Lattice-Boltzmann-methods working group

In the last decade the lattice Boltzmann method (LBM) has become an established computational tool for fluid dynamics. In comparison to well-engineered Navier-Stokes solvers the lattice Boltzmann method provides efficient algorithms to calculate turbulent, thermal or multi-phase flows.
The simulation lab deals with the development of these method since 2013. The developed algorithms are transferred to applications to discuss relevant research issues.

Head of research group

Prof. Dr Dirk Reith

Ph.D students

Dominik Wilde
Mario Bedrunka

Research topics

  • Turbulent flows: Implementation of lattice Boltzmann methods on irregular grids
  • Compressible flows: Thermal Evolution due to compressibility
  • Development of the lattice Boltzmann method with the aid of neural networks

Methods, competences and applications

The simulation lab utilizes the self developed LBM-software NATriuM (Numerik und Algorithmen für Tribologie unter Verwendung von Mehrkernprozessoren. Eng: Numerics and algorithms for tribology using multi-core system). This software package was established by Andreas Krämer and has been developed since that time.

NATriuM provides 2 options to use LBM on irregular grids: The Discontinuous-Galerkin-LBM and the Semi-Lagrangian-LBM. The present focus is to develop efficient algorithms for thermal, compressible and turbulent flows.

The research group is also developing a software package written in Python, called Lettuce, which incorporates the lattice Boltzmann method. This software package is based on PyTorch, which is mainly a software library for machine learning algorithms. This not only enables efficient computations on the graphics card, but moreover, it also enables the use of neural networks in the lattice Boltzmann method.


The computer cluster of Bonn-Rhein-Sieg University of Applied Sciences is used for the simulations. An efficient implementation of the method as well as an effective parallelization enable high performance calculations that lead to accurate simulation results.


We support the supervision of a thesis, with a focus on computational flow simulations. For applications for a thesis please contact Prof. Dr. Dirk Reith. 

Selected / new publications

  • ​Wilde, D., Krämer, A., Küllmer, K., Foysi, H., & Reith, D. (2019). Multistep Lattice Boltzmann Methods: Theory and Applications. International Journal for Numerical Methods in Fluids.
  • Krämer, A., Wilde, D., Küllmer, K., Reith, D., Foysi, H., & Joppich, W. (2018). Lattice Boltzmann simulations on irregular grids: Introduction of the NATriuM library. Computers & Mathematics with Applications.
  • Küllmer, K., Krämer, A., Reith, D., Joppich, W., & Foysi, H. (2016). Numerical optimisation of the pseudopotential-based lattice Boltzmann method. Journal of Computational Science17, 384-393.



  • Prof. Dr. Holger Foysi - University of Siegen