A CONSERVATIVE ALGORITHM FOR MULTIDIMENSIONAL CONDUCTION PHASE-CHANGE

In this paper, a generally applicable version of an algorithm, for multidimensional phase change conduction, is presented which bridges the gap between ‘full enthalpy’ and ‘equivalent heat capacity’ methods. In the text the problem is formulated first with reference to the three‐time‐level method for the FE analysis of non‐linear heat conduction. Then the suggested algorithm is utilized as a ‘corrector’ which can be activated for the analysis of isothermal phase change problems. In the corrector step the enthalpy balance is recovered from the standard formulation, and temperatures are post‐calculated by means of the inverse temperature vs. enthalpy function. The algorithm is verified in one‐dimensional situations by comparing the results obtained with available analytical and numerical solutions for boundary conditions of the first kind (temperature) and of the third kind (convection). Finally, as a 2‐D test problem, a solution is presented for inward solidification in a cylinder, using Cartesian co‐ordinates to demonstrate robustness with respect to space deformation of the mesh. Copyright © 1990 John Wiley & Sons, Ltd