Second-Order, Fully Decoupled, Linearized, and Unconditionally Stable Scalar Auxiliary Variable Schemes for Cahn–Hilliard–Darcy System

Author

Yali Gao
Xiaoming He, Missouri University of Science and TechnologyFollow
Yufeng Nie

Abstract

In this paper, we establish the fully decoupled numerical methods by utilizing scalar auxiliary variable approach for solving Cahn–Hilliard–Darcy system. We exploit the operator splitting technique to decouple the coupled system and Galerkin finite element method in space to construct the fully discrete formulation. The developed numerical methods have the features of second order accuracy, totally decoupling, linearization, and unconditional energy stability. The unconditionally stability of the two proposed decoupled numerical schemes are rigorously proved. Abundant numerical results are reported to verify the accuracy and effectiveness of proposed numerical methods.

Recommended Citation

Y. Gao et al., "Second-Order, Fully Decoupled, Linearized, and Unconditionally Stable Scalar Auxiliary Variable Schemes for Cahn–Hilliard–Darcy System," Numerical Methods for Partial Differential Equations, vol. 38, no. 6, pp. 1658 - 1683, Wiley, Nov 2022.

The definitive version is available at https://doi.org/10.1002/num.22829

Department(s)

Mathematics and Statistics

Comments

National Science Foundation, Grant 11971386

Keywords and Phrases

Cahn–Hilliard–Darcy system; finite element method; fully decoupled; scalar auxiliary variable approach; second-order; unconditional stability

International Standard Serial Number (ISSN)

1098-2426; 0749-159X

Document Type

Article - Journal

Document Version

Final Version

File Type

text

Language(s)

English

Rights

© 2023 Wiley, All rights reserved.

Publication Date

01 Nov 2022