A fast algorithm for semi-analytically solving the homogenization boundary value problem for block locally-isotropic heterogeneous media

Direct numerical simulation of diffusion through heterogeneous media can be difficult due to the computational cost resolving fine-scale heterogeneities. One method overcome this difficulty is homogenize model by replacing spatially-varying diffusivity with an effective calculated from solution appropriate boundary value problem. In paper, we present a new semi-analytical for solving problem and computing pixellated, locally-isotropic, media. We compare our standard finite volume show that equivalent accuracy achieved in less time several test cases. also demonstrate how applied complex geometries represented two-dimensional grid rectangular blocks. These results indicate has potential significantly speed up simulations