A Time Integration Method for Phase-Field Modeling

A novel numerical time integration for solving phase-field problems is presented. This method includes the generalized single step single solve (GSSSS) family of algorithms, which can preserve second-order time accuracy as well as provide controllable numerical dissipation independently on each time variable. Furthermore, we demonstrate an enhancement of the time integration method that can reduce numerical oscillation of differential algebraic equation from phase-field model. The algebraic equation is evaluated at \(t_{n+1}\) instead of the general time level \(t_{n+W_{1}}\). The enhancement reduces the numerical oscillation due to the non-dissipative scheme. Two popular phase-field examples, the Cahn–Hilliard equations and simple phase-field-crystal equations, are used to demonstrate the capability of proposed time integration scheme. We conclude that this approach has a significant advantage over currently used algorithms, and provides a new avenue for robustness of time integration schemes for phase-field problems with a high-order term in free energy.