  The traffic modelling often keeps the mesoscopic scale in the theoretical
sphere because the integro-differential nature of its equations. In the present
work we suggest to use the lattice Boltzmann method to overcome these
difficulties. In particular, the method has a strong theoretical foundation. An
improved version of the lattice Boltzmann method for multi-class and
heterogeneities, has been introduced here. Its ability to reproduce the
fundamental diagram is proved here, for both single-class and multi-class
flows. This allows easily simulating complex and realistic cases of mixture of
multi-class traffic flow. These simulations are able to capture jamming in
various traffic situations such as road merging, reduction of number of lanes
or change of speed limits.

Physics and Society