Simulation of interface dynamics: a diffuse-interface model

Interface modeling involves surface tension effects and topological transitions such as breakup and coalescence. In order to simulate the dynamics of interfaces as well as phase transitions, we introduce diffuse-interface modeling. This model describes the interface evolution with a high-order diffusion equation based on the van der Waals-Cahn-Hilliard theory of interfaces. Thus, unlike other methods proposed in graphics, phase dynamics is derived from interface physics regardless of the numerical solution. Small-scale interfacial events and phase transitions develop naturally as a result of the Cahn-Hilliard equation. With the fast, stable and conservative spectral method we used and also due to the characteristics of the diffuse-interface description, the numerical method does not suffer from oscillations or other difficulties caused by interface singularities, which could be very problematic in other interface methods, and numerical diffusion and mass loss are minimized. Besides, the implementation is simple and practical. This model also allows the control of interface features, such as thickness and mobility. The Cahn-Hilliard equation can be coupled with the Navier-Stokes equations to model the surface tension force in fluid equations at the macroscopic level. More importantly, the interface dynamics that uses a free-energy function provides the flexibility and versatility of modeling complex material behaviors simply by designing an appropriate free-energy functional. In this way, we modeled certain elastic behaviors and multicomponent phase evolutions, which could be computationally complex in other methods.