Asymptotic Analysis and Layer Decomposition for the Couplex Exercise

This document explores the possibilities of multiscale expansions and domain decomposition to solve part of the Couplex 1 exercise. We concentrate on the hydrostatic pressure and show that the slenderness of the domain and the large variations of the Darcy constants allows an analytical approximation which our test reveals to be true to relative errors smaller than 10^–3. The numerical tests are done in 2D with freefem+ and in 3D with freefem3D. Some considerations are also given for Iodine transport.