Volume 53, Issue 2
Efficient and Energy Stable Scheme for an Anisotropic Phase-field Dendritic Crystal Growth Model Using the Scalar Auxiliary Variable (SAV) Approach

Xiaofeng Yang

J. Math. Study, 53 (2020), pp. 212-236.

Published online: 2020-05

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  • 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.

  • Keywords

Phase-field, dendritic, stabilized-SAV method, anisotropy, Allen-Cahn, decoupled.

  • AMS Subject Headings

65M12, 65M70, 65Z05

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

xfyang@math.sc.edu (Xiaofeng Yang)

  • BibTex
  • RIS
  • TXT
@Article{JMS-53-212, author = {Yang , Xiaofeng }, title = {Efficient and Energy Stable Scheme for an Anisotropic Phase-field Dendritic Crystal Growth Model Using the Scalar Auxiliary Variable (SAV) Approach}, journal = {Journal of Mathematical Study}, year = {2020}, volume = {53}, number = {2}, pages = {212--236}, 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.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v53n2.20.05}, url = {http://global-sci.org/intro/article_detail/jms/16805.html} }
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://dor.org/10.4208/jms.v53n2.20.05 UR - https://global-sci.org/intro/jms/16805.html KW - Phase-field, dendritic, stabilized-SAV method, anisotropy, Allen-Cahn, decoupled. AB -

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.

Xiaofeng Yang. (2020). 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. 53 (2). 212-236. doi:10.4208/jms.v53n2.20.05
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