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This paper deals with simulation of flow and transport in porous media suchas transport of groundwater contaminants. We first discuss how macro scaleequations are derived and which terms have to be closed by models. Thetransport of tracers is strongly influenced by pore scale velocity structureand large scale inhomogeneities in the permeability field. The velocitystructure on the pore scale is investigated by direct numerical simulations ofthe 3D velocity field in a random sphere pack. The velocity probability densityfunctions are strongly skewed, including some negative velocities. The largeprobability for very small velocities might be the reason for non-Fickiandispersion in the initial phase of contaminant transport. We present a methodto determine large scale distributions of the permeability field frompoint-wise velocity measurements. The adjoint-based optimisation algorithmdelivers fully satisfying agreement between input and estimated permeabilityfields. Finally numerical methods for convection dominated tracer transportsare investigated from a theoretical point of view. It is shown that high orderFinite Element Methods can reduce or even eliminate non-physical oscillationsin the solution without introducing additional numerical diffusivity.

Numerical simulation of transport in porous media: some problems from micro to macro scale