Kw. Westerberg et al., TIME-DEPENDENT FINITE-ELEMENT MODELS OF PHASE-CHANGE PROBLEMS WITH MOVING HEAT-SOURCES, Numerical heat transfer. Part B, Fundamentals, 25(2), 1994, pp. 119-143
A mathematical model is developed for melting of a multilayered medium
while a heat source traverses one boundary. The finite-element method
uses moving meshes, front-tracking using spines, an automatic time-st
ep algorithm, and an efficient solution of the linearized equations. A
novel solution method allows the fixed-mesh code to work unchanged bu
t allows a moving mesh in other problems. The finite-element method is
applied when the heater mesh moves with respect to the multilayered m
edium mesh. The same technique allows parallel processing for finite-e
lement codes. The model is applied to several test problems and then t
o the title problem.