Analysis of a Coupled Darcy Multiple Scale Flow Model Under Geometric Perturbations of the Interface

Abstract

For a Darcy flow coupled system modeling fluid exchange between two regions with fluid resistance at different scale, we address the question of continuity of the solution with respect to geometric perturbations of the interface. The original interface and its perturbation define three flow regions exchanging fluid, these are modeled as a coupled system in mixed variational formulation. For numerical purposes a-posteriori perturbation/error estimates are given.

Notes on the nonlinear dependence of a multiscale coupled system with respect to the interface

“…(ii) The conditions of convergence for the interface are acceptable in the context of saturated porous media fluid flow. Moreover, for the modeling of saturated fluid flow through deformable porous media in the elastic regime, these conditions are natural, because for high gradients of deformation the elasto-plastic and plastic regimes start taking place, see [17].…”

“…Most of the theoretical achievements in the field of multiscale coupled systems, concentrate their efforts in removing the singularities introduced by the scales using homogenization processes. These techniques can be either formal [17,13], analytic [11] or numerical [14].…”