A fast convergent and accurate temperature model for phase-change heat conduction

This work proposes a temperature-based finite element model for transient heat conduction involving phase-change. Like preceding temperature-based models, it is characterized by the discontinuous spatial integration over the elements affected by the phase-change. Using linear triangles or tetrahedrals, integration can be performed in a closed analytical way, assuring an exact evaluation of the discrete balance equation. Because of its unconditional stability, an Euler-backward time-stepping scheme is implemented. A crucial fact is the computation of the exact tangent matrices for the Newton–Raphson solution of the non-linear system of discretized equations. Efficiency of the model is tested by means of the results obtained for the Neumann problem and the solidification of a steel ingot.