Cargando…

An Explicit Adaptive Finite Difference Method for the Cahn–Hilliard Equation

In this study, we propose an explicit adaptive finite difference method (FDM) for the Cahn–Hilliard (CH) equation which describes the process of phase separation. The CH equation has been successfully utilized to model and simulate diverse field applications such as complex interfacial fluid flows a...

Descripción completa

Detalles Bibliográficos
Autores principales: Ham, Seokjun, Li, Yibao, Jeong, Darae, Lee, Chaeyoung, Kwak, Soobin, Hwang, Youngjin, Kim, Junseok
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer US 2022
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9444276/
https://www.ncbi.nlm.nih.gov/pubmed/36089998
http://dx.doi.org/10.1007/s00332-022-09844-3
_version_ 1784783182083653632
author Ham, Seokjun
Li, Yibao
Jeong, Darae
Lee, Chaeyoung
Kwak, Soobin
Hwang, Youngjin
Kim, Junseok
author_facet Ham, Seokjun
Li, Yibao
Jeong, Darae
Lee, Chaeyoung
Kwak, Soobin
Hwang, Youngjin
Kim, Junseok
author_sort Ham, Seokjun
collection PubMed
description In this study, we propose an explicit adaptive finite difference method (FDM) for the Cahn–Hilliard (CH) equation which describes the process of phase separation. The CH equation has been successfully utilized to model and simulate diverse field applications such as complex interfacial fluid flows and materials science. To numerically solve the CH equation fast and efficiently, we use the FDM and time-adaptive narrow-band domain. For the adaptive grid, we define a narrow-band domain including the interfacial transition layer of the phase field based on an undivided finite difference and solve the numerical scheme on the narrow-band domain. The proposed numerical scheme is based on an alternating direction explicit (ADE) method. To make the scheme conservative, we apply a mass correction algorithm after each temporal iteration step. To demonstrate the superior performance of the proposed adaptive FDM for the CH equation, we present two- and three-dimensional numerical experiments and compare them with those of other previous methods.
format Online
Article
Text
id pubmed-9444276
institution National Center for Biotechnology Information
language English
publishDate 2022
publisher Springer US
record_format MEDLINE/PubMed
spelling pubmed-94442762022-09-06 An Explicit Adaptive Finite Difference Method for the Cahn–Hilliard Equation Ham, Seokjun Li, Yibao Jeong, Darae Lee, Chaeyoung Kwak, Soobin Hwang, Youngjin Kim, Junseok J Nonlinear Sci Article In this study, we propose an explicit adaptive finite difference method (FDM) for the Cahn–Hilliard (CH) equation which describes the process of phase separation. The CH equation has been successfully utilized to model and simulate diverse field applications such as complex interfacial fluid flows and materials science. To numerically solve the CH equation fast and efficiently, we use the FDM and time-adaptive narrow-band domain. For the adaptive grid, we define a narrow-band domain including the interfacial transition layer of the phase field based on an undivided finite difference and solve the numerical scheme on the narrow-band domain. The proposed numerical scheme is based on an alternating direction explicit (ADE) method. To make the scheme conservative, we apply a mass correction algorithm after each temporal iteration step. To demonstrate the superior performance of the proposed adaptive FDM for the CH equation, we present two- and three-dimensional numerical experiments and compare them with those of other previous methods. Springer US 2022-09-05 2022 /pmc/articles/PMC9444276/ /pubmed/36089998 http://dx.doi.org/10.1007/s00332-022-09844-3 Text en © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022, Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic.
spellingShingle Article
Ham, Seokjun
Li, Yibao
Jeong, Darae
Lee, Chaeyoung
Kwak, Soobin
Hwang, Youngjin
Kim, Junseok
An Explicit Adaptive Finite Difference Method for the Cahn–Hilliard Equation
title An Explicit Adaptive Finite Difference Method for the Cahn–Hilliard Equation
title_full An Explicit Adaptive Finite Difference Method for the Cahn–Hilliard Equation
title_fullStr An Explicit Adaptive Finite Difference Method for the Cahn–Hilliard Equation
title_full_unstemmed An Explicit Adaptive Finite Difference Method for the Cahn–Hilliard Equation
title_short An Explicit Adaptive Finite Difference Method for the Cahn–Hilliard Equation
title_sort explicit adaptive finite difference method for the cahn–hilliard equation
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9444276/
https://www.ncbi.nlm.nih.gov/pubmed/36089998
http://dx.doi.org/10.1007/s00332-022-09844-3
work_keys_str_mv AT hamseokjun anexplicitadaptivefinitedifferencemethodforthecahnhilliardequation
AT liyibao anexplicitadaptivefinitedifferencemethodforthecahnhilliardequation
AT jeongdarae anexplicitadaptivefinitedifferencemethodforthecahnhilliardequation
AT leechaeyoung anexplicitadaptivefinitedifferencemethodforthecahnhilliardequation
AT kwaksoobin anexplicitadaptivefinitedifferencemethodforthecahnhilliardequation
AT hwangyoungjin anexplicitadaptivefinitedifferencemethodforthecahnhilliardequation
AT kimjunseok anexplicitadaptivefinitedifferencemethodforthecahnhilliardequation
AT hamseokjun explicitadaptivefinitedifferencemethodforthecahnhilliardequation
AT liyibao explicitadaptivefinitedifferencemethodforthecahnhilliardequation
AT jeongdarae explicitadaptivefinitedifferencemethodforthecahnhilliardequation
AT leechaeyoung explicitadaptivefinitedifferencemethodforthecahnhilliardequation
AT kwaksoobin explicitadaptivefinitedifferencemethodforthecahnhilliardequation
AT hwangyoungjin explicitadaptivefinitedifferencemethodforthecahnhilliardequation
AT kimjunseok explicitadaptivefinitedifferencemethodforthecahnhilliardequation