Fast, Unconditionally Energy Stable Large Time Stepping Method for a New Allen-Cahn Type Square Phase-Field Crystal Model

Abstract

In this paper, we develop a new square phase-field crystal model using the L2-gradient flow approach, where the total mass of atoms is conserved through a nonlocal Lagrange multiplier. We construct a fast, provably unconditionally energy stable, second-order scheme by using the recently developed SAV approach with the stabilization technique, where an extra stabilization term is added to enhance the stability and keep the required accuracy while using large time steps. Through the comparisons with the classical Cahn-Hilliard type square phase-field crystal model and the non-stabilized SAV scheme for simulating some benchmark numerical examples, we demonstrate the robustness of the new model, as well as the stability and the accuracy of the developed scheme, numerically.

Department(s)

Mathematics and Statistics

Research Center/Lab(s)

Center for High Performance Computing Research

Keywords and Phrases

Linear; Phase-field crystal; Second-order; Stabilized-SAV; Unconditionally energy stable

International Standard Serial Number (ISSN)

0893-9659

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2019 Elsevier Ltd, All rights reserved.

Publication Date

01 Dec 2019

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