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A Relaxed Decoupled Second-Order Energy-Stable Scheme for the Binary Phase-Field Crystal Model

A Relaxed Decoupled Second-Order Energy-Stable Scheme for the Binary Phase-Field Crystal Model

Year:    2025

Author:    Xin Zhang, Junxiang Yang, Zhijun Tan

East Asian Journal on Applied Mathematics, Vol. 15 (2025), Iss. 2 : pp. 344–372

Abstract

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/eajam.2023-159.170324

East Asian Journal on Applied Mathematics, Vol. 15 (2025), Iss. 2 : pp. 344–372

Published online:    2025-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    29

Keywords:    Binary phase-field crystal unconditional energy stability relaxed technique second-order scheme.

Author Details

Xin Zhang

Junxiang Yang

Zhijun Tan