  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.
