Interface spaces for the Multiscale Robin Coupled Method in reservoir simulation

Author(s)

Guiraldello, Rafael T. ; Ausas, Roberto F. ; Sousa, Fabricio S. ; Pereira, Felipe ; Buscaglia, Gustavo C.

• Document type: Journal article
• Source: MATHEMATICS AND COMPUTERS IN SIMULATION; v. 164, p. 17-pg., 2019-10-01.

Abstract

The Multiscale Robin Coupled Method (MRCM) is a recent multiscale numerical method based on a non-overlapping domain decomposition procedure. One of its hallmarks is that the MRCM allows for the independent definition of interface spaces for pressure and flux over the skeleton of the decomposition. The accuracy of the MRCM depends on the choice of these interface spaces, as well as on an algorithmic parameter beta in the Robin interface conditions imposed at the subdomain boundaries. This work presents an extensive numerical assessment of the MRCM in both of these aspects. Two types of interface spaces are implemented: usual piecewise polynomial spaces and informed spaces, the latter obtained from sets of snapshots by dimensionality reduction. Different distributions of the unknowns between pressure and flux are explored. Two non-dimensionalizations of beta are tested. The assessment is conducted on realistic, high contrast, channelized permeability fields from a SPE benchmark database. The results show that beta, suitably non-dimensionalized, can be fixed to unity to avoid any indeterminacy in the method. Further, with both types of spaces it is observed that a balanced distribution of the interface unknowns between pressure and flux renders the MRCM quite attractive both in accuracy and in computational cost, competitive with other multiscale methods from the literature (C) 2018 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved. (AU)

• FAPESP's process: 16/08115-0 - Implicit multiscale methods for multiphase flows in porous media
• Grantee: Fabrício Simeoni de Sousa
• Support Opportunities: Scholarships abroad - Research
• FAPESP's process: 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry
• Grantee: Francisco Louzada Neto
• Support Opportunities: Research Grants - Research, Innovation and Dissemination Centers - RIDC
• FAPESP's process: 15/02649-0 - New methods for microscale multiphase flows: application to separation processes
• Grantee: Fabrício Simeoni de Sousa
• Support Opportunities: Regular Research Grants