Identification of Thermophysical Properties of the Soil in 3D-axisymmetric Coordinate System Using Inverse Problem

Abstract : This paper is motivated by the studies of agricultural and archaeological soils. We introduce a numerical strategy in 3D axisymmetric coordinate system to estimate the thermophysical properties of a saturated porous medium (volumetric heat capacity, thermal conductivity and porosity) where a phase change problem (liquid/vapor) appears due to strong heating. The estimation of these thermophysical properties is done by inverse problem knowing the heating curves at selected points of the porous medium. In order to solve the inverse problem, we use the least square criterion in which sensitivity coefficients appear and which leads to a system of ordinary differential equations (ODE). At the stage of numerical computations, we propose a global approach based on the method of lines, where time and space discretizations are considered separately. The space discretization is done using a vertex-centered finite volume method; the discretization in time is done via an ODE solver combined with a modified Newton's method to deal with the nonlinearity of the system of coupled equations.