SENSITIVITY OF DARCY'S LAW TO DISCONTINUITIES

The authors investigate the sensitivity of hydrostatic pressure of flows through porous media with respect to the position of the soil layers. Indeed, these induce discontinuities of the porosity which is a piecewise constant coefficient κ of the partial differential equation satisfied by the pressure u and it leads to the computation of the derivative of u with respect to changes in position of discontinuity surface of κ.

The analysis relies on a mixed formulation of the problem. Preliminary numerical simulations are given to illustrate the theory. An application to a simple inverse problem is also given.