TY - JOUR
T1 - A Relaxed Decoupled Second-Order Energy-Stable Scheme for the Binary Phase-Field Crystal Model
AU - Zhang , Xin
AU - Yang , Junxiang
AU - Tan , Zhijun
JO - East Asian Journal on Applied Mathematics
VL - 2
SP - 344
EP - 372
PY - 2025
DA - 2025/01
SN - 15
DO - http://doi.org/10.4208/eajam.2023-159.170324
UR - https://global-sci.org/intro/article_detail/eajam/23753.html
KW - Binary phase-field crystal, unconditional energy stability, relaxed technique, second-order scheme.
AB - <p style="text-align: justify;">In this study, we construct a relaxed second-order time-accurate scheme for
the binary phase-field crystal model based on the recent paper [J. Wu, J. Yang and Z. Tan,
Eng. Comput. (2023)]. This scheme can significantly improve the consistency between
original and modified energies. Using the exponential SAV method, we construct the
first- and second-order time-accurate schemes by using the backward Euler formula and
the second-order backward difference formula, respectively. Then a new second-order
numerical scheme with relaxation is developed. This new numerical scheme satisfies
the energy dissipation law. Meanwhile, it is fully decoupled and efficient. Extensive
numerical experiments are carried out in 2D and 3D to verify the accuracy and stability
of the proposed scheme, as well as its ability to improve the consistency between the
original energy and modified energy.</p>