具有不连续压力的两相冲程问题的浸入式有限元新方法

IF 1 4区 数学 Q3 MATHEMATICS, APPLIED Computational Methods in Applied Mathematics Pub Date : 2023-04-27 DOI:10.1515/cmam-2022-0122
Gwanghyun Jo, D. Kwak
{"title":"具有不连续压力的两相冲程问题的浸入式有限元新方法","authors":"Gwanghyun Jo, D. Kwak","doi":"10.1515/cmam-2022-0122","DOIUrl":null,"url":null,"abstract":"Abstract In this paper, we develop a new immersed finite element method (IFEM) for two-phase incompressible Stokes flows. We allow the interface to cut the finite elements. On the noninterface element, the standard Crouzeix–Raviart element and the P 0 {P_{0}} element pair is used. On the interface element, the basis functions developed for scalar interface problems (Kwak et al., An analysis of a broken P 1 {P_{1}} -nonconforming finite element method for interface problems, SIAM J. Numer. Anal. (2010)) are modified in such a way that the coupling between the velocity and pressure variable is different. There are two kinds of basis functions. The first kind of basis satisfies the Laplace–Young condition under the assumption of the continuity of the pressure variable. In the second kind, the velocity is of bubble type and is coupled with the discontinuous pressure, still satisfying the Laplace–Young condition. We remark that in the second kind the pressure variable has two degrees of freedom on each interface element. Therefore, our methods can handle the discontinuous pressure case. Numerical results including the case of the discontinuous pressure variable are provided. We see optimal convergence orders for all examples.","PeriodicalId":48751,"journal":{"name":"Computational Methods in Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2023-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A New Immersed Finite Element Method for Two-Phase Stokes Problems Having Discontinuous Pressure\",\"authors\":\"Gwanghyun Jo, D. Kwak\",\"doi\":\"10.1515/cmam-2022-0122\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract In this paper, we develop a new immersed finite element method (IFEM) for two-phase incompressible Stokes flows. We allow the interface to cut the finite elements. On the noninterface element, the standard Crouzeix–Raviart element and the P 0 {P_{0}} element pair is used. On the interface element, the basis functions developed for scalar interface problems (Kwak et al., An analysis of a broken P 1 {P_{1}} -nonconforming finite element method for interface problems, SIAM J. Numer. Anal. (2010)) are modified in such a way that the coupling between the velocity and pressure variable is different. There are two kinds of basis functions. The first kind of basis satisfies the Laplace–Young condition under the assumption of the continuity of the pressure variable. In the second kind, the velocity is of bubble type and is coupled with the discontinuous pressure, still satisfying the Laplace–Young condition. We remark that in the second kind the pressure variable has two degrees of freedom on each interface element. Therefore, our methods can handle the discontinuous pressure case. Numerical results including the case of the discontinuous pressure variable are provided. We see optimal convergence orders for all examples.\",\"PeriodicalId\":48751,\"journal\":{\"name\":\"Computational Methods in Applied Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2023-04-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Computational Methods in Applied Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1515/cmam-2022-0122\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computational Methods in Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/cmam-2022-0122","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0

摘要

摘要本文提出了一种新的求解两相不可压缩Stokes流的浸入式有限元方法。我们允许界面切割有限元。在非接口元素上,使用标准的Crouzeix–Raviart元素和P0{P_{0}}元素对。在界面单元上,对为标量界面问题开发的基函数(Kwak et al.,An analysis of a breaked P1{P_{1}}-conformant finite element method for interface problems,SIAM J.Numer.Anal.(2010))进行了修改,使得速度和压力变量之间的耦合不同。基函数有两种。在压力变量连续性的假设下,第一类基满足拉普拉斯-杨条件。在第二种情况下,速度是气泡型的,并与不连续压力耦合,仍然满足拉普拉斯-杨条件。我们注意到,在第二类中,压力变量在每个界面元件上有两个自由度。因此,我们的方法可以处理不连续压力的情况。给出了包括不连续压力变量情况下的数值结果。我们看到所有例子的最优收敛阶。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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
A New Immersed Finite Element Method for Two-Phase Stokes Problems Having Discontinuous Pressure
Abstract In this paper, we develop a new immersed finite element method (IFEM) for two-phase incompressible Stokes flows. We allow the interface to cut the finite elements. On the noninterface element, the standard Crouzeix–Raviart element and the P 0 {P_{0}} element pair is used. On the interface element, the basis functions developed for scalar interface problems (Kwak et al., An analysis of a broken P 1 {P_{1}} -nonconforming finite element method for interface problems, SIAM J. Numer. Anal. (2010)) are modified in such a way that the coupling between the velocity and pressure variable is different. There are two kinds of basis functions. The first kind of basis satisfies the Laplace–Young condition under the assumption of the continuity of the pressure variable. In the second kind, the velocity is of bubble type and is coupled with the discontinuous pressure, still satisfying the Laplace–Young condition. We remark that in the second kind the pressure variable has two degrees of freedom on each interface element. Therefore, our methods can handle the discontinuous pressure case. Numerical results including the case of the discontinuous pressure variable are provided. We see optimal convergence orders for all examples.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
CiteScore
2.40
自引率
7.70%
发文量
54
期刊介绍: The highly selective international mathematical journal Computational Methods in Applied Mathematics (CMAM) considers original mathematical contributions to computational methods and numerical analysis with applications mainly related to PDEs. CMAM seeks to be interdisciplinary while retaining the common thread of numerical analysis, it is intended to be readily readable and meant for a wide circle of researchers in applied mathematics. The journal is published by De Gruyter on behalf of the Institute of Mathematics of the National Academy of Science of Belarus.
期刊最新文献
Variational Approximation for a Non-Isothermal Coupled Phase-Field System: Structure-Preservation & Nonlinear Stability A Space-Time Finite Element Method for the Eddy Current Approximation of Rotating Electric Machines An Inverse Matrix Eigenvalue Problem for Constructing a Vibrating Rod On Error Estimates of a discontinuous Galerkin Method of the Boussinesq System of Equations Computational Methods in Applied Mathematics (CMAM 2022 Conference, Part 2)
×
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