Porous media and transport within them play important roles across industries and beyond, including in water and pollutant transport in soils, flow in petroleum and geothermal reservoirs, and water treatment in deep bed filtration to list just a few key examples. The study of such flows has traditionally been dominated by experiment.
Simulation is, however, playing an increasing role in this field both because of the
advent of X-ray microtomography (XRMT), which now permits the mapping of pore structures down to sub-micrometer resolution, and the ubiquitous availability of powerful compute clusters built on cheap commodity machines. Simulation in this
context involves solving for the flow field in a model of a porous solid derived from XRMT - in this sense, the simulations mimic reality and are hence termed by us as explicit numerical simulation (ENS). The particular challenge in doing ENS is correctly solving the flow problem in extremely complex geometries. This challenge
has led to the use of various methods such as lattice-gas automata (LGA) and the related lattice-Boltzmann method (LBM), which are particularly suited to resolving flows in complex geometries. All of this work to date has been restricted to low
velocity flows termed Darcy flows because of limitations associated with LGA, LBM and other methods. There is, however, a range of applications where higher speed flows are of relevance and hence extension of the ENS approach to higher speed flows in porous media is important. This has been done here using an LGA
model that does not include the deficiency of more standard LGA models that restricts them to slow flows. The thesis first details this little-known and used LGA model before demonstrating it on a range of benchmark problems. The model is then
used to predict ab initio the hydrodynamic properties of a random packing from the
Darcy to the turbulent regime. Comparison with experiment is excellent. The approach is then used to study, for the first time to our knowledge, the interstitial flow patterns from the Darcy to turbulent regimes.