In this paper we provide a FFT algorithm to compute the effective permeability of doubly porous solids constituted of two populations of pores which are different in size. The paper focuses on the resolution of the fluid flow at the intermediate scale, that of the macropores, that requires the resolution of the coupled Darcy/Stokes problem. The permeability associated with the first population of cavities is assumed to be known. A two-field FFT based iterative scheme is derived to compute the solution of the Darcy/Stokes problem. The principle is to reformulate the problem by considering a unique Brinkman equation with different coefficients for the Darcy and the Stokes regions. As a first application, we determine the macroscopic permeability of a porous solid containing circular macropores. The results are compared to analytic expressions and simplified modeling which use an equivalent Darcy medium in place of the macropores. Next, we apply the FFT method to a bi-porous polymer. The computations are performed on 2D and 3D cells extracted from X-ray computed microtomography.

在本文中，我们提供了一种FFT算法来计算由两个大小不同的孔组成的双孔固体的有效渗透率。本文着重于解决中等尺度流体流动的问题，即大孔的问题，这需要解决达西/斯托克斯耦合问题。假定与第一腔体相关的渗透率是已知的。推导了基于两场FFT的迭代方案，以计算Darcy / Stokes问题的解。原理是通过考虑达西和斯托克斯地区具有不同系数的唯一Brinkman方程来重新构造问题。作为第一个应用程序，我们确定了包含圆形大孔的多孔固体的宏观渗透率。将结果与使用等效Darcy介质代替大孔的解析表达式和简化模型进行比较。接下来，我们将FFT方法应用于双孔聚合物。对从X射线计算机断层摄影术提取的2D和3D细胞进行计算。