Prof. Dr. Claus Feuchter

In contrast to the macroscopic description of a fluid using the Navier-Stokes equations, the Lattice-Boltzmann methods are based on molecular-kinetic models. The distribution function of the molecules and their development over time is considered as the central variable by the Boltzmann equation. All relevant macroscopic flow variables can be calculated from this molecular distribution function. The formulation of the Lattice-Boltzmann methods at the kinetic level of the molecules enables efficient simulation algorithms, a relatively simple implementation of framework conditions, efficient parallelization and the implementation of complex physical properties of fluids.

A central advantage of the Lattice-Boltzmann methods is the possible extension of the process, procedures to flow phenomena beyond the range of validity of the Navier-Stokes equations. Such high-order processes, procedures can describe flow processes that are characterized by high Knudsen numbers and strong deviations from thermodynamic equilibrium. Examples of applications are air flows within nanostructures and flows in micro-electromechanical systems (MEMS).

DSMC (Direct Simulation Monte Carlo) is a method for flow simulation at the molecular level in which the free movement of molecules and the collision processes between individual molecules are modeled. While the positions and velocities of the molecules are calculated directly, the collision processes of the molecules are based on suitable stochastic models. All macroscopic flow variables, such as flow velocity, density or temperature, can then be determined from a statistical averaging of the molecular variables.

Conventional applications of this method are flow processes of highly diluted fluids in the supersonic and hypersonic range, such as the re-entry of space probes into the earth's atmosphere.

Another important field of application is flow processes at high Knudsen numbers, i.e. when the funds, financial resources of the molecules are comparable to the characteristic lengths of the flow problem. Such flow phenomena occur in microstructures (e.g. nanofibers) and can no longer be described using the macroscopic Navier-Stokes equations.