An Adaptive Time-Stepping Scheme for Phase-Field Equations

Abstract

The phase field method is a versatile method for modeling the temporal and spatial morphological evolution of complex material systems. However, three-dimensional (3D) long time-scale simulations can be computationally expensive due to the multiple time scales involved in many material phenomena. Here we propose an energy-based adaptive time stepping algorithm and evaluate it using common benchmark problems. It is shown that the proposed scheme outperforms several algorithms in existing literature. We expect it to be widely adopted due to its ease of implementation and computational efficiency.

Keywords: Adaptive Time Stepping, Allen-Cahn equation, Cahn-Hilliard equation, phase-field