Phase-field models (PFMs) are a class of partial differential equation (PDE) models for studying multiphase and multicomponent systems. PFMs introduce and track the evolution of one or more auxiliary fields (the phase field(s)) whose values specify which phase is in each spatial location in the simulated domain. PFMs are constructed using the Cahn-Hilliard and Allen-Cahn equations for conserved (e.g., concentration) and non-conserved (e.g., crystalline order) respectively as a basis. Depending on the application, PFMs can be solved by themselves or coupled to species, momentum, and energy conservation equations which typically result in a nonlinear coupled PDE model that requires numerical methods for solution.
To accurately model physical systems, supplying an accurate thermodynamic description of the system is necessary. The Flory-Huggins equation, which has a simple functional form and is suitable for describing the thermodynamics of many real systems, is commonly used with the Cahn-Hilliard equation. However, the numerical solution of PFMs using the Flory-Huggins equation for realistic parameter values (i.e., large values of the Flory-Huggins interaction parameter) is challenging with a fully implicit scheme requiring prohibitively small timesteps for convergence. This presentation explores strategies for developing numerical methods that can accurately and efficiently solve the Cahn-Hilliard equation. We consider various aspects of the solution procedure such as the choice of the discretization scheme and nonlinear solver method. Results for the two- and three-component Cahn-Hilliard equations are presented.
