Domain embedding methods for interface estimation in a phase change problem

摘要

This paper deals with Domain Embedding Methods (DEMs) for the estimation of a solid-liquid interface evolution, from measurements performed on the solid phase only, during a 1D phase-change process. The DEMs consist in extending a moving boundary domain to a larger, but simpler and fixed domain. The original unknown interface is then replaced by a new unknown parameter, which could be a boundary condition or an internal heat source. In this way, the nonlinear identification problem is transformed into a linear one. These methods are analysed numerically from various points of view, by comparison with a common front-tracking method (FTM).