An Adaptive Time-Step Control Strategy for the Solidification Processes Based on Modified Local Time Truncation Error

摘要

Choosing appropriate time steps to model the transient and discontinuous characteristics of solidification processes is difficult. The current study develops a modified local time truncation error (LTE)-based strategy designed to adaptively adjust the size of the time step during the simulated solidification procedure in such a way that the time steps can be adapted in accordance with the local variations in latent heat released during phase change or the effects of pure conduction in a single solid or liquid phase. The computational accuracy, efficiency and convergence of the proposed method are demonstrated via the simulation of the one-dimensional and two-dimensional solidification problems and compared with those of other uniform time step and adaptive time step methods. Consequently, the effects of latent heat release are more accurately modeled, the precision and efficiency of the computational solutions is correspondingly improved, and the computational errors are minimized. Furthermore, in solving the 2-D problem, it is shown that the line Gauss-Seidel iteration method and the proposed nonlinear iteration method can be combined to construct a highly efficient and accurate solver.