Tracking of a moving interface during a 2D melting or solidification process from measurements on the solid part only

The moving solid-liquid interface of a melting solid in a rectangular enclosure is identified from temperature and flux measurements performed on the cold side of the solid only. The lack of measurement in the liquid phase prevents the interface to be recovered by straightforward use of the direct Stefan solution. The identification of this melting front is an inverse problem that requires particular solution methods. An algorithm is used, based on a regularized least squares approach, that is extended to this nonlinear case by a predictive sliding horizon technique