Computational aspects of temperature-based finite element technique for the phase-change heat conduction problem

Liquid–solid phase transition is accompanied by a latent heat release, both in isothermal and non-isothermal phase transformations. The latent heat, the discontinuous phase-change function, and the local exchange of field variables during phase-changes increase the difficulties for obtaining a solution for the Fourier heat conduction equation. Celentano et al. [3] (COO) proposed a temperature-based finite element model for solving the multidimensional transient heat conduction problem involving phase-change. The present work addresses the computational aspects of the COO model. The importance of a line-search algorithm for improving the convergence of the Newton–Raphson iterations are explained in detail. While performing the iterations in this kind of fixed domain methods, the phase front moves back and forth fictitiously. The introduced phase-change matrix handles the latent effect efficiently. Three numerical examples including Direct Chill casting are presented, and the benefits and difficulties of the solution technique are elaborately discussed.