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

Rocha, Franciane Fracalossi; Sousa, Fabrício S.; Ausas, Roberto F.; Buscaglia, Gustavo C.; Pereira, Felipe

doi:10.1016/j.jcp.2020.109316

Cited by 21 publications

(29 citation statements)

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“…The Multiscale Robin Coupled Method has been introduced to solve elliptic equations accurately, presenting advantages when compared to other existing multiscale mixed methods for flows in highly heterogeneous porous media [14,15]. The MRCM solves equation ( 1) by a decomposition of the domain Ω into non-overlapping subdomains Ω i , i " 1, 2, ¨¨¨, N .…”

Section: The Multiscale Robin Coupled Methodsmentioning

confidence: 99%

“…We use the MRCM with the physics-based interface spaces to capture the geometry of the highpermeability channels and low-permeability structures at each interface. We also consider the adaptivity in the αpxq function according to permeability variations [15]. Thus, one can control the relative importance of each interface space at each location.…”

Section: Interface Spacesmentioning

confidence: 99%

“…Thus, one can control the relative importance of each interface space at each location. As proposed in [15], we take a small value (pressure is favored) at the high-permeability channels and a large value (flux is favored) for the remaining areas.…”

Section: Interface Spacesmentioning

confidence: 99%

“…Several multiscale methods have been presented in the context of the finite volume method [4,5], the finite element method [6,7,8], and mixed finite elements [9,10,11,12,13]. We consider here the Multiscale Robin Coupled Method (MRCM [14,15]) for the solution of two-phase flow problems. It is a generalization of the Multiscale Mixed Method (MuMM [12]) that allows for the independent choice of pressure and flux interface spaces through local Robin boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

“…In the literature the coupling of multiscale flow and transport problems has been treated by explicit operator splitting techniques [18,19] and implicit formulations [20,21]. We have considered operator splitting techniques with explicit approximations for the transport problem in previous works [15,17]. Here, we propose to combine the MRCM with a Sequential Implicit (SI) scheme [22] that allows for the use of large time steps for the coupled flow and transport problem, in contrast to explicit time integration approaches where a CFL-type condition restricts the size of the time step for the transport calculation.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

A multiscale Robin-coupled implicit method for two-phase flows in high-contrast formations

Rocha¹,

Sousa²,

Ausas³

et al. 2021

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In the presence of strong heterogeneities, it is well known that the use of explicit schemes for the transport of species in a porous medium suffers from severe restrictions on the time step. This has led to the development of implicit schemes that are increasingly favoured by practitioners for their computational efficiency. The transport equation requires knowledge of the velocity field, which results from an elliptic problem (Darcy problem) that is the most expensive part of the computation. When considering large reservoirs, a cost-effective way of approximating the Darcy problems is using multiscale domain decomposition (MDD) methods. They allow for the pressure and velocity fields to be computed on coarse meshes (large scale), while detailed basis functions are defined locally, usually in parallel, in a much finer grid (small scale). In this work we adopt the Multiscale Robin Coupled Method (MRCM, [Guiraldello, et al., J. Comput. Phys., 355 (2018) pp. 1-21], [Rocha, et al., J. Comput. Phys., (2020) 109316]), which is a generalization of previous MDD methods that allows for great flexibility in the choice of interface spaces. In this article we investigate the combination of the MRCM with implicit transport schemes. A sequentially implicit strategy is proposed, with different trust-region algorithms ensuring the convergence of the transport solver. The method is assessed on several very stringent 2D two-phase problems, demonstrating its stability even for large time steps. It is also shown that the best accuracy is achieved by considering recently introduced non-polynomial interface spaces, since polynomial spaces are not optimal for high-contrast channelized permeability fields.

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Section: The Multiscale Robin Coupled Methodsmentioning

confidence: 99%

Section: Interface Spacesmentioning

confidence: 99%

Section: Interface Spacesmentioning

confidence: 99%