Unconditionally stable fully explicit finite difference solution of solidification problems

An unconditionally stable fully explicit finite difference method for solution of conduction dominated phase-change problems is presented. This method is based on an asymmetric stable finite difference scheme for approximation of diffusion terms and application of the temperature recovery method as a phase-change modeling method. The computational cost of the presented method is the same as the explicit method per time-step, while it is free from time-step limitation due to stability criteria. It robustly handles isothermal and nonisothermal phase-change problems and is very efficient when the global temperature field is desirable (not accurate front position). The robustness, stability, accuracy, and efficiency of the presented method are demonstrated with several benchmarks. Comparison with some stable implicit time integration methods is also included. Numerical experiments show that the evaluated temperature field for large values of the Fourier numbers has good/reasonable agreement with the result of small Fourier numbers and the exact/reference solution.