Efficient and Energy Stable Scheme for an Anisotropic Phase-Field Dendritic Crystal Growth Model Using the Scalar Auxiliary Variable (SAV) Approach

Abstract

The phase-field dendritic crystal growth model is a highly nonlinear system that couples the anisotropic Allen-Cahn type equation and the heat equation. By combining the recently developed SAV (Scalar Auxiliary Variable) method with the linear stabilization approach, as well as a special decoupling technique, we arrive at a totally decoupled, linear, and unconditionally energy stable scheme for solving the dendritic model. We prove its unconditional energy stability rigorously and present various numerical simulations to demonstrate the stability and accuracy.