The formulation of lattice gas automata (LGA) for given partial differential equations is notstraightforward and still requires `some sort of magic`. Lattice Boltzmann equation (LBE) modelsare much more flexible than LGA because of the freedom in choosing equilibrium distributions withfree parameters which can be set after a multiscale expansion according to certain requirements.Here a LBE is presented for diffusion in an arbitrary number of dimensions. The model is probablythe simplest LBE which can be formulated. It is shown that the resulting algorithm with relaxationparameter omega = 1 is identical to an explicit finite differences (EFD) formulation at its stabilitylimit. Underrelaxation (0 < omega < 1) allows stable integration beyond the stability limit of EFD.The time step of the explicit LBE integration is limited by accuracy and not by stabilityrequirements.
AWI Organizations > Biosciences > BioGeoScience