On the unconditionally stable phase field model of ternary components system considering liquid-solid phase transition

Abstract

This study develops an unconditionally stable phase-field model for a ternary system considering liquid-solid phase transitions. The model modifies the Cahn-Hilliard equation to describe the interface between gas and the liquid-solid mixture, while the Allen-Cahn equation models the phase transition between the liquid and solid phases. Additionally, momentum and energy equations are introduced to simulate the quasi-incompressible three-phase flow dynamics. The resulting governing equations account for the coupling effects of phase transition, fluid flow, and heat transfer, effectively capturing the dynamic behavior of the mixture. The system satisfies mass conservation and adheres to the energy dissipation principle. A second-order numerical discretization scheme is developed and validated through a series of tests to confirm its mass conservation and unconditional energy stability. Numerical results demonstrate that the model accurately captures the evolution of the interface morphology, temperature field, and velocity field, showing excellent numerical stability and efficiency.