Direct simulation of fluid flow with cellular automata and the lattice-Boltzmann equation

With the invention of the Hexagonal Lattice Gas it was hoped that this new technique would facilitate direct simulation of turbulent flow. In the past years, however, we have learned about its barriers on numerical accuracy and computational efficiency, which cannot easily be taken. The work on lattice gases has evolved in the introduction of the lattice-Boltzmann scheme. With the appropriate refinements this scheme provides the essential balance between robustness and numerical accuracy and enables us to simulate three-dimensional time-dependent flows at Reynolds numbers up to 50000.