  Over the last two decades, lattice Boltzmann methods have become an
increasingly popular tool to compute the flow in complex geometries such as
porous media. In addition to single phase simulations allowing, for example, a
precise quantification of the permeability of a porous sample, a number of
extensions to the lattice Boltzmann method are available which allow to study
multiphase and multicomponent flows on a pore scale level. In this article we
give an extensive overview on a number of these diffuse interface models and
discuss their advantages and disadvantages. Furthermore, we shortly report on
multiphase flows containing solid particles, as well as implementation details
and optimization issues.
