The lattice Boltzmann method is used for the numerical simulation of physical phenomena and serves as an alternative to classical solvers of partial differential equations. The primary domain of application is fluid dynamics, and in particular the numerical solution of the incompressible, time-dependent Navier-Stokes equation. The strength of the LBM is however based on its ability to easily represent complex physical phenomena, ranging from multiphase flows to fluids with chemical reactions. As the method is based on a molecular description of a fluid, knowledge of the microscopic physics can directly be used to formulate an adequate numerical model. The LBM is an invaluable tool in fundamental research, as it keeps the cycle between the elaboration of a theory and the formulation of a corresponding numerical model short.
This site contains an overview of the method and links to further resources.