On the influence of boundary conditions when determining transport coefficients from digital images of heterogeneous media

Sensitivity to the boundary conditions (BC's) when determining macroscopic transport coefficients by numerical upscaling in finite domains is a well known methodological issue, explored here with the purpose of: quantifying the influence of the BC's in relation with the parameters of the system (porosity, characteristic length scale, conductivity contrast); assessing the level of confidence associated with the predictions; devising criteria to anticipate the risk of serious artifacts, and proposing ways to limit them. The terminology of thermal transfer is used but the developments apply to any transport mechanism governed by a diffusion equation, including conduction, mass diffusion or Darcy flow. Quantitative indicators are defined for a rigorous individual or comparative assessment of conductivity tensors, and used in the analysis of extensive numerical data obtained in tomographic images and model materials, with a broad range of properties. Practical criteria are proposed for the a priori and a posteriori detection of at-risk situations, and a self-diagnosing protocol is proposed to screen out the BC's influence, whenever possible.