Enthalpy gradient methods for capturing latent heat in phase change simulations using biquadratic isoparametric finite elements

Methods that use spatial gradients of enthalpy to evaluate effective specific heats and capture latent heat effects in phase change problems have been used successfully in finite element formulations based on linear interpolation. In view of the greater geometrical flexibility and efficiency of biquadratic isoparametric elements, it is of interest to assess the use of the methods with these elements. In comparisons with an accurate semi‐analytic solution for a test problem, it is shown that the enthalpy gradient methods with quadratic interpolation are prone to error. A new procedure is proposed that uses bilinear sub‐elements for enthalpy, formed by subdivision of the biquadratic temperature elements. This is shown to be accurate and robust, for phase change intervals as small as 0.02°C.