A Linear Energy and Entropy-Production-Rate Preserving Scheme for Thermodynamically Consistent Crystal Growth Models
Applied Mathematics Letters
NSF, Division of Mathematical Sciences 1816783
NSF, Division of Mathematical Sciences
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.
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.