以物理学为基础的基于多比例混合方法物理学的界面空间,这些多比例混合方法适用于破碎的类似多孔质介质的流体 (Interface spaces based on physics for multiscale mixed methods applied to flows in fractured-like porous media)

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., J. Comput. Phys., 355 (2018) pp. 1-21], 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., J. Comput. Phys., 409 (2020), 109316] 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 unprecedented 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.

翻译：众所周知,基于域分解的多尺度混合方法依赖于以分解骨架骨架为主的界面空间,以连接非重叠子区间的解决办法;但是,基于多元面板的现有多尺度方法可以利用拟议的界面空间,以展示和测试我们的结果,我们使用新开发的多尺度Robine Compad 方法(MRCM)[Guiraldello et al., J.Comput. Phys., 355 (2018) pp. 1-211]。我们在此提议,以物理为基础的新的界面空间,以在同时存在由压力和通量空间分别容纳的骨折和障碍时,处理可渗透的字段。基于压力和通气压和通量障碍的现有多尺度方法,以混合法的现有多尺度方法利用现有的多尺度方法,而基于混合法的现有的混合方法可以利用拟议接口空间空间空间空间空间空间空间空间空间结构的适应性版本[Rocha, 4RMMRal-al-al-al-al-ral-ral-ral-ral-ral-ral-ral-lation-lation-ral-ral-lation-lation-lation-lex-lation-lation-lation-lation-lation-lation-lex-lex-lation-lation-lation-lation-lation-lation-lation-lation-lation-lation-l-lation-lex-lex-l-lation-lation-l), 和M-lut-lation-lut-l-lation-lation-lation-lation-lut-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-lation-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l