Analysis and finite element approximation of a diffuse interface approach to the Stokes–Biot coupling

IF 2.3 2区 数学 Q1 MATHEMATICS, APPLIED IMA Journal of Numerical Analysis Pub Date : 2025-03-10 DOI:10.1093/imanum/draf002
Francis R A Aznaran, Martina Bukač, Boris Muha, Abner J Salgado
{"title":"Analysis and finite element approximation of a diffuse interface approach to the Stokes–Biot coupling","authors":"Francis R A Aznaran, Martina Bukač, Boris Muha, Abner J Salgado","doi":"10.1093/imanum/draf002","DOIUrl":null,"url":null,"abstract":"We consider the interaction between a poroelastic structure, described using the Biot model in primal form, and a free-flowing fluid, modelled with the time-dependent incompressible Stokes equations. We propose a diffuse interface model in which a phase field function is used to write each integral in the weak formulation of the coupled problem on the entire domain containing both the Stokes and Biot regions. The phase field function continuously transitions from one to zero over a diffuse region of width $\\mathcal{O}(\\varepsilon)$ around the interface; this allows the weak forms to be integrated uniformly across the domain, and obviates tracking the subdomains or the interface between them. We prove convergence in weighted norms of a finite element discretization of the diffuse interface model to the continuous diffuse model; here the weight is a power of the distance to the diffuse interface. We, in turn, prove convergence of the continuous diffuse model to the standard, sharp interface, model. Numerical examples verify the proven error estimates, and illustrate application of the method to fluid flow through a complex network, describing blood circulation in the circle of Willis.","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":"54 1","pages":""},"PeriodicalIF":2.3000,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"IMA Journal of Numerical Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1093/imanum/draf002","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0

Abstract

We consider the interaction between a poroelastic structure, described using the Biot model in primal form, and a free-flowing fluid, modelled with the time-dependent incompressible Stokes equations. We propose a diffuse interface model in which a phase field function is used to write each integral in the weak formulation of the coupled problem on the entire domain containing both the Stokes and Biot regions. The phase field function continuously transitions from one to zero over a diffuse region of width $\mathcal{O}(\varepsilon)$ around the interface; this allows the weak forms to be integrated uniformly across the domain, and obviates tracking the subdomains or the interface between them. We prove convergence in weighted norms of a finite element discretization of the diffuse interface model to the continuous diffuse model; here the weight is a power of the distance to the diffuse interface. We, in turn, prove convergence of the continuous diffuse model to the standard, sharp interface, model. Numerical examples verify the proven error estimates, and illustrate application of the method to fluid flow through a complex network, describing blood circulation in the circle of Willis.
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
我们考虑了用毕奥特模型描述的原始形式的孔弹性结构与用时变不可压缩斯托克斯方程模拟的自由流动流体之间的相互作用。我们提出了一种扩散界面模型,在该模型中,相场函数被用于在包含斯托克斯和比奥特区域的整个域上写入耦合问题弱表述中的每个积分。相场函数在界面周围宽度为 $\mathcal{O}(\varepsilon)$ 的扩散区域内连续地从一过渡到零;这使得弱式可以在整个域内均匀地积分,而无需跟踪子域或它们之间的界面。我们用加权规范证明了扩散界面模型的有限元离散化与连续扩散模型的收敛性;这里的权重是到扩散界面距离的幂。反过来,我们也证明了连续扩散模型对标准锐界面模型的收敛性。数值示例验证了已证明的误差估计,并说明了该方法在流体流经复杂网络(描述威利斯圈中的血液循环)时的应用。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 去求助
来源期刊
IMA Journal of Numerical Analysis
IMA Journal of Numerical Analysis 数学-应用数学
CiteScore
5.30
自引率
4.80%
发文量
79
审稿时长
6-12 weeks
期刊介绍: The IMA Journal of Numerical Analysis (IMAJNA) publishes original contributions to all fields of numerical analysis; articles will be accepted which treat the theory, development or use of practical algorithms and interactions between these aspects. Occasional survey articles are also published.
期刊最新文献
Numerical schemes for radial Dunkl processes Well-posedness of first-order acoustic wave equations and space-time finite element approximation A-posteriori error estimates for systems of hyperbolic conservation laws via computing negative norms of local residuals A noncoforming virtual element approximation for the Oseen eigenvalue problem Analysis and finite element approximation of a diffuse interface approach to the Stokes–Biot coupling
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1