Numerical solution to phase-field model of solidification: A review

Recent advances in improving the computational efficiency of the phase-field simulations of solidification microstructures are reviewed. The parallel progress of four typical approaches, namely, multigrid, adaptive mesh refinement method, semi-implicit Fourier spectral method, and graphical processing units (GPUs) architecture, is highlighted. Large-scale spatiotemporal simulations are successfully performed to cover essential aspects of multiphysics with the capability of these algorithms. Focus is put on the principles, applications, and comparison of the four algorithms, while solidification theories and discretization methods are outlined.