Lattice Boltzmann Method

The behaviour of fluids can be described by systems of partial differential equations. Since the analytical solution of these systems is in general not known, numerical approximation schemes are applied.
In contrast to traditional computational fluid dynamics (CFD) approaches based on the conservation of macroscopic quantities like mass, momentum, and energy, the LBM models the fluid by the kinetics of discrete particles that propagate (streaming step) and collide (relaxation step) on a discrete lattice mesh.
Due to its particular nature, LBM has several advantages, such as dealing with complex boundaries, incorporating microscopic interactions, and parallelization of the algorithm.
Within this lecture we will study the Lattice Boltzmann method, in particular the derivation of the scheme and its mathematical analysis. Moreover we plan to illustrate numerical simulations with current state of the art software.

At the end of the lecture students have a profound knowledge about the lattice Boltzmann method, and are able to apply the scheme to different model problems. Further, they know the theoretical aspects and implementation.

MA3303 Numerical Methods for Partial Differential Equations

lecture, exercice module
The module is offered as lectures with accompanying practice sessions. In the lectures, the contents will be presented in a talk with demonstrative examples, as well as through discussion with the students. The lectures should motivate the students to carry out their own analysis of the themes presented and to independently study the relevant literature. Corresponding to each lecture, practice sessions will be offered, in which exercise sheets and solutions will be available. In this way, students can deepen their understanding of the methods and concepts taught in the lectures and independently check their progress.

Blackboard presentation, beamer slides, computer lab work

S. Succi, The Lattice Boltzmann Equation for Fluid Dynamics and Beyond, Oxford University Press, 2001
D. Hänel: Molekulare Gasdynamik. Einführung in die kinetische Theorie der Gase und Lattice-Boltzmann-Methoden.
D. Wolf-Gladrow, Lattice-Gas Cellular Automata and Lattice Boltzmann Models, Springer, 2000

The module examination is based on an oral exam (20 minutes). Students have to reflect theoretical foundations of the lattice Boltzmann method and can adequately apply them to different model problems.