A Numerical Method for an Inverse Problem Arising in Two-Phase Fluid Flow Transport Through a Homogeneous Porous Medium

In this paper we study the inverse problem arising in the model describing the transport of two-phase flow in porous media. We consider some physical assumptions so that the mathematical model (direct problem) is an initial boundary value problem for a parabolic degenerate equation. In the inverse problem we want to determine the coefficients (flux and diffusion functions) of the equation from a set of experimental data for the recovery response. We formulate the inverse problem as a minimization of a suitable cost function and we derive its numerical gradient by means of the sensitivity equation method. We start with the discrete formulation and, assuming that the direct problem is discret…