  Computational modelling of diffusion in heterogeneous media is prohibitively
expensive for problems with fine-scale heterogeneities. A common strategy for
resolving this issue is to decompose the domain into a number of
non-overlapping sub-domains and homogenize the spatially-dependent diffusivity
within each sub-domain (homogenization cell). This process yields a
coarse-scale model for approximating the solution behaviour of the original
fine-scale model at a reduced computational cost. In this paper, we study
coarse-scale diffusion models in block heterogeneous media and investigate, for
the first time, the effect that various factors have on the accuracy of
resulting coarse-scale solutions. We present new findings on the error
associated with homogenization as well as confirm via numerical experimentation
that periodic boundary conditions are the best choice for the homogenization
cell and demonstrate that the smallest homogenization cell that is
computationally feasible should be used in numerical simulations.
