TY - JOUR
T1 - Efficient and Energy Stable Scheme for an Anisotropic Phase-Field Dendritic Crystal Growth Model Using the Scalar Auxiliary Variable (SAV) Approach
AU - Yang , Xiaofeng
JO - Journal of Mathematical Study
VL - 2
SP - 212
EP - 236
PY - 2020
DA - 2020/05
SN - 53
DO - http://doi.org/10.4208/jms.v53n2.20.05
UR - https://global-sci.org/intro/article_detail/jms/16805.html
KW - Phase-field, dendritic, stabilized-SAV method, anisotropy, Allen-Cahn, decoupled.
AB - <p style="text-align: justify;">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.</p>