Adaptive Time-Stepping Methods for Phase Field Simulations

Phase field models have become an important tool to simulate many important physical problems, such as simulating crystal growth, thin film growth, and multi-phase flow interactions. The relevant phase-field methods are capable of computing topological changes such as splitting and merging, and thus have been applied successfully to multi-component fluid flows involving large interface deformations. The typical governing equations for the phase field models are of Cahn-Hilliard type, which involves a small positive parameter, strong nonlinearity and higher-order derivatives in space. These difficulties require careful study of the numerical discretization methods. Another feature of the phase filed computations is long time simulations, which make the standard (small) constant time-stepping approach difficult due to rounding errors and computational resource constraints. If both the solution dynamics and the steady-state solutions are required, it is desirable to use some time-adaptive strategies which allow to use small time steps in a few critical time levels (where the solution properties such as energy may change rapidly) and larger time steps in other time levels (where solution varies quite slowly). This project is to give a systematic study on the adaptive time- stepping approaches for the phase-filed equations. The goal is to obtain highly efficient adaptive methods for the phase-filed simulations.