It is well known that domain-decomposition-based multiscale mixed methods rely on interface spaces, defined on the skeleton of the decomposition, to connect the solution among the non-overlapping subdomains. Usual spaces, such as polynomial-based ones, cannot properly represent high-contrast channelized features such as fractures (high permeability) and barriers (low permeability) for flows in heterogeneous porous media. We propose here new interface spaces, which are based on physics, to deal with permeability fields in the simultaneous presence of fractures and barriers, accommodated respectively, by the pressure and flux spaces. Existing multiscale methods based on mixed formulations can take advantage of the proposed interface spaces, however, in order to present and test our results, we use the newly developed Multiscale Robin Coupled Method (MRCM) (Guiraldello et al., 2018), which generalizes most well-known multiscale mixed methods, and allows for the independent choice of the pressure and flux interface spaces. An adaptive version of the MRCM (Rocha et al., 2020) is considered that automatically selects the physics-based pressure space for fractured structures and the physics-based flux space for regions with barriers, resulting in a procedure with improved accuracy. The features of the proposed approach are investigated through several numerical simulations of single-phase and two-phase flows, in different heterogeneous porous media. The adaptive MRCM combined with the interface spaces based on physics provides promising results for challenging problems with the simultaneous presence of fractures and barriers.

众所周知，基于域分解的多尺度混合方法依赖于在分解骨架上定义的接口空间，以连接非重叠子域之间的解决方案。通常的空间，例如基于多项式的空间，无法正确表示高对比度的通道化特征，例如非均质多孔介质中流动的裂缝（高渗透性）和障碍（低渗透性）。我们在此提出了基于物理学的新界面空间，以在压力和通量空间分别容纳的裂缝和障碍同时存在的情况下处理渗透场。现有的基于混合公式的多尺度方法可以利用所提出的界面空间，但是，为了展示和测试我们的结果，我们使用新开发的多尺度罗宾耦合方法 (MRCM)（Guiraldello 等人，2018 年），它概括了大多数著名的多尺度混合方法，并允许独立选择压力和通量界面空间。MRCM 的自适应版本（Rocha 等人，2020 年）被认为可以自动为断裂结构选择基于物理的压力空间，并为具有障碍的区域自动选择基于物理的通量空间，从而提高程序的准确性。通过在不同的非均质多孔介质中对单相和两相流进行多次数值模拟，研究了所提出方法的特征。自适应 MRCM 与基于物理的界面空间相结合，为同时存在裂缝和障碍的挑战性问题提供了有希望的结果。