Comparison of interface-following techniques for numerical analysis of phase-change problems

The analysis of phase-change heat transfer is of interest because of the importance of phase change in many physical situations, but such analyses are difficult because of the nonlinear governing equations. The extensive use of numerical methods to analyze heat transfer problems has great potential but also some pitfalls. This article analyzes the advantages and disadvantages of the enthalpy method and several interface-following methods for modeling solid?liquid phase-change problems using the finite-difference method. Since the initiation of melting always presents numerical difficulties, this article also analyzes the effect of the initial melt region size. Finally, the use of first-order finite-difference models for the moving-interface term in the interface-following method is shown to be inaccurate for high heat transfer rates. A second-order-accurate method is presented that gives accurate results in all situations.