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Title: Linear and unconditionally energy stable schemes for the binary fluid–surfactant phase field model

Authors:
;
Publication Date:
Sponsoring Org.:
USDOE
OSTI Identifier:
1398623
Grant/Contract Number:
SC0008087-ER6539; SC0016540
Resource Type:
Journal Article: Publisher's Accepted Manuscript
Journal Name:
Computer Methods in Applied Mechanics and Engineering
Additional Journal Information:
Journal Volume: 318; Journal Issue: C; Related Information: CHORUS Timestamp: 2017-10-07 09:17:07; Journal ID: ISSN 0045-7825
Publisher:
Elsevier
Country of Publication:
Netherlands
Language:
English

Citation Formats

Yang, Xiaofeng, and Ju, Lili. Linear and unconditionally energy stable schemes for the binary fluid–surfactant phase field model. Netherlands: N. p., 2017. Web. doi:10.1016/j.cma.2017.02.011.
Yang, Xiaofeng, & Ju, Lili. Linear and unconditionally energy stable schemes for the binary fluid–surfactant phase field model. Netherlands. doi:10.1016/j.cma.2017.02.011.
Yang, Xiaofeng, and Ju, Lili. Mon . "Linear and unconditionally energy stable schemes for the binary fluid–surfactant phase field model". Netherlands. doi:10.1016/j.cma.2017.02.011.
@article{osti_1398623,
title = {Linear and unconditionally energy stable schemes for the binary fluid–surfactant phase field model},
author = {Yang, Xiaofeng and Ju, Lili},
abstractNote = {},
doi = {10.1016/j.cma.2017.02.011},
journal = {Computer Methods in Applied Mechanics and Engineering},
number = C,
volume = 318,
place = {Netherlands},
year = {Mon May 01 00:00:00 EDT 2017},
month = {Mon May 01 00:00:00 EDT 2017}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.1016/j.cma.2017.02.011

Citation Metrics:
Cited by: 6works
Citation information provided by
Web of Science

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  • In this paper, we develop a series of linear, unconditionally energy stable numerical schemes for solving the classical phase field crystal model. The temporal discretizations are based on the first order Euler method, the second order backward differentiation formulas (BDF2) and the second order Crank–Nicolson method, respectively. The schemes lead to linear elliptic equations to be solved at each time step, and the induced linear systems are symmetric positive definite. We prove that all three schemes are unconditionally energy stable rigorously. Various classical numerical experiments in 2D and 3D are performed to validate the accuracy and efficiency of the proposedmore » schemes.« less
  • Here, we consider solid state phase transformations that are caused by free energy densities with domains of non-convexity in strain-composition space; we refer to the non-convex domains as mechano-chemical spinodals. The non-convexity with respect to composition and strain causes segregation into phases with different crystal structures. We work on an existing model that couples the classical Cahn-Hilliard model with Toupin’s theory of gradient elasticity at finite strains. Both systems are represented by fourth-order, nonlinear, partial differential equations. The goal of this work is to develop unconditionally stable, second-order accurate time-integration schemes, motivated by the need to carry out large scalemore » computations of dynamically evolving microstructures in three dimensions. We also introduce reduced formulations naturally derived from these proposed schemes for faster computations that are still second-order accurate. Although our method is developed and analyzed here for a specific class of mechano-chemical problems, one can readily apply the same method to develop unconditionally stable, second-order accurate schemes for any problems for which free energy density functions are multivariate polynomials of solution components and component gradients. Apart from an analysis and construction of methods, we present a suite of numerical results that demonstrate the schemes in action.« less
  • Cited by 19
  • This paper describes novel explicit algorithms that are unconditionally stable. The algorithms are applied to some 1 D convection and diffusion problems, including nonlinear problems. Algorithms such as these are of particular interest for massively parallel computers, where one is trying to minimize communications while at the same time maintain the stability properties normally associated with implicit schemes. It is shown how these stable algorithms can be applied in higher spatial dimensions and how they can be extended to problems defined on unstructured meshes.