The Multiscale Robin Coupled Method for flows in porous media

Enhanced multiscale mixed methods for two-phase flows in high-contrast porous media

“…We are interested on studying the Multiscale Robin Coupled Method (GUIRALDELLO et al, 2018;GUIRALDELLO et al, 2019), which is based on the domain decomposition described in (DOUGLAS et al, 1993) and on the MuMM (FRANCISCO et al, 2014). The MRCM formulation can take advantage of parallel computations with a computational cost comparable to existing procedures and producing more accurate solutions than some standard multiscale mixed methods.…”

“…For example, a recursive formulation to replace multiscale global interface problems by linear combinations of the local subdomain solutions (AKBARI et al, 2019), and the development of the Multiscale Perturbation Method (MPM) (ALSADIG et al, 2020), a novel procedure to speed-up the parallel numerical solution of multiphase flow problems. A new multiscale method based on the MuMM has been introduced: the Multiscale Robin Coupled Method (MRCM) (GUIRALDELLO et al, 2018). The MRCM generalizes the MMMFEM and MHM, which are the extreme cases for the Robin boundary conditions of subdomain coupling.…”

“…Singlephase Highcontrast (FRANCISCO et al, 2014;GUIRALDELLO et al, 2018;GUIRALDELLO et al, 2019;AKBARI et al, 2019;GUIRALDELLO et al, 2020;ALSADIG et al, 2020) Multiphase or blackoil Highcontrast (ROCHA et al, 2020b) Fractured (ROCHA et al, 2020a) Source: Research data.…”

“…where N U = dim(U H ) and N P = dim(P H ) are the respective dimensions of the interface spaces. In terms of degrees of freedom per interface, these dimensions are given by N U = k U × N I and N P = k P × N I , where k U , k P and N I are, respectively, the flux degrees of freedom, pressure degrees of freedom and number of interfaces between subdomains (see (GUIRALDELLO et al, 2018) for more details).…”

“…In section 1.1, we present a literature review on the multiscale methods related to the one that we investigate, namely the Multiscale Robin Coupled Method (GUIRALDELLO et al, 2018). Then, in section 1.2 we show how the thesis is organized.…”