Adaptive time stepping strategy for solidification processes based on modified local time truncation error

Adaptive time step methods provide a computationally efficient means of simulating transient problems with a high degree of numerical accuracy. However, choosing appropriate time steps to model the transient characteristics of solidification processes is difficult. The Gresho-Lee-Sani predictor-corrector strategy, one of the most commonly applied adaptive time step methods, fails to accurately model the latent heat release associated with phase change due to its exaggerated time steps while the apparent heat capacity method is applied. Accordingly, the current study develops a modified local time truncation error-based strategy designed to adaptively adjust the size of the time step during the simulated solidification procedure in such a way that the effects of latent heat release are more accurately modeled and the precision of the computational solutions correspondingly improved. The computational accuracy and efficiency of the proposed method are demonstrated via the simulation of several one-dimensional and two-dimensional thermal problems characterized by different phase change phenomena and boundary conditions. The feasibility of the proposed method for the modeling of solidification processes is further verified via its applications to the enthalpy method.