Multiscale nonlocal flow in a fractured porous medium

Abstract

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.

Homogenization of reaction-diffusion equations in fractured porous media

“…where T > 0 is a fixed real number representing the final time of the process, Ω ε is a fractured porous domain in which the process occurred and whose structure follows in the lines below (see [22]).…”