Efficient and Energy Stable Scheme for an Anisotropic Phase-Field Dendritic Crystal Growth Model Using the Scalar Auxiliary Variable (SAV) Approach (Journal of Mathematical Study, 2020)
The phase-field dendritic crystal growth model is a highly nonlinear systemthat couples the anisotropic Allen-Cahn type equation and the heat equation. By combining the recently developed SAV (Scalar Auxiliary Variable) method with the linearstabilization approach, as well as a special decoupling technique, we arrive at a totallydecoupled, linear, and unconditionally energy stable scheme for solving the dendritic model. We prove its unconditional energy stability rigorously and present variousnumerical simulations to demonstrate the stability and accuracy.
Keywords: Phase-field; dendritic; stabilized-SAV method; anisotropy; Allen-Cahn; decoupled.