Estimation of the Time-Dependent Profile of a Melting Front by Inverse Resolution

Abstract

The profile and time evolution of a solid/liquid interface in a phase change process is estimated by solving an inverse heat transfer problem, using data measurements in the solid phase only. One then faces the inverse resolution of a heat equation in a variable and a priori unknown 2D domain. This ill-posed problem is solved by a regularization approach: the unknown function (position of the melting front) is obtained by minimization of a two component criterion, consisting of a distance between the output of a simulation model and the measured data, to which a penalizing function is added in order to restore the continuity of the inverse operator. A numerical study is developed to analyze the validity domain of the identification method. From simulation tests, it is shown that the minimum signal/noise ratio that can be handled depends strongly on the position of the measurement sensors.