  We describe a method to address efficiently problems of two-phase flow in the
regime of low particle Reynolds number and negligible Brownian motion. One of
the phases is an incompressible continuous fluid and the other a discrete
particulate phase which we simulate by following the motion of single
particles. Interactions between the phases are taken into account using locally
defined drag forces. We apply our method to the problem of flow through random
media at high porosity where we find good agreement to theoretical expectations
for the functional dependence of the pressure drop on the solid volume
fraction. We undertake further validations on systems undergoing gravity
induced sedimentation.
