Comparison of General Purpose Finite Element Methods for the Stefan Problem

A number of fixed grid finite element methods were tested on problems involving heat conduction with phase change. Only methods that can deal with arbitrary enthalpytemperature relationships were considered. Comparisons were made of temperature gradient vs enthalpy gradients formulations, lumped vs distributed capacitance, timeaverage vs space-average apparent heat capacity, iterative vs non-iterative methods. The apparent heat capacity methods which incorporates lumped capacitances and Pham’s correction performed best, in terms of agreement with analytical solutions and speed of computation (as measured by the number of matrix solutions). The best iterative method allows marginally larger time intervals to be used and guarantees perfect heat balance, but for a given accuracy it is usually slower than the best non-iterative methods. A further advantage of the non-iterative methods is that the heat balance can serve as a useful check of convergence, a heat balance error of more than 1% generally indicating that convergence has not been reached.