Abstract 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.

中文翻译：

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从异构媒体的数字图像中确定传输系数时边界条件的影响。

摘要 在有限域中通过数值放大确定宏观输运系数时对边界条件 (BC) 的敏感性是一个众所周知的方法论问题，这里探讨的目的是：量化边界条件 (BC) 与系统参数（孔隙率）相关的影响，特征长度尺度，电导率对比）；评估与预测相关的置信水平；制定标准来预测严重工件的风险，并提出限制它们的方法。使用了热传递的术语，但其发展适用于由扩散方程控制的任何传输机制，包括传导、质量扩散或达西流。定量指标是为对电导率张量进行严格的单独或比较评估而定义的，并用于分析在断层图像和模型材料中获得的大量数值数据，具有广泛的特性。提出了用于风险情况的先验和后验检测的实用标准，并提出了一种自我诊断协议，以在可能的情况下筛选出 BC 的影响。