An efficient unconditional energy stable scheme for a phase field model for superalloys

This study aims to improve the efficiency and stability of numerical methods for a phase-field model for super alloys. To this end, a second-order-in-time and unconditionally energy-stable scheme is developed based on the constant scalar auxiliary variable (CSAV) method. By introducing two CSAVs and corresponding ordinary differential equations, we establish the connection between the conservative and non-conservative time derivatives of the nonlinear terms. This formulation enables a rigorous proof of the scheme’s unconditional energy stability. Numerical simulations are conducted to validate the proposed method, demonstrating both its effectiveness and accuracy. Extensive numerical experiments are performed to study the effect of the elastic parameters on the precipitate morphology. These results demonstrate that precipitate morphology is not determined by a single parameter but emerges from a complex interplay between misfit strain, elastic modulus mismatch, and phase volume fraction. The numerical scheme effectively captures these elastostatic effects, providing a reliable tool for predicting microstructural evolution in superalloys under various thermodynamic conditions.