the method on hydrodynamic scales is shown via the Chapman-Enskog theory. The fluctuating model is incorporated into waLBerla, which is a widely applicable lattice Boltzmannsolver developed at the chair for system simulation at the university Erlangen-Nuremberg. It is then validated and results for nanoparticles of different shapes in Brownian motion are presented using amongst others newly integrated visualisation routines capable of POV-Ray compatible simulation data output. Moreover, a performance optimisation approach for the simulation of Brownian particles is pointed out.