LBRG Mathematical Modeling and Numerics Lab

The LBRG Mathematical Modeling and Numerics Lab derives, analyzes and implements lattice Boltzmann methods (LBMs) for initial boundary value problems in multi-physics applications and beyond. New construction methods for LBMs are designed that consider consistency and stability of the numerical schemes. Besides, we research multi-limit procedures that couple LBMs with established mathematical and numerical methods, such as homogenization and large eddy simulations in space and time. Finally, we extend the LBMs implemented in OpenLB toward large-scale data generation, blending the robust numerical schemes with e.g., uncertainty quantification and machine learning. All of the topics above are combined with extensive usage of high-performance computers to uncover and explore previously unconsidered multi-dimensional parameter regimes for compute-heavy simulations in benchmarks and applications.

KIT

Selected Publications

• S. Simonis, M.J. Krause. Limit consistency of lattice Boltzmann equations. In: ESAIM: M2AN (2025). DOI: 10.1051/m2an/2025026.
• S. Simonis, N. Hafen, J. Jeßberger, D. Dapelo, G. Thäter, M.J. Krause. Homogenized lattice Boltzmann methods for fluid flow through porous media – Part I: Kinetic model derivation. In: ESAIM: M2AN (2025). DOI: 10.1051/m2an/2025005.
• R. Molinaro, S. Lanthaler, B. Raonić, T. Rohner, V. Armegioiu, S. Simonis, D. Grund, Y. Ramic, Z.Y. Wan, F. Sha, S. Mishra, L. Zepeda-Núñez. Generative AI for fast and accurate statistical computation of fluids. arXiv preprint (2025). DOI: 10.48550/arXiv.2409.18359.
• E. Kummer, S. Simonis. Nonuniqueness of lattice Boltzmann schemes derived from finite difference methods. In: Examples and Counterexamples (2025). DOI: 10.1016/j.exco.2024.100171.
• M. Zhong, T. Xiao, M.J. Krause, M. Frank, S. Simonis. A stochastic Galerkin lattice Boltzmann method for incompressible fluid flows with uncertainties. In: Journal of Computational Physics (2024). DOI: 10.1016/j.jcp.2024.113344.
• S. Simonis, S. Mishra. Computing statistical Navier–Stokes solutions. In: Hyperbolic Balance Laws: Interplay between Scales and Randomness, Eds.: Rémi Abgrall, Mauro Garavello, Mária Lukáčová-Medvid’ová, Konstantin Trivisa. Oberwolfach Reports (2024). DOI: 10.4171/owr/2024/10.
• S. Simonis, J. Nguyen, S.J. Avis, W. Dörfler, M.J. Krause. Binary fluid flow simulations with free energy lattice Boltzmann methods. In: Discrete and Continuous Dynamical Systems-S (2024). DOI: 10.3934/dcdss.2023069.
• S. Simonis, M. Frank, M.J. Krause. Constructing relaxation systems for lattice Boltzmann methods. In: Applied Mathematics Letters (2023). DOI: 10.1016/j.aml.2022.108484.
• S. Simonis, D. Oberle, M. Gaedtke, P. Jenny, M.J. Krause. Temporal large eddy simulation with lattice Boltzmann methods. In: Journal of Computational Physics (2022). DOI: 10.1016/j.jcp.2022.110991.
• S. Simonis, M. Haussmann, L. Kronberg, W. Dörfler, M.J. Krause. Linear and brute force stability of orthogonal moment multiple-relaxation-time lattice Boltzmann methods applied to homogeneous isotropic turbulence. In: Philosophical Transactions of the Royal Society A (2021). DOI: 10.1098/rsta.2020.0405.
• S. Simonis, M. Frank, M.J. Krause. On relaxation systems and their relation to discrete velocity Boltzmann models for scalar advection–diffusion equations. In: Philosophical Transactions of the Royal Society A (2020). DOI: 10.1098/rsta.2019.0400.
• M.J. Krause, A. Kummerländer, S.J. Avis, H. Kusumaatmaja, D. Dapelo, F. Klemens, M. Gaedtke, N. Hafen, A. Mink, R. Trunk, J.E. Marquardt, M.L. Maier, M. Haussmann, and S. Simonis. OpenLB–Open source lattice Boltzmann code. In: Computers & Mathematics with Applications (2020). DOI: 10.1016/j.camwa.2020.04.033.