  This paper deals with simulation of flow and transport in porous media such
as transport of groundwater contaminants. We first discuss how macro scale
equations are derived and which terms have to be closed by models. The
transport of tracers is strongly influenced by pore scale velocity structure
and large scale inhomogeneities in the permeability field. The velocity
structure on the pore scale is investigated by direct numerical simulations of
the 3D velocity field in a random sphere pack. The velocity probability density
functions are strongly skewed, including some negative velocities. The large
probability for very small velocities might be the reason for non-Fickian
dispersion in the initial phase of contaminant transport. We present a method
to determine large scale distributions of the permeability field from
point-wise velocity measurements. The adjoint-based optimisation algorithm
delivers fully satisfying agreement between input and estimated permeability
fields. Finally numerical methods for convection dominated tracer transports
are investigated from a theoretical point of view. It is shown that high order
Finite Element Methods can reduce or even eliminate non-physical oscillations
in the solution without introducing additional numerical diffusivity.
