Lattice Boltzmann Method
Module MA5344
This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.
Module version of SS 2015
There are historic module descriptions of this module. A module description is valid until replaced by a newer one.
Whether the module’s courses are offered during a specific semester is listed in the section Courses, Learning and Teaching Methods and Literature below.
| available module versions | ||
|---|---|---|
| WS 2021/2 | SS 2021 | SS 2015 |
Basic Information
MA5344 is a semester module in English language at Master’s level which is offered irregular.
This Module is included in the following catalogues within the study programs in physics.
- Specialization Modules in Elite-Master Program Theoretical and Mathematical Physics (TMP)
| Total workload | Contact hours | Credits (ECTS) |
|---|---|---|
| 180 h | 60 h | 6 CP |
Content, Learning Outcome and Preconditions
Content
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.
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.
Learning Outcome
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.
Preconditions
MA3303 Numerical Methods for Partial Differential Equations
Courses, Learning and Teaching Methods and Literature
Courses and Schedule
| Type | SWS | Title | Lecturer(s) | Dates | Links |
|---|---|---|---|---|---|
| VO | 2 | Lattice Boltzmann methods [MA5344] |
Wohlmuth, B.
Responsible/Coordination: Muhr, M. |
Tue, 14:30–16:00, MI 03.06.011 |
|
| UE | 1 | Exercises for Lattice Boltzmann methods [MA5344] | Muhr, M. Wohlmuth, B. |
Tue, 16:00–18:00, MI 03.06.011 |
Learning and Teaching Methods
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.
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.
Media
Blackboard presentation, beamer slides, computer lab work
Literature
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
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
Module Exam
Description of exams and course work
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.
Exam Repetition
The exam may be repeated at the end of the semester.