Fixed Mesh Finite Element Solution for Cartesian Two-Dimensional Phase Change

Abstract

An algorithm has been developed for two-dimensional freezing and thawing problems, which may also be useful for some other phase change problems. It is designed to be implemented simply in standard finite element heat conduction computer codes which use linear interpolation within elements. Substances with discrete phase change temperatures, such as water, suffer a step change in enthalpy across a phase change isotherm, and hence, feature a theoretically infinite heat capacity there. The algorithm handles this potentially troublesome phenomenon in a natural way through usual finite element procedures, using simple closed form expressions. A program incorporating the algorithm produced stable, accurate, and economical simulations when run for radial and two-dimensional test cases with exact analytical solutions.