Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Linear, Second-Order Accurate, and Energy Stable Scheme for a Ternary Cahn–Hilliard Model by Using Lagrange Multiplier Approach

Linear, Second-Order Accurate, and Energy Stable Scheme for a Ternary Cahn–Hilliard Model by... We develop a second-order accurate, energy stable, and linear numerical method for a ternary Cahn–Hilliard (CH) model. The proposed scheme is an extension of typical Lagrange multiplier approach for binary CH system. The second-order backward difference formula (BDF2) is applied to construct time discretization. We theoretically prove the mass conservation, unique solvability, and energy stability of the proposed scheme. We efficiently solve the resulting discrete linear system by using a multigrid algorithm. The numerical solutions demonstrate that the proposed scheme is practically stable and second-order accurate in time and space. Moreover, we can use the proposed scheme as an effective solver to calculate the ternary CH equations in ternary phase-field fluid systems. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

Linear, Second-Order Accurate, and Energy Stable Scheme for a Ternary Cahn–Hilliard Model by Using Lagrange Multiplier Approach

Acta Applicandae Mathematicae , Volume 172 (1) – Apr 2, 2021

Loading next page...
 
/lp/springer-journals/linear-second-order-accurate-and-energy-stable-scheme-for-a-ternary-47tc494rg2

References (42)

Publisher
Springer Journals
Copyright
Copyright © The Author(s), under exclusive licence to Springer Nature B.V. 2021
ISSN
0167-8019
eISSN
1572-9036
DOI
10.1007/s10440-021-00405-6
Publisher site
See Article on Publisher Site

Abstract

We develop a second-order accurate, energy stable, and linear numerical method for a ternary Cahn–Hilliard (CH) model. The proposed scheme is an extension of typical Lagrange multiplier approach for binary CH system. The second-order backward difference formula (BDF2) is applied to construct time discretization. We theoretically prove the mass conservation, unique solvability, and energy stability of the proposed scheme. We efficiently solve the resulting discrete linear system by using a multigrid algorithm. The numerical solutions demonstrate that the proposed scheme is practically stable and second-order accurate in time and space. Moreover, we can use the proposed scheme as an effective solver to calculate the ternary CH equations in ternary phase-field fluid systems.

Journal

Acta Applicandae MathematicaeSpringer Journals

Published: Apr 2, 2021

There are no references for this article.