Comparison of Corrected and Uncorrected Enthalpy Methods for Solving Conduction-Driven Solid/Liquid Phase Change Problems

The numerical study of solid/liquid phase change problems represents a large and ongoing field of research with many applications. These simulations should run as fast and accurately as possible. Therefore, proceeding from previous work and findings from the literature, this study investigates enthalpy methods for solving solid/liquid phase change problems. The relationship between temperature and enthalpy is strongly non-linear and requires special treatment; iteratively corrected methods, as well as approaches that do not correct the temperature/enthalpy relationship at all or only once per time step, were considered for a one-dimensional test problem. Based on the results of this study, two solvers can be recommended, the so-called optimum approach and a simple explicit method; both provide accurate results. The explicit method is easy to program, but the optimum approach allows larger time steps and is, therefore, faster. The influence of several parameters was investigated. The mesh resolution strongly influenced the accuracy and the computational speed, and the time step size barely influenced the accuracy but did affect the computational speed. An artificial melting temperature range influenced the accuracy but had hardly any influence on the simulation speed. Higher-order time discretization schemes were not superior compared to the first-order implicit optimum approach.