Efficient method for phase-field model with finite interface dissipation

In order to increase the time step and ensure the stability of the numerical solution, the error balancing method (EBM) is presented to solve the phase-field model with finite interface dissipation. An error is introduced to the phase-field to balance the error introduced to its gradient term in discretization. For solving this model, the EBM in the explicit scheme improves numerical stability and simulation efficiency with the same accuracy as the traditional scheme. Both theory and realistic tests demonstrate that the EBM keeps the solute conservation effectively. An intermediate variable that denotes concentration is introduced in order to ensure the phase concentration equations have the same form within both the interface and the bulk. Then, the EBM is extended to the implicit scheme. Two cases presented in this paper demonstrate that the EBM in the explicit scheme can enhance efficiency by 120 times compared with the traditional scheme; the EBM in the implicit scheme can enhance efficiency by 5 times compared with it in the explicit scheme.