A Linear Energy and Entropy-Production-Rate Preserving Scheme for Thermodynamically Consistent Crystal Growth Models

Authors

Yucan Zhao, Beijing Computational Science Research CenterFollow
Jun Li, Tianjin Normal UniversityFollow
Jia Zhao, Utah State UniversityFollow
Qi Wang, University of South CarolinaFollow

Document Type

Article

Journal/Book Title/Conference

Applied Mathematics Letters

Volume

98

Publisher

Elsevier Ltd

Publication Date

6-5-2019

Award Number

NSF, Division of Mathematical Sciences 1816783

Funder

NSF, Division of Mathematical Sciences

First Page

142

Last Page

148

Abstract

We present a linear, second order, energy and entropy-production-rate preserving scheme for a thermodynamically consistent phase field model for dentritic crystal growth, combining an energy quadratization strategy with the finite element method. The scheme can be decomposed into a series of Poisson equations for efficient numerical implementations. Numerical tests are carried out to verify the accuracy of the scheme and simulations are conducted to demonstrate the effectiveness of the scheme on benchmark examples.

Recommended Citation

Zhao, Yucan, et al. “A Linear Energy and Entropy-Production-Rate Preserving Scheme for Thermodynamically Consistent Crystal Growth Models.” Applied Mathematics Letters, vol. 98, Dec. 2019, pp. 142–48. DOI.org (Crossref), doi:10.1016/j.aml.2019.05.029.