自由流动与多孔介质流动耦合的Uzawa方法

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design Pub Date : 2025-09-19 DOI:10.1016/j.finel.2025.104460

Qingzhou Wang, Guangzhi Du

{"title":"自由流动与多孔介质流动耦合的Uzawa方法","authors":"Qingzhou Wang, Guangzhi Du","doi":"10.1016/j.finel.2025.104460","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, two kinds of Uzawa algorithms are proposed and investigated to solve the coupling of free flow and porous medium flow, which is modeled by the mixed Stokes-Darcy problem with the Beavers-Joseph-Saffman interface condition. The first Uzawa method as an iterative method can avoid solving the saddle point problem at each iteration step. The second method aims to optimize the first one by combining the two-grid strategy. Rigorously theoretical analysis is established for these two algorithms. Some numerical experiments are carried out to verify the theoretical findings.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"252 ","pages":"Article 104460"},"PeriodicalIF":3.5000,"publicationDate":"2025-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Uzawa methods for the coupling of free flow and porous medium flow\",\"authors\":\"Qingzhou Wang, Guangzhi Du\",\"doi\":\"10.1016/j.finel.2025.104460\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>In this paper, two kinds of Uzawa algorithms are proposed and investigated to solve the coupling of free flow and porous medium flow, which is modeled by the mixed Stokes-Darcy problem with the Beavers-Joseph-Saffman interface condition. The first Uzawa method as an iterative method can avoid solving the saddle point problem at each iteration step. The second method aims to optimize the first one by combining the two-grid strategy. Rigorously theoretical analysis is established for these two algorithms. Some numerical experiments are carried out to verify the theoretical findings.</div></div>\",\"PeriodicalId\":56133,\"journal\":{\"name\":\"Finite Elements in Analysis and Design\",\"volume\":\"252 \",\"pages\":\"Article 104460\"},\"PeriodicalIF\":3.5000,\"publicationDate\":\"2025-09-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Finite Elements in Analysis and Design\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0168874X25001490\",\"RegionNum\":3,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Finite Elements in Analysis and Design","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0168874X25001490","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

本文提出并研究了两种Uzawa算法来解决自由流动和多孔介质流动的耦合问题，该问题由带有beaver - joseph - saffman界面条件的混合Stokes-Darcy问题建模。第一种Uzawa方法作为一种迭代方法，可以避免在每个迭代步骤都求解鞍点问题。第二种方法旨在通过结合两网格策略对第一种方法进行优化。对这两种算法进行了严格的理论分析。通过数值实验对理论结果进行了验证。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Uzawa methods for the coupling of free flow and porous medium flow

In this paper, two kinds of Uzawa algorithms are proposed and investigated to solve the coupling of free flow and porous medium flow, which is modeled by the mixed Stokes-Darcy problem with the Beavers-Joseph-Saffman interface condition. The first Uzawa method as an iterative method can avoid solving the saddle point problem at each iteration step. The second method aims to optimize the first one by combining the two-grid strategy. Rigorously theoretical analysis is established for these two algorithms. Some numerical experiments are carried out to verify the theoretical findings.

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

Finite Elements in Analysis and Design 工程技术-力学

CiteScore

4.80

自引率

3.20%

发文量

审稿时长

27 days

期刊介绍： The aim of this journal is to provide ideas and information involving the use of the finite element method and its variants, both in scientific inquiry and in professional practice. The scope is intentionally broad, encompassing use of the finite element method in engineering as well as the pure and applied sciences. The emphasis of the journal will be the development and use of numerical procedures to solve practical problems, although contributions relating to the mathematical and theoretical foundations and computer implementation of numerical methods are likewise welcomed. Review articles presenting unbiased and comprehensive reviews of state-of-the-art topics will also be accommodated.