Inverse-Based reconstruction of internal solid-liquid phase boundaries and associated solid phase temperature fields

Abstract

This paper describes an inverse technique for imaging multi-dimensional optically opaque phase change boundaries and associated near-melt solid phase temperature fields. The algorithm confines calculations to the solid region immediately surrounding the melt interface, uses a coarse, spatially limited finite element mesh, and is capable of determining phase boundaries in nonlinear, heterogeneous, anisotropic materials. Upwind differencing is introduced to circumvent instabilities associated with large grid Peclet numbers while first order regularization is used to enhance solution stability. Since all a priori unknown boundary heat fluxes are determined by the inverse procedure and ad hoc assumptions are eliminated, the technique is non-problem-specific and portable. Algorithm performance is examined using a simple analog welding experiment. In cases where the fusion boundary is known and fixed in the inverse code, and for initial heat flux guesses that differ by up to four orders of magnitude from the ch...