Interface spaces based on physics for multiscale mixed methods applied to flows in fractured-like porous media

• Published in: Computer methods in applied mechanics and engineering 2021-11, Vol.385, p.114035, Article 114035
• Main Authors: Rocha, Franciane F., Sousa, Fabricio S., Ausas, Roberto F., Pereira, Felipe, Buscaglia, Gustavo C.
• Format: Article
• Language: English
• Subjects: Domain decomposition methods; Fractures; High-contrast porous media; Interface spaces; Mathematical analysis; Mixed methods research; Multiscale analysis; Multiscale mixed methods; Multiscale Robin coupled method; Permeability; Physics; Polynomials; Porous media; Two phase flow; Two-phase flows
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2021.114035

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. •New interface spaces based on physics are developed for multiscale domain decomposition methods.•The new spaces can be used on most multiscale methods based on mixed formulations.•They accurately capture large heterogeneities such as fractures and barriers.•An adaptive method is built based on the MRCM, automatically choosing appropriate spaces.•The accuracy obtained by the new technique is improved for multiscale mixed methods.