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

by   Franciane F. Rocha, et al.

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.



page 15

page 17

page 23

page 27

page 29

page 31

page 33

page 35


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

In the presence of strong heterogeneities, it is well known that the use...

Recursive formulation and parallel implementation of multiscale mixed methods

Multiscale methods for second order elliptic equations based on non-over...

Towards HPC simulations of Billion-cell Reservoirs by Multiscale Mixed Methods

A three dimensional parallel implementation of Multiscale Mixed Methods ...

Mixed GMsFEM for linear poroelasticity problems in heterogeneous porous media

Accurate numerical simulations of interaction between fluid and solid pl...

The Multiscale Perturbation Method for Two-Phase Reservoir Flow Problems

In this work we formulate and test a new procedure, the Multiscale Pertu...

Learning Algorithms for Coarsening Uncertainty Space and Applications to Multiscale Simulations

In this paper, we investigate and design multiscale simulations for stoc...

A projection based Variational Multiscale Method for Atmosphere-Ocean Interaction

The proposed method aims to approximate a solution of a fluid-fluid inte...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.