Summary: We examine the problem of simulating single and multiphase flow in porous medium systems at the pore scale using the lattice Boltzmann (LB) method. The LB method is a powerful approach, but one which is also computationally demanding; the resolution needed to resolve fundamental phenomena at the pore scale leads to very large lattice sizes, and hence substantial computational and memory requirements that necessitate the use of massively parallel computing approaches. Common LB implementations for simulating flow in porous media store the full lattice, making parallelization straightforward but wasteful. We investigate a two-stage implementation consisting of a sparse domain decomposition stage and a simulation stage that avoids the need to store and operate on lattice points located within a solid phase. A set of five domain decomposition approaches are investigated for single and multiphase flow through both homogeneous and heterogeneous porous medium systems on different parallel computing platforms. An orthogonal recursive bisection method yields the best performance of the methods investigated, showing near linear scaling and substantially less storage and computational time than the traditional approach.