Multiscale nonlocal flow in a fractured porous medium

TL;DR

This paper develops a multiscale model for viscoelastic fluid flow in fractured porous media, demonstrating that the macroscopic behavior mirrors the microscopic equations using advanced convergence techniques.

Contribution

It introduces a multiscale convergence approach to derive an effective macroscopic model for viscoelastic flow in fractured media, extending prior models to include complex convolution-based dynamics.

Findings

The macroscopic model retains the form of the microscopic Stokes-Volterra equations.

Multiscale convergence methods effectively handle convolution sequences in porous media.

The approach confirms the equivalence of microscopic and macroscopic models in a fixed domain.

Abstract

We study the flow generated by an incompressible viscoelastic fluid in a fractured porous medium. The model consists of a fluid flow governed by Stokes-Volterra equations evolving in a periodic double-porosity medium. Using the multiscale convergence method associated to some recent tools about the convergence of convolution sequences, we show that the equivalent macroscopic model is of the same type as the microscopic one, but in a fixed domain.