Numerical Investigation into Coarse-Scale Models of Diffusion in Complex Heterogeneous Media

Abstract

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.