Martin Bauer, Florian Schornbaum, Christian Godenschwager, Matthias Markl, Daniela Anderl, Harald Köstler, and Ulrich Rüde. A python extension for the massively parallel multiphysics simulation framework walberla. International Journal of Parallel, Emergent and Distributed Systems, 2015.


Prabhu Lal Bhatnagar, Eugene P Gross, and Max Krook. A model for collision processes in gases. i. small amplitude processes in charged and neutral one-component systems. Physical review, 94(3):511, 1954.


Dominique d'Humières. Multiple–relaxation–time lattice boltzmann models in three dimensions. Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 360(1792):437–451, 2002.


Martin Geier, Martin Schönherr, Andrea Pasquali, and Manfred Krafczyk. The cumulant lattice boltzmann equation in three dimensions: Theory and validation. Computers & Mathematics with Applications, 70(4):507–547, 2015.


Irina Ginzburg, Frederik Verhaeghe, and Dominique d'Humières. Study of simple hydrodynamic solutions with the two-relaxation-times lattice boltzmann scheme. Communications in computational physics, 3(3):519–581, 2008.


Irina Ginzburg, Frederik Verhaeghe, and Dominique d'Humières. Two-relaxation-time lattice boltzmann scheme: About parametrization, velocity, pressure and mixed boundary conditions. Communications in computational physics, 3(2):427–478, 2008.


Christian Godenschwager, Florian Schornbaum, Martin Bauer, Harald Köstler, and Ulrich Rüde. A framework for hybrid parallel flow simulations with a trillion cells in complex geometries. In Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis, page 35. ACM, 2013.


Zhaoli Guo, Chuguang Zheng, and Baochang Shi. Discrete lattice effects on the forcing term in the lattice boltzmann method. Physical Review E, 65(4):046308, 2002.


AL Kupershtokh. Calculations of the action of electric forces in the lattice boltzmann equation method using the difference of equilibrium distribution functions. In Proc. 7th Int. Conf. on Modern Problems of Electrophysics and Electrohydrodynamics of Liquids, St. Petersburg State University, St. Petersburg, Russia, volume 152, page 155. 152 155, 2003.


AL Kupershtokh. Incorporating a body force term into the lattice boltzmann equation. Bulletin of Novosibirsk State University: Series of Mathematics, Mechanics and Informatics, 4(2):75, 2004.


Jonas Latt. Hydrodynamic limit of lattice Boltzmann equations. PhD thesis, University of Geneva, 2007.


Li-Shi Luo. Lattice-gas automata and lattice boltzmann equations for two-dimensional hydrodynamics. 1993.


Chongxun Pan, Li-Shi Luo, and Cass T Miller. An evaluation of lattice boltzmann schemes for porous medium flow simulation. Computers & fluids, 35(8):898–909, 2006.


Christoph Rettinger and Ulrich Rüde. Simulations of particle-laden flows with the lattice boltzmann method. PAMM, 16(1):607–608, 2016.


Christoph Rettinger and Ulrich Rüde. A comparative study of fluid-particle coupling methods for fully resolved lattice boltzmann simulations. arXiv preprint arXiv:1702.04910, 2017.


Ulf D Schiller. Thermal fluctuations and boundary conditions in the lattice Boltzmann method. PhD thesis, Johannes Gutenberg-Universität, Mainz, 2008.


Florian Schornbaum and Ulrich Rüde. Massively parallel algorithms for the lattice boltzmann method on nonuniform grids. SIAM Journal on Scientific Computing, 38(2):C96–C126, 2016.


Xiaowen Shan and Hudong Chen. Simulation of nonideal gases and liquid-gas phase transitions by the lattice boltzmann equation. Physical Review E, 49(4):2941, 1994.