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Computational modelling of diffusion in heterogeneous media is prohibitivelyexpensive for problems with fine-scale heterogeneities. A common strategy forresolving this issue is to decompose the domain into a number ofnon-overlapping sub-domains and homogenize the spatially-dependent diffusivitywithin each sub-domain (homogenization cell). This process yields acoarse-scale model for approximating the solution behaviour of the originalfine-scale model at a reduced computational cost. In this paper, we studycoarse-scale diffusion models in block heterogeneous media and investigate, forthe first time, the effect that various factors have on the accuracy ofresulting coarse-scale solutions. We present new findings on the errorassociated with homogenization as well as confirm via numerical experimentationthat periodic boundary conditions are the best choice for the homogenizationcell and demonstrate that the smallest homogenization cell that iscomputationally feasible should be used in numerical simulations.

Numerical investigation into coarse-scale models of diffusion in complex heterogeneous media