Hybrid Multiscale Formulation for Coupled Flow and Geomechanics

We devise a hybrid MultiScale Finite Element-Finite Volume (h-MSFE-FV) framework to simulate single-phase flow through elastic deformable porous media. The coupled problem is solved based on a two-field fine-scale mixed finite element-finite volume formulation of the governing equations, namely conservation laws of linear momentum and mass, in which the primary unknowns are the displacement vector and pressure. For the MSFE displacement stage, we develop sets of local basis functions for the displacement vector over coarse cells, subject to reduced boundary condition. This MSFE stage is then coupled with the MSFV method for flow, where coarse and dual-coarse grids are imposed to obtain approximate but conservative multiscale solutions. Numerical experiments are presented to demonstrate accuracy and robustness of the proposed h-MSFE-FV method---both as an approximate, non-iterative solver, and a preconditioner.